mrskemners.weebly.commrskemners.weebly.com/uploads/4/6/7/0/4670766/glossary.pdf · A English Español Glossary/Glosario absolute value(58) The distance a number is from zero on the

AEnglish Español

Glossary/Glosario

absolute value (58) The distance a number is fromzero on the number line.

accuracy (589) The degree of conformity of ameasurement with the true value.

acute angle (449) An angle with a measure greaterthan 0° and less than 90°.

acute triangle (454) A triangle that has three acuteangles.

adjacent angles (493) Two angles that have the samevertex, share a common side, and do not overlap.

algebraic expression (17) An expression that is builtout of numbers and variables using one or moreoperations.

algebraic fraction (170) A fraction with one or morevariables in the numerator or denominator.

alternate exterior angles (492) Nonadjacent exteriorangles found on opposite sides of the transversal.In the figure below, �1 and �7, �2 and �8 arealternate exterior angles.

alternate interior angles (492) Nonadjacent interiorangles found on opposite sides of the transversal.In the figure above, �4 and �6, �3 and �5 arealternate interior angles.

altitude (520) A line segment that is perpendicular tothe base of a figure with endpoints on the baseand the side opposite the base.

angle (447) Two rays with a common endpoint forman angle. The rays and vertex are used to namean angle. The angle below is �ABC.

area (132) The measure of the surface enclosed by ageometric figure.

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valor absoluto Distancia que un número dista decero en la recta numérica.

exactitud Grado de conformidad de una medida conel valor verdadero.

ángulo agudo Ángulo con una medida mayor que 0°y menor que 90°.

triángulo acutángulo Triángulo que posee tresángulos agudos.

ángulos adyacentes Dos ángulos que poseen elmismo vértice, comparten un lado y no setraslapan.

expresión algebraica Expresión compuesta pornúmeros y variables que usan una o másoperaciones.

fracción algebraica Fracción con una o más variablesen el numerador o denominador.

ángulos alternos externos Ángulos exteriores noadyacentes que se encuentran en lados opuestosde una transversal. En la siguiente figura, �1 y�7, �2 y �8 son ángulos alternos externos.

ángulos alternos internos Ángulos interiores noadyacentes que se encuentran en lados opuestosde una transversal. En la figura anterior, �4 y �6,�3 y �5 son ángulos alternos internos.

altura Segmento de recta perpendicular a la base deuna figura y cuyos extremos yacen en la base y enel lado opuesto de la base.

ángulo Dos rayos con un punto común forman unángulo. Los rayos y el vértice se usan para identi-ficar el ángulo. El siguiente ángulo es �ABC.

área Medida de la superficie que encierra una figurageométrica.

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Cómo usar el glosario en español:1. Busca el término en inglés que desees encontrar.2. El término en español, junto con la definición,

se encuentran en la columna de la derecha.

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arithmetic sequence (249) A sequence in which thedifference between any two consecutive terms isthe same.

average (82) The sum of data divided by the numberof items in the data set, also called the mean.

back-to-back stem-and-leaf plot (607) Used tocompare two sets of data. The leaves for one setof data are on one side of the stem and the leavesfor the other set of data are on the other side.

bar graph (722) A graphic form using bars to makecomparisons of statistics.

bar notation (201) In repeating decimals the line orbar placed over the digits that repeat. Forexample, 2.6�3� indicates the digits 63 repeat.

base (153) In 24, the base is 2. The base is used as afactor as many times as given by the exponent(4). That is, 24 � 2 � 2 � 2 � 2 .

base (288) In a percent proportion, the wholequantity, or the number to which the part is being compared.

�bpaasret

� � �pe

1r0ce0nt

�

base (520, 521, 522) The base of a parallelogram or atriangle is any side of the figure. The bases of atrapezoid are the parallel sides.

base (557) The bases of a prism are any two parallelcongruent faces.

best-fit line (409) On a scatter plot, a line drawn thatis very close to most of the data points. The linethat best fits the data.

binomial (669) A polynomial with exactly two terms.

boundary (419) A line that separates a graph intohalf planes.

box-and-whisker plot (617) A diagram that divides aset of data into four parts using the median andquartiles. A box is drawn around the quartilevalues and whiskers extend from each quartile tothe extreme data points.

center (533) The given point from which all points onthe circle are the same distance.

sucesión aritmética Sucesión en que la diferenciaentre dos términos consecutivos cualesquiera essiempre la misma.

promedio Suma de los datos dividida entre elnúmero de elementos en el conjunto de datos.También llamado media.

diagrama de tallo y hojas consecutivo Se usa paracomparar dos conjuntos de datos. Las hojas deuno de los conjuntos de datos aparecen en unlado del tallo y las del otro al otro lado de éste.

gráfica de barras Tipo de gráfica que usa barras paracomparar estadísticas.

notación de barra En decimales periódicos, la línea obarra que se escribe encima de los dígitos que serepiten. Por ejemplo, en 2.6�3� la barra encima del63 indica que los dígitos 63 se repiten.

base En 24, la base es 2. La base se usa como factor lasveces que indique el exponente (4). Es decir, 24 � 2 � 2 � 2 � 2 .

base En una proporción porcentual, toda la cantidado número al que se compara la parte.

�pbaarstee

� � �por

1c0ie0nto

�

base La base de un paralelogramo o de un triánguloes cualquier lado de la figura. Las bases de untrapecio son los lados paralelos.

base Las bases de un prisma son cualquier par decaras paralelas y congruentes.

recta de ajuste óptimo En una gráfica de dispersión,una recta que está muy cercana a la mayoría delos puntos de datos. La recta que mejor se ajusta alos datos.

binomio Polinomio con exactamente dos términos.

frontera Recta que divide una gráfica en semiplanos.

diagrama de caja y patillas Diagrama que divide unconjunto de datos en cuatro partes usando lamediana y los cuartiles. Se dibuja una cajaalrededor de los cuartiles y se extienden patillasde cada uno de ellos a los valores extremos.

centro Punto dado del cual equidistan todos lospuntos de un círculo.

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círculo Conjunto de todos los puntos del plano queestán a la misma distancia de un punto dado delplano llamado centro.

gráfica circular Tipo de gráfica estadística que se usapara comparar las partes de un todo.

circunferencia Longitud del contorno de un círculo.

coeficiente Parte numérica de un término quecontiene una variable.

combinación Arreglo o lista en que el orden no esimportante.

diferencia común Diferencia entre dos términosconsecutivos cualesquiera de una sucesiónaritmética.

múltiplos comunes Múltiplos compartidos por dos omás números. Por ejemplo, algunos múltiploscomunes de 4 y 6 son 0, 12 y 24.

razón común Razón entre dos términos consecutivoscualesquiera de una sucesión geométrica.

números compatibles Números redondeados demodo que cuando se dividen, el residuo es cero.

complementarios Dos ángulos son complementariossi la suma de sus medidas es 90°.

número compuesto Número entero que posee másde dos factores.

evento compuesto Dos o más eventos simples.

cono Sólido con una base circular que yace en unplano, más un vértice que no yace en ese plano.La superficie restante del cono se forma de launión del vértice a puntos en el círculo mediantesegmentos de recta.

congruentes Segmentos de recta que tienen la mismalongitud o ángulos que tienen la misma medida ofiguras que poseen la misma forma y tamaño.

conjetura Suposición informada.

constante Término sin variables.

constante de variación La pendiente, o tasa decambio, en la ecuación y � kx, representada por k.

recíproca Un enunciado que se forma intercambian-do los enunciados que vienen a continuación desi-entonces en un enunciado si-entonces.

circle (533) The set of all points in a plane that arethe same distance from a given point called thecenter.

circle graph (723) A type of statistical graph used tocompare parts of a whole.

circumference (533) The distance around a circle.

coefficient (103) The numerical part of a term thatcontains a variable.

combination (642) An arrangement or listing inwhich order is not important.

common difference (249) The difference betweenany two consecutive terms in an arithmeticsequence.

common multiples (226) Multiples that are sharedby two or more numbers. For example, somecommon multiples of 4 and 6 are 0, 12, and 24.

common ratio (250) The ratio between any twoconsecutive terms in a geometric sequence.

compatible numbers (714) Numbers that have beenrounded so when the numbers are divided byeach other, the remainder is zero.

complementary (493) Two angles are complementaryif the sum of their measures is 90°.

composite number (159) A whole number that hasmore than two factors.

compound event (650) Two or more simple events.

cone (569) A solid with a circular base lying in oneplane plus a vertex not lying on that plane. Theremaining surface of the cone is formed byjoining the vertex to points on the circle by linesegments.

congruent (455, 493, 500) Line segments that have thesame length, or angles that have the same measure,or figures that have the same size and shape.

conjecture (7) An educated guess.

constant (103) A term without a variable.

constant of variation (394) The slope, or rate ofchange, in the equation y � kx, represented by k.

converse (462) The statement formed by reversingthe phrases after if and then in an if-thenstatement.


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coordenada Número que corresponde a un punto enla recta numérica.

plano de coordenadas Otro nombre para el sistemade coordenadas.

sistema de coordenadas Un sistema de coordenadasse forma de la intersección de dos rectas numéricasperpendiculares que se intersecan en sus puntoscero. También llamado plano de coordenadas.

ángulos correspondientes Ángulos que tienen lamisma posición en dos rectas paralelas distintascortadas por una transversal. En la figura, �1 y �5, �2 y �6, �3 y �7, �4 y �8 son ánguloscorrespondientes.

partes correspondientes Partes de figuras congruenteso semejantes que se corresponden mutuamente.

coseno Si �ABC es un ángulo rectángulo y A es unode sus ángulos agudos,

coseno �A �

contraejemplo Ejemplo que muestra que unaconjetura no es verdadera.

productos cruzados Si �ac

� � �db

�, entonces ad � bc. Si

ad � bc, entonces �ac

� � �db

�.

función cúbica Función que puede describirse por una ecuación de la forma y � ax3 � bx2 � cx� d, donde a � 0.

cilindro Sólido con dos bases circulares congruentesy paralelas. La tercera superficie del cilindroconsta de todos los círculos paralelos del mismoradio cuyos centros yacen en el segmento queune los centros de las bases.

razonamiento deductivo Proceso de usar hechos,propiedades o reglas para justificar unrazonamiento o para sacar conclusiones válidas.

definir una variable Seleccionar una variable y unacantidad para la variable psts representst en unaecuación.

medida del cateto adyacente a �A��

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coordinate (57) A number that corresponds with apoint on a number line.

coordinate plane (33) Another name for thecoordinate system.

coordinate system (33) A coordinate system isformed by the intersection of two number linesthat meet at right angles at their zero points, alsocalled a coordinate plane.

corresponding angles (492) Angles that have thesame position on two different parallel lines cut by a transversal. In the figure, �1 and �5, �2 and �6, �3 and �7, �4 and �8 arecorresponding angles.

corresponding parts (500) Parts of congruent orsimilar figures that match.

cosine (477) If �ABC is a right triangle and A is anacute angle,

cosine �A �

counterexample (25) An example that shows aconjecture is not true.

cross products (270) If �ac

� � �db

�, then ad � bc. If

ad � bc, then �ac

� � �db

�.

cubic function (688) A function that can be described by an equation of the form y � ax3 � bx2 � cx� d, where a � 0.

cylinder (565) A solid with two parallel congruentcircular bases. The third surface of the cylinderconsists of all parallel circles of the same radiuswhose centers lie on the segment joining thecenters of the bases.

deductive reasoning (25) The process of using facts,properties, or rules to justify reasoning or reachvalid conclusions.

defining a variable (18) Choosing a variable and aquantity for the variable to represent in anequation.

measure of the leg adjacent to �A��

measure of the hypotenuse

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degree (448) The most common unit of measure forangles.

degree (670) The sum of the exponents of thevariables of a monomial.

dependent events (651) Two or more events in whichthe outcome of one event does affect the outcomeof the other event(s).

diagonal (528) A line segment that joins twononconsecutive vertices of a polygon.

diameter (533) The distance across a circle throughits center.

dilation (512) A transformation that alters the size ofa figure but not its shape.

dimensional analysis (212) The process of includingunits of measurement when computing.

direct variation (394) A special type of linearequation that describes rate of change. Arelationship such that as x increases in value, y increases or decreases at a constant rate.

discount (299) The amount by which the regularprice of an item is reduced.

Distance Formula (466) The distance between twopoints, with coordinates (x1, y1) and (x2, y2), is

given by d � �(x2 ��x1)2 �� (y2 �� y1)2�.

divisible (148) A number is divisible by another if,upon division, the remainder is zero.

domain (35) The domain of a relation is the set of allx-coordinates from each pair.

edge (556) Where two planes intersect in a line.

empty set (336) A set with no elements shown by thesymbol { } or �.

equation (28) A mathematical sentence that containsan equals sign (�).

equilateral triangle (455) A triangle with all sidescongruent.

equivalent equations (111) Two or more equationswith the same solution. For example, x � 4 � 7and x � 3 are equivalent equations.

grado La unidad de medida angular más común.

grado Suma de los exponentes de las variables de unmonomio.

eventos dependientes Dos o más eventos en que elresultado de uno de ellos afecta el resultado delotro o de los otros eventos.

diagonal Segmento de recta que une dos vértices noconsecutivos de un polígono.

diámetro Distancia de un lado a otro de un círculomedida a través de su centro.

dilatación Transformación que altera el tamaño deuna figura, pero no su forma.

análisis dimensional Proceso que incorpora lasunidades de medida al hacer cálculos.

variación directa Tipo especial de ecuación lineal quedescribe tasas de cambio. Relación en que amedida que x aumenta de valor, y aumenta odisminuye a una tasa constante .

descuento Cantidad por la que se reduce el precionormal de un artículo.

Fórmula de la distancia La distancia entre dospuntos, con coordenadas (x1, y1) y (x2, y2), se

calcula con d � �(x2 ��x1)2 �� (y2 �� y1)2�.

divisible Un número es divisible entre otro si, aldividirlos, el residuo es cero.

dominio El dominio de una relación es el conjuntode coordenadas x de todos los pares .

arista Recta en donde se intersecan dos planos.

conjunto vacío Conjunto que carece de elementos yque se denota con el símbolo { } o �.

ecuación Enunciado matemático que contiene elsigno de igualdad (�).

triángulo equilátero Un triángulo cuyos lados sontodos congruentes.

ecuaciones equivalentes Dos o más ecuaciones conlas mismas soluciones. Por ejemplo, x � 4 � 7 yx � 3 son ecuaciones equivalentes.

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equivalent expressions (98) Expressions that havethe same value.

evaluate (12) Find the numerical value of anexpression.

expanded form (154) A number expressed usingplace value to write the value of each digit in thenumber.

experimental probability (311) What actually occurswhen repeating a probability experiment manytimes.

exponent (153) In 24, the exponent is 4. The exponenttells how many times the base, 2, is used as afactor. So, 24 � 2 � 2 � 2 � 2.

exterior angles (492, 531) Four of the angles formedby the transversal and two parallel lines. Exteriorangles lie outside the two parallel lines.

face (556) A flat surface, the side or base of a prism.

factorial (642) The expression n factorial (n!) is theproduct of all counting numbers beginning withn and counting backward to 1.

factors (148) Two or more numbers that aremultiplied to form a product.

factor tree (160) A way to find the primefactorization of a number. The factors branch outfrom the previous factors until all the factors areprime numbers.

formula (131) An equation that shows a relationshipamong certain quantities.

frequency table (623) A chart that indicates thenumber of values in each interval.

function (369) A function is a special relation inwhich each element of the domain is paired withexactly one element in the range.

Fundamental Counting Principle (636) If event Mcan occur in m ways and is followed by event Nthat can occur in n ways, then the event Mfollowed by event N can occur in m � n ways.

geometric sequence (250) A sequence in which theratio between any two consecutive terms is thesame.

graph (34) A dot at the point that corresponds to anordered pair on a coordinate plane.

expresiones equivalentes Expresiones que tienen elmismo valor.

evaluar Calcular el valor numérico de una expresión.

forma desarrollada Número que se escribe usando elvalor de posición para indicar el valor de cadadígito de un número.

probabilidad experimental Lo que en realidadocurre al repetir muchas veces un experimento deprobabilidad.

exponente En 24, el exponente es 4. El exponenteindica cuántas veces se usa la base, 2, comofactor. Así, 24 � 2 � 2 � 2 � 2.

ángulos exteriores Cuatro de los ángulos formadospor una transversal y dos rectas paralelas. Losángulos exteriores yacen fuera de las dos rectasparalelas.

cara Superficie plana, el lado o la base de un prisma.

factorial La expresión n factorial (n!) es el producto detodos los números naturales, comenzando con n ycontando al revés hasta llegar al 1.

factores Dos o más números que se multiplican paraformar un producto.

árbol de factores Forma de encontrar la factorizaciónprima de un número. Los factores se ramifican delos factores anteriores hasta que todos los factoresson números primos.

fórmula Ecuación que muestra la relación entreciertas cantidades.

tabla de frecuencias Tabla que indica el número devalores en cada intervalo.

función Una función es una relación especial en quea cada elemento del dominio le corresponde unúnico elemento del rango.

Principio fundamental de contar Si el evento Mpuede ocurrir de m maneras y lo sigue un eventoN que puede ocurrir de n maneras, entonces elevento M seguido del evento N puede ocurrir dem � n maneras.

sucesión geométrica Sucesión en que la razón entredos términos consecutivos cualesquiera essiempre la misma.

gráfica Marca puntual en el punto que corresponde aun par ordenado en un plano de coordenadas.

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greatest common factor (GCF) (164) The greatestnumber that is a factor of two or more numbers.

greatest possible error (594) One-half the precisionunit, used to describe the actual measure.

half plane (419) The region that contains the solutionfor an inequality.

histogram (623) A histogram uses bars to displaynumerical data that have been organized intoequal intervals.

hypotenuse (460) The side opposite the right angle ina right triangle.

identity (336) An equation that is true for everyvalue of the variable.

independent events (650) Two or more events inwhich the outcome of one event does notinfluence the outcome of the other event(s).

indirect measurement (472) Using the properties ofsimilar triangles to find measurements that aredifficult to measure directly.

inductive reasoning (7) Reasoning based on apattern of examples or past events.

inequality (57, 340) A mathematical sentence thatcontains �, �, �, �, or �.

integers (56) The whole numbers and their opposites.. . . , �3, �2, �1, 0, 1, 2, 3, . . .

interior angles (492, 528) Four of the angles formed by the transversal and two parallel lines. Interior angles lie between the two parallel lines.

interquartile range (613) The range of the middlehalf of a set of data. It is the difference betweenthe upper quartile and the lower quartile.

inverse operations (110) Operations that undo eachother, such as addition and subtraction.

irrational number (441) A number that cannot be expressed as �

ba

�, where a and b are integers and bdoes not equal 0.

hypotenuse

máximo común divisor (MCD) El número mayorque es factor de dos o más números.

error máximo posible La mitad de la unidad deprecisión. Se usa para describir la medida exacta.

semiplano Región que contiene la solución de unadesigualdad.

histograma Un histograma usa barras para exhibirdatos numéricos que han sido organizados enintervalos iguales.

hipotenusa Lado opuesto al ángulo recto en untriángulo rectángulo.

identidad Ecuación que es verdadera para cada valorde la variable.

eventos independientes Dos o más eventos en que elresultado de uno de ellos no afecta el resultadodel otro o de los otros eventos .

medición indirecta Uso de las propiedades detriángulos semejantes para hacer mediciones queson difíciles de realizar directamente.

razonamiento inductivo Rezonamiento basada en unpatrón de ejemplos o de sucesos pasados.

desigualdad Enunciado matemático que contiene�, �, �, � o �.

enteros Los números enteros y sus opuestos.. . . , �3, �2, �1, 0, 1, 2, 3, . . .

ángulos interiores Cuatro de los ángulos formadospor una transversal y dos rectas paralelas. Los ángulos interiores yacen entre las dos rectasparalelas.

amplitud intercuartílica Amplitud de la mitadcentral de un conjunto de datos. Es la diferenciaentre el cuartil superior y el inferior.

operaciones inversas Operaciones que se anulanmutuamente, como la adición y la sustracción.

número irracional Número que no puede escribirse como �

ba

�, donde a y b son enteros y bno es igual a 0.

hipotenusa

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isosceles triangle (455) A triangle that has at leasttwo congruent sides.

lateral area (578) The sum of the areas of the lateralfaces of a solid.

lateral faces (578) The lateral faces of a prism,cylinder, pyramid, or cone are all the surface ofthe figure except the base or bases.

least common denominator (LCD) (227) The leastcommon multiple of the denominators of two ormore fractions.

least common multiple (LCM) (226) The least of the nonzero common multiples of two or morenumbers. The LCM of 4 and 6 is 12.

leaves (606) In a stem-and-leaf plot, the next greatestplace value of the data after the stem forms theleaves.

legs (460) The sides that are adjacent to the rightangle of a right triangle.

like terms (103, 674) Expressions that contain thesame variables to the same power, such as 2n and5n or 6xy2 and 4xy2.

line (447) A never-ending straight path.

line graph (722) A type of statistical graph used toshow how values change over a period of time.

line of symmetry (506) Each half of a figure is amirror image of the other half when a line ofsymmetry is drawn.

line segment (453) Part of a line containing twoendpoints and all the points between them.

linear equation (375) An equation in which thevariables appear in separate terms and neithervariable contains an exponent other than 1. Thegraph of a linear equation is a straight line.

lower quartile (613) The median of the lower half ofa set of data, indicated by LQ.

legs

triángulo isósceles Triángulo que posee por lomenos dos lados congruentes.

área lateral Suma de las àreas de las caras lateralesde un sólido.

caras laterales Las caras laterales de un prisma,cilindro, pirámide o cono son todas las superficiesde la figura, excluyendo la base o las bases.

mínimo común denominador (mcd) El mínimocomún múltiplo de los denominadores de dos omás fracciones.

mínimo común múltiplo (mcm) El menor de losmúltiplos comunes no nulos de dos o másnúmeros. El MCM de 4 y 6 es 12.

hojas En un diagrama de tallo y hojas, las hojas lasforma el segundo valor de posición mayordespués del tallo.

catetos Lados adyacentes al ángulo recto de untriángulo rectángulo.

términos semejantes Expresiones que tienen lasmismas variables elevadas a los mismosexponentes, como 2n y 5n ó 6xy2 y 4xy2.

recta Trayectoria rectilínea interminable.

gráfica lineal Tipo de gráfica estadística que se usapara mostrar cómo cambian los valores duranteun período de tiempo.

eje de simetría Cuando se traza un eje de simetría,cada mitad de una figura es una imagenespecular de la otra mitad.

segmento de recta Parte de una recta que contienedos extremos y todos los puntos entre éstos.

ecuación lineal Ecuación en que las variables apare-cen en términos separados y en la cual ningunade ellas tiene un exponente distinto de 1. Lagráfica de una ecuación lineal es una recta.

cuartil inferior Mediana de la mitad inferior de unconjunto de datos, se denota con CI.

catetos

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mean (82, 238) The sum of data divided by thenumber of items in the data set, also called theaverage.

measures of central tendency (238) For a list ofnumerical data, numbers that can represent thewhole set of data.

measures of variation (612) Used to describe thedistribution of statistical data.

median (238) In a set of data, the middle number ofthe ordered data, or the mean of the two middlenumbers.

midpoint (468) On a line segment, the point that ishalfway between the endpoints.

Midpoint Formula (468) On a coordinate plane, thecoordinates of the midpoint of a segment whoseendpoints have coordinates at (x1, y1) and (x2, y2)

are given by ��x1 �

2x2�, �

y1 �

2y2��.

mixed number (200) The indicated sum of a whole number and a fraction. For example, 3�

12

�.

mode (238) The number or numbers that occurs mostoften in a set of data.

monomial (150) An expression that is a number, a variable, or a product of numbers and/or variables.

multiple (226) The product of a number and a wholenumber.

mutually exclusive events (652) Two or more eventsthat cannot happen at the same time.

negative number (56) A number less than zero.

nonlinear function (687) A function with a graphthat is not a straight line.

null set (336) A set with no elements shown by thesymbol { } or �.

numerical expression (12) A combination ofnumbers and operations such as addition,subtraction, multiplication, and division.

obtuse angle (449) An angle with a measure greaterthan 90° but less than 180°.

media Suma de los datos dividida entre el númerode elementos en el conjunto de datos. Tambiénllamada promedio.

medidas de tendencia central Números que puedenrepresentar todo el conjunto de datos en una listade datos numéricos.

medidas de variación Se usan para describir ladistribución de datos estadísticos.

mediana En un conjunto de datos, el número centralde los datos ordenados numéricamente o lamedia de los dos números centrales.

punto medio En un segmento de recta, el punto queequidista de ambos extremos.

Fórmula del punto medio En el plano de coordena-das, el punto medio de un segmento cuyosextremos son (x1, y1) y (x2, y2) se calcula con la

fórmula ��x1 �

2x2�, �

y1 �

2y2��.

número mixto Suma de un entero y una fracción. Por ejemplo, 3�

12

�.

moda Número o números de un conjunto de datosque aparecen más frecuentemente.

monomio Expresión que es un número, una variabley/o un producto de números y variables.

múltiplo Producto de un número por un númeroentero.

eventos mutuamente exclusivos Dos o más eventosque no pueden ocurrir simultáneamente.

número negativo Número menor que cero.

función no lineal Función cuya gráfica no es unarecta.

conjunto vacío Conjunto que carece de elementos yque se denota con el símbolo { } o �.

expresión numérica Combinación de números yoperaciones, como adición, sustracción,multiplicación y división.

ángulo obtuso Ángulo que mide más de 90°, peromenos de 180°.

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obtuse triangle (454) A triangle with one obtuseangle.

odds (646) A way to describe the chance of an eventoccurring.

open sentence (28) An equation that contains avariable.

opposites (66) Two numbers with the same absolutevalue but different signs.

ordered pair (33) A pair of numbers used to locateany point on a coordinate plane.

order of operations (12)1. Simplify the expressions inside grouping

symbols.2. Evaluate all powers.3. Do all multiplications and/or divisions from

left to right.4. Do all additions and/or subtractions from left

to right.

origin (33) The point at which the number linesintersect in a coordinate system.

outcomes (310) Possible results of a probabilityevent.

outliers (621) Data that are more than 1.5 times theinterquartile range from the quartiles.

parallel lines (492) Two lines in the same plane thatdo not intersect.

parallelogram (514) A quadrilateral with oppositesides parallel and congruent.

part (288) In a percent proportion, the number beingcompared to the whole quantity.

percent (281) A ratio that compares a number to 100.

percent equation (298) An equivalent form ofpercent proportion, where % is written as adecimal.

Part � Percent � Base

percent of change (304) The ratio of the increase ordecrease of an amount to the original amount.

obtuseangle

triángulo obtusángulo Triángulo que posee unángulo obtuso.

posibilidades Una manera de describir laoportunidad de que ocurra un evento.

enunciado abierto Ecuación que contiene unavariable.

opuestos Dos números que tienen el mismo valorabsoluto, pero que tienen distintos signos.

par ordenado Par de números que se usa para ubicarcualquier punto en un plano de coordenadas.

orden de las operaciones

1. Reduce las expresiones dentro de símbolos deagrupamiento.

2. Evalúa todas las potencias.3. Ejecuta todas las multiplicaciones y/o

divisiones de izquierda a derecha.4. Ejecuta todas las adiciones y/o sustracciones

de izquierda a derecha.

origen Punto de intersección de las rectas numéricasde un sistema de coordenadas.

resultado Resultados posibles de un experimentoprobabilístico.

valores atípicos Datos que distan de los cuartilesmás de 1.5 veces la amplitud intercuartílica.

rectas paralelas Dos rectas en el mismo plano que nose intersecan.

paralelogramo Cuadrilátero con lados opuestoscongruentes y paralelos.

parte En una proporción porcentual, el número quese compara con la cantidad total.

por ciento Razón que compara un número con 100.

ecuación porcentual Forma equivalente a la propor-ción porcentual en que el % se escribe comodecimal.

Parte � Por ciento � Base

porcentaje de cambio Razón del aumento o disminu-ción de una cantidad a la cantidad original.

triánguloobtusángulo

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percent of decrease (306) The ratio of an amount ofdecrease to the previous amount, expressed as apercent. A negative percent of change.

percent of increase (305) The ratio of an amount ofincrease to the original amount, expressed as apercent.

percent proportion (288)

�bpaasret

� � �pe

1r0ce0nt

� or �ab

� � �1p00�

perfect squares (436) Rational numbers whosesquare roots are whole numbers. 25 is a perfectsquare because �25� � 5.

perimeter (132) The distance around a geometricfigure.

period (201) In a repeating decimal, the digit ordigits that repeats. The period of 0.6� is 6.

permutation (641) An arrangement or listing inwhich order is important.

perpendicular lines (494) Lines that intersect to forma right angle.

pi, � (533) The ratio of the circumference of a circleto the diameter of the circle. Approximations for � are 3.14 and �

272�.

plane (556) A two-dimensional flat surface thatextends in all directions and contains at leastthree noncollinear points.

point (447) A specific location in space with no sizeor shape.

polygon (527) A simple closed figure in a planeformed by three or more line segments.

polyhedron (556) A solid with flat surfaces that arepolygons.

polynomial (669) An algebraic expression thatcontains the sums and/or products of one ormore monomials.

power (153) A number that is expressed using anexponent.

precision (590) The exactness to which ameasurement is made.

prime factorization (160) A composite numberexpressed as a product of prime factors. Forexample, the prime factorization of 63 is 3 � 3 � 7.

porcentaje de disminución Razón de la cantidad dedisminución a la cantidad original, escrita comopor ciento. Un por ciento de cambio negativo.

porcentaje de aumento Razón de la cantidad deaumento a la cantidad original, escrita como porciento.

proporción porcentual

�pbaarstee

� � �por

1c0ie0nto

� o �ab

� � �1p00�

cuadrados perfectos Números racionales cuyasraíces cuadradas son números racionales. 25 esun cuadrado perfecto porque �25� � 5.

perímetro Longitud alrededor de una figurageométrica.

período En un decimal periódico, el dígito o dígitosque se repiten. El período de 0.6� es 6.

permutación Arreglo o lista en que el orden esimportante.

rectas perpendiculares Rectas que se intersecanformando un ángulo recto.

pi, � Razón de la circunferencia de un círculo al diámetro del mismo. 3.14 y �

272� son

aproximaciones de �.

plano Superficie plana bidimensional que se extiendeen todas direcciones y que contiene por lo menostres puntos no colineales.

punto Ubicación específica en el espacio sin tamañoo forma.

polígono Figura simple y cerrada en el planoformada por tres o más segmentos de recta.

poliedro Sólido con superficies planas que sonpolígonos.

polinomio Expresión algebraica que contiene sumasy/o productos de uno o más monomios.

potencia Número que puede escribirse usando unexponente.

precisión Exactitud con que se realiza una medida.

factorización prima Número compuesto escritocomo producto de factores primos. Por ejemplo,la factorización prima de 63 es 3 � 3 � 7.



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prime number (159) A whole number that hasexactly two factors, 1 and itself.

principle (300) The amount of money in an account.

prism (557) A solid with two congruent parallelpolygonal bases. The remaining edges joincorresponding vertices of the bases so that theremaining faces are rectangles.

probability (310) If outcomes are equally likely, theratio of the number of ways a certain event canoccur to the number of possible outcomes.

P(event) �

proportion (270) A statement of equality of two ormore ratios.

protractor (448) An instrument used to measureangles.

pyramid (557) A solid with a polygonal base lyingin one plane plus one additional vertex not lyingon that plane. The remaining edges of thepyramid join the additional vertex to thevertices of the base.

Pythagorean Theorem (460) If a triangle is a righttriangle, then the square of the length of thehypotenuse is equal to the sum of the squares ofthe lengths of the legs or c2 � a2 � b2.

quadrants (86) The four regions into which the x-axis and y-axis separate the coordinate plane.

quadratic function (688) A function that can be described by an equation of the form y � ax2 � bx � c, where a � 0.

a

b

c

number of favorable outcomes��number of possible outcomes

triangular prismrectangular prism

número primo Número entero que sólo tiene dosfactores, 1 y sí mismo.

capital Cantidad de dinero en una cuenta.

prisma Sólido con dos bases poligonales paralelas ycongruentes. Las aristas restantes unen losvértices correspondientes de las bases de modoque las caras restantes son rectángulos.

probabilidad Si los resultados son equiprobables, larazón del número de maneras en que puedeocurrir el evento al número de resultados posibles.

P(evento) �

proporción Enunciado de la igualdad de dos o másrazones.

transportador Instrumento que se usa para medirángulos.

pirámide Sólido con una base que es un polígonoque yace en un plano, más un vértice adicionalque no yace en ese plano. Las aristas restantes dela pirámide juntan los vértices adicionales a losvértices de la base.

Teorema de Pitágoras Si un triángulo es rectángulo,entonces el cuadrado de la longitud de lahipotenusa es igual a la suma de los cuadradosde las longitudes de los catetos, o c2 � a2 � b2.

cuadrantes Las cuatro regiones en que los ejes x y ydividen el plano de coordenadas.

función cuadrática Función que puede describirsepor una ecuación de la formay � ax2 � bx � c, donde a � 0.

a

b

c

número de resultados favorables��número de resultados posibles

prisma triangularprisma rectangular

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quadrilateral (513) A closed figure with four sidesand four vertices, including squares, rectangles,and trapezoids.

quartiles (613) The values that divide a set of datainto four equal parts.

radical sign (436) The symbol �� used to indicatea positive square root of a number.

radius (533) The distance from the center to anypoint on the circle.

range (35) The range of a relation is the set of all y-coordinates from each ordered pair.

range (612) A measure of variation that is thedifference between the least and greatest valuesin a set of data.

rate (265) A ratio of two measurements havingdifferent units.

rate of change (393) A change in one quantity withrespect to another quantity.

ratio (264) A comparison of two numbers orquantities. The ratio of 2 to 4 can be stated as 2 outof 4, 2 to 4, 2:4, or �

24

�.

rational number (205) A number that can be written as a fraction in the form �

ba

�, where a and bare integers and b � 0.

ray (447) A part of a line that extends indefinitely inone direction.

real numbers (441) The set of rational numberstogether with the set of irrational numbers.

reciprocal (215) Another name for a multiplicativeinverse.

rectangle (514) A parallelogram with four right angles.

reflection (506) A transformation where a figure isflipped over a line. Also called a flip.

regular polygon (529) A polygon having all sidescongruent and all angles congruent.

relation (35) A set of ordered pairs.

repeating decimal (201) A decimal whose digitsrepeat in groups of one or more. Examples are0.181818… and 0.8333… .

rhombus (514) A parallelogram with four congruentsides.

cuadrilátero Figura cerrada de cuatro lados y cuatrovértices, incluyendo cuadrados, rectángulos ytrapecios.

cuartiles Valores que dividen un conjunto de datosen cuatro partes iguales.

signo radical El símbolo �� que se usa paraindicar la raíz cuadrada positiva de un número.

radio Distancia del centro a cualquier punto de uncírculo.

rango El rango de una relación es el conjunto decoordenadas y de todos los pares.

amplitud Medida de variación que es la diferenciaentre los valores máximo y mínimo de unconjunto de datos.

tasa Razón de dos medidas que tienen unidadesdistintas.

tasa de cambio Cambio de una cantidad con respectoa otra.

razón Comparación de dos números o cantidades. Larazón de 2 a 4 se puede expresar como,2 de 4, 2:4, ó �

24

�.

número racional Número que puede escribirse como una fracción de la forma �

ba

� donde a y b sonenteros y b � 0.

rayo Parte de una recta que se extiendeindefinidamente en una dirección.

números reales El conjunto de los números racio-nales junto con el de números irracionales.

recíproco Otro nombre del inverso multiplicativo.

rectángulo Paralelogramo con cuatro ángulos rectos.

reflexión Transformación en que una figura se volteaa través de una recta.

polígono regular Polígono cuyos lados son todoscongruentes y cuyos ángulos son también todoscongruentes.

relación Conjunto de pares ordenados.

decimal periódico Decimal cuyos dígitos se repitenen grupos de uno o más. 0.181818… y 0.8333…son ejemplos de este tipo de decimales.

rombo Paralelogramo con cuatro lados congruentes.

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right angle (449) An angle that measures 90°.

right triangle (454) A triangle with one right angle.

rotation (506) A transformation where a figure isturned around a fixed point. Also called a turn.

sample (309) A subgroup or subset of a populationused to represent the whole population.

sample space (311) The set of all possible outcomes.

scale (276) The relationship between themeasurements on a drawing or model and themeasurements of the real object.

scale drawing (276) A drawing that is used torepresent an object that is too large or too small tobe drawn at actual size.

scale factor (277) The ratio of a length on a scaledrawing or model to the corresponding length onthe real object.

scale model (276) A model used to represent anobject that is too large or too small to be built atactual size.

scalene triangle (455) A triangle with no congruentsides.

scatter plot (40) A graph that shows the relationshipbetween two sets of data.

scientific notation (186) A number in scientificnotation is expressed as a � 10n, where 1 � a � 10 and n is an integer. For example, 5,000,000 � 5.0 � 106.

sequence (249) An ordered list of numbers, such as, 0, 1, 2, 3, or 2, 4, 6, 8.

sides (447) The two rays that make up an angle.

significant digits (590) The digits recorded frommeasurement, indicating the precision of themeasurement.

similar solids (584) Solids that have the same shapebut not necessarily the same size.

similar triangles (471) Triangles that have the sameshape but not necessarily the same size.

ángulo recto Ángulo que mide 90°.

triángulo rectángulo Triángulo que tiene un ángulorecto.

rotación Transformación en que una figura se hacegirar alrededor de un punto fijo. También sellama vuelta.

muestra Subgrupo o subconjunto de una poblaciónque se usa para representarla.

espacio muestral Conjunto de todos los resultadosposibles.

escala Relación entre las medidas de un dibujo omodelo y las medidas de la figura verdadera.

dibujo a escala Dibujo que se usa para representaruna figura que es demasiado grande o pequeñacomo para ser dibujada de tamaño natural.

factor de escala Razón de la longitud en un dibujo aescala o modelo a la longitud correspondiente enla figura verdadera.

modelo a escala Modelo que se usa para representaruna figura que es demasiado grande o pequeñacomo para ser construida de tamaño natural.

triángulo escaleno Triángulo que no tiene ladoscongruentes.

gráfica de dispersión Gráfica en que se muestra larelación entre dos conjuntos de datos.

notación científica Un número en notación científica se escribe como a � 10n, donde 1 � a � 10 y n es un entero. Por ejemplo, 5,000,000 � 5.0 � 106.

sucesión Lista ordenada de números, como 0, 1, 2, 3 ó 2, 4, 6, 8.

lados Los dos rayos que forman un ángulo.

dígitos significativos Los dígitos de una mediciónque indican la precisión de la medición.

sólidos semejantes Sólidos que tienen la mismaforma, pero no necesariamente el mismo tamaño.

triángulos semejantes Triángulos que tienen lamisma forma, pero no necesariamente el mismotamaño.

S



simple event (310) One outcome or a collection ofoutcomes.

simple interest (300) The amount of money paid orearned for the use of money.

I � prt (Interest � principal � rate � time)

simplest form (104) An algebraic expression insimplest form has no like terms and noparentheses.

simplest form (169) A fraction is in simplest formwhen the GCF of the numerator and thedenominator is 1.

simplify (25) To write an expression in a simplerform.

simulation (656) The process of acting out a situationto see possible outcomes.

sine (477) If �ABC is a right triangle and A is anacute angle,

sine �A � .

skew lines (558) Lines that are neither intersectingnor parallel. Skew lines lie in different planes.

slant height (578) The length of the altitude of alateral face of a regular pyramid.

slope (387) The ratio of the rise, or vertical change, tothe run, or horizontal change. The slope describesthe steepness of a line.

slope � �rriusne

�

slope-intercept form (398) A linear equation in theform y � mx � b, where m is the slope and b isthe y-intercept.

solution (28) A value for the variable that makes anequation true. For x � 7 � 19, the solution is 12.

solving the equation (28) The process of finding asolution to an equation.

solving a right triangle (461) Using the PythagoreanTheorem to find the length of the third side of aright triangle, if the lengths of the other two sidesare known.

square (514) A parallelogram with all sidescongruent and four right angles.

square root (436) One of the two equal factors of anumber. The square root of 25 is 5 since 52 � 25.

standard form (154) A number is in standard formwhen it does not contain exponents. The standardform for seven hundred thirty-nine is 739.

measure of the leg opposite �A��

measure of the hypotenuse

evento simple Resultado o colección de resultados.

interés simple Cantidad que se paga o que se ganapor usar el dinero.

I � crt (Interés � capital � rédito � tiempo)

forma reducida Una expresión algebraica reducidano tiene ni términos semejantes ni paréntesis.

forma reducida Una fracción está reducida si elMCD de su numerador y denominador es 1.

reducir Escribir una expresión en forma más simple.

simulación Proceso de representación de unasituación para averiguar los resultados posibles.

seno Si �ABC es un triángulo rectángulo y A es unángulo agudo,

seno �A � .

rectas alabeadas Rectas que no se intersecan y queno son paralelas. Las rectas alabeadas yacen endistintos planos.

altura oblicua En una pirámide regular, la longitudde la altura de una cara lateral.

pendiente Razón de la elevación o cambio vertical aldesplazamiento o cambio horizontal. Lapendiente describe la inclinación de una recta.

pendiente ��deseplleavzaacmióiennto

�

forma pendiente-intersección Una ecuación lineal dela forma y � mx � b, donde m es la pendiente y bes la intersección y.

solución Valosss y que posee cuatro ángulos rectos.

resolver la ecuación (28) Proceso de hallar unasolución a una ecuación.

resolver un triángulo rectángulo Uso del Teoremade Pitágoras para hallar la longitud de un tercerlado de un triángulo rectángulo, si se conocen laslongitudes de los otros dos lados.

cuadrado Paralelogramo cuyos lados son todoscongruentes y que posee cuatro ángulos rectos.

raíz cuadrada Uno de los dos factores iguales de unnúmero. Una raíz cuadrada de 25 es 5 porque52 � 25.

forma estándar Un número está en forma estándar sino contiene exponentes. Por ejemplo, la formaestándar de setecientos treinta y nueve es 739.

medida del cateto opuesto a �A��

medida de la hipotenusa

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stem-and-leaf plot (606) A system used to condensea set of data where the greatest place value of thedata forms the stem and the next greatest placevalue forms the leaves.

stems (606) The greatest place value common to allthe data values is used for the stem of a stem-and-leaf plot.

straight angle (449) An angle with a measure equalto 180°.

supplementary (494) Two angles are supplementaryif the sum of their measures is 180°.

surface area (573) The sum of the areas of all thesurfaces (faces) of a 3-dimensional figure.

system of equations (414) A set of equations with thesame variables. The solution of the system is theordered pair that is a solution for all of theequations.

tangent (477) If �ABC is a right triangle and A is anacute angle,

tangent �A �

term (103) When plus or minus signs separate analgebraic expression into parts, each part is aterm.

term (249) Each number within a sequence is called aterm.

terminating decimal (200) A decimal whose digitsend. Every terminating decimal can be written asa fraction with a denominator of 10, 100, 1000,and so on.

theoretical probability (311) What should occur in aprobability experiment.

transformation (506) A movement of a geometricfigure.

translation (506) A transformation where a figure isslid from one position to another without beingturned. Also called a slide.

transversal (492) A line that intersects two parallellines to form eight angles.

trapezoid (514) A quadrilateral with exactly one pairof parallel sides.

tree diagram (635) A diagram used to show the totalnumber of possible outcomes.

measure of the leg opposite �A��measure of the leg adjacent to �A

diagrama de tallo y hojas Sistema que se usa paracondensar un conjunto de datos, en que el valorde posición máximo de los datos forma el tallo yel segundo valor de posición máximo forma lashojas.

tallos Máximo valor de posición común a todos losdatos que se usa como el tallo en un diagrama detallo y hojas.

ángulo llano Ángulo que mide 180°.

suplementarios Dos ángulos son suplementarios sisus medidas suman 180°.

área de superficie Suma de las áreas de todas lassuperficies (caras) de una figura tridimensional.

sistema de ecuaciones Conjunto de ecuaciones conlas mismas variables. La solución del sistema esel par ordenado que resuelve ambas ecuaciones.

tangente Si �ABC es un triángulo rectángulo y A esun ángulo agudo,

tangente �A �

término Cada una de las partes de una expresiónalgebraica separadas por los signos de adición osustracción.

término Cada número de una sucesión se llamatérmino.

decimal terminal Decimal cuyos dígitos terminan.Todo decimal terminal puede escribirse como unafracción con un denominador de 10, 100, 1000, etc.

probabilidad teórica Lo que debería ocurrir en unexperimento probabilístico.

transformación Desplazamiento de una figurageométrica.

translación Transformación en que una figura sedesliza sin girar, de una posición a otra. Tambiénse llama deslizamiento.

transversal Recta que interseca dos rectas paralelasformando ocho ángulos.

trapecio Cuadrilátero con sólo un par de ladosparalelos.

diagrama de árbol Diagrama que se usa paramostrar el número total de resultados posibles.

medida del cateto opuesto al �A��medida del cateto adyacente a �A

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triangle (453) A polygon having three sides.

trigonometric ratio (477) A ratio of the lengths oftwo sides of a right triangle. The tangent, sine,and cosine ratios are three trigonometric ratios.

trigonometry (477) The study of the properties oftriangles. Trigonometry means angle measurement.

trinomial (669) A polynomial with three terms.

two-step equation (120) An equation that containstwo operations.

unit rate (265) A rate simplified so that it has adenominator of 1.

upper quartile (613) The median of the upper half ofa set of data, indicated by UQ.

variable (17) A placeholder for any value.

Venn diagram (164) A diagram that is used to show the relationships among sets of numbers or objects by using overlapping circles in arectangle.

vertex (447) The common endpoint of the raysforming an angle.

vertex (453) A vertex of a polygon is a point wheretwo sides of the polygon intersect.

vertex (556) Where three or more planes intersect in apoint.

vertical angles (493) Two pairs of opposite anglesformed by two intersecting lines. The anglesformed are congruent. In the figure, the verticalangles are �1 and �3, �2 and �4.

vertical line test (370) If any vertical line drawn onthe graph of a relation passes through no morethan one point on the graph for each value of x inthe domain, then the relation is a function.

volume (563) The measure of space occupied by asolid region.

x-axis (33) The horizontal number line which helps toform the coordinate system.

14

32

triángulo Polígono de tres lados.

razón trigonométrica Razón de las longitudes de doslados de un triángulo rectángulo. La tangente, elseno y el coseno son tres razones trigonométricas.

trigonometría Estudio de las propiedades de lostriángulos. La palabra significa medida de ángulos.

trinomio Polinomio de tres términos.

ecuación de dos pasos Ecuación que contiene dosoperaciones.

tasa unitaria Tasa reducida que tiene denominadorigual a 1.

cuartil superior Mediana de la mitad superior de unconjunto de datos, denotada por CS.

variable Marcador de posición para cualquier valor.

diagrama de Venn Diagrama que se usa paramostrar las relaciones entre conjuntos denúmeros o elementos mediante círculos, quepueden traslaparse, dentro de un rectángulo.

vértice Extremo común de los dos rayos que formanun ángulo.

vértice El vértice de un polígono es un punto en quese intersecan dos lados del mismo.

vértice Punto en que se intersecan tres o más planos.

ángulos opuestos por el vértice Dos pares de ángu-los opuestos formados por dos rectas que seintersecan. Los ángulos que resultan soncongruentes. En la figura, los ángulos opuestospor el vértice son �1 y �3, �2 y �4.

prueba de la recta vertical Si todas las rectas vertica-les trazadas en la gráfica de una relación nopasan por más un punto para cada valor de x enel dominio, entonces la relación es una función.

volumen Medida del espacio que ocupa un sólido.

eje x Recta numérica horizontal que forma parte deun sistema de coordenadas.

14

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Y

x-coordinate (33) The first number of an orderedpair.

x-intercept (381) The x-coordinate of a point where agraph crosses the x-axis.

y-axis (33) The vertical number line which helps toform the coordinate system.

y-coordinate (33) The second number of an orderedpair.

y-intercept (381) The y-coordinate of a point where agraph crosses the y-axis.

coordenada x El primer número de un par ordenado.

intersección x La coordenada x de un punto en queuna gráfica interseca el eje x.

eje y Recta numérica vertical que forma parte de unsistema de coordenadas.

coordenada y El segundo número en un parordenado.

intersección y La coordenada y de un punto en queuna gráfica interseca el eje y.



Selected Answers R19

Chapter 1 The Tools of Algebra

Page 5 Chapter 1 Getting Started1. 14.8 3. 3.1 5. 2.95 7. 3.55 9. 7.88 11. Sampleanswer: 1200 13. Sample answer: 120 15. Sample answer:20,000 17. Sample answer: 220 19. Sample answer: 1421. Sample answer: $5 23. Sample answer: 12025. Sample answer: 4 27. Sample answer: 10

Pages 9–10 Lesson 1-11. when an exact answer is not needed 3. 1:33 P.M. 5. 177. 3072 9. 178 beats per min 11. 17 13. 25 15. 34 17. 2719.

21. Since $68 � $15 � $20 � $16 � $119, Ryan does not haveenough money for the ski trip. 23. about 5 h 25. Sampleanswer: about 21,800 transplants 27a. There are more even products. Since any even number multiplied by anynumber is even, and only an odd number multiplied by anodd number is odd, there are more even products in thetable. There are about 3 times as many evens as odds.27b. Yes; in the addition table, there is only one more evennumber than odd. 29. B 31. 3 33. 35 35. 109

Pages 14–16 Lesson 1-21. Sample answer: (8 � 3) � 2 3. Emily; she followed theorder of operations and divided first. 5. �; 20 7. �; 669. �; 15 11. 12 � 9 13. 4 15. 25 17. 38 19. 2 21. 5523. 24 25. 64 27. 180 29. 50 31. 6 � 3 33. 9 � 535. 24 � 6 37. 3 � $6 39. (4 � 2) � (2 � 13)41. (3 � 57) � (2 � 12) 43. 61 � (15 � 3) � 4345. 56 � (2 � 6) � 4 � 347. (50 � 25) � (7 � 24) � (4 � 22) � (3 � 16)49. 0-07-825200-8 51. Sample answer: 111 � (1 � 1 � 1) � (11 � 1) 53. C 55. 64 57. 2859. $275 61. Sample answer: about 26 compact cars63. 126 65. 563

Pages 19–21 Lesson 1-31. Sample answer: 7n and 3x � 1; 2 � 3 and 3 � 83. Sample answer: 4 � c � d 5. 6 7. 17 9. g � 511. 7 � n � 8 13. 11 15. 38 17. 2 19. 9 21. 27 23. 5625. 53 27. 44 29. 32 31. 71°F 33. s � $200 35. h � 637. 5q � 4 39. n � 6 � 9 41. 17 � 4w 43. 10 45. x � 347. p � 4 49. s � c � m � d 51. 1 53. D 55. 7 57. 959. 36 61. 22

Page 21 Practice Quiz 11. 14 3. 79 5. 22

Pages 26–27 Lesson 1-41. Sample answer: 3 · 4 � 4 · 3 3. Kimberly; theAssociative Property only holds true if all numbers areadded or all numbers are multiplied, not a combination ofthe two. 5. Additive Identity 7. 28 9. 45 11. n � 1313. $42; To find the total cost, add the three costs together.

Since the order in which the costs are added does notmatter, the Commutative Property of Addition holds trueand makes the addition easier. By adding 4 and 26, theresult is 30, and 30 � 12 is 42. 15. Multiplicative Identity 17. Commutative Property of Multiplication19. Associative Property of Addition 21. Additive Identity 23. Associative Property of Multiplication25. Commutative Property of Addition 27. 55 29. 4031. 990 33. 0 35. false; (100 � 10) � 2 � 100 � (10 � 2)37. false; 9 � 3 � 3 � 9 39. m � 12 41. a � 27 43. 12y45. 48c 47. 75s49. There are many real-life situations in which the order inwhich things are completed does not matter. Answersshould include the following.• Reading the sports page and then the comics, or reading

the comics and then the sports page. No matter theorder, both parts of the newspaper will be read.

• When washing clothes, you would add the detergent andthen wash the clothes, not wash the clothes and then addthe detergent. Order matters.

51. B 53. 36 55. w � 12 57. 35 59. 15, 21 61. 29663. 1050 65. 7493

Pages 30–32 Lesson 1-51. Sample answer: b � 7 � 12 and 8 � h � 3 3. 6 5. 57. 6 9. Symmetric 11. Let n � the number; n � 8 � 23; 1513. C 15. 11 17. 12 19. 5 21. 15 23. 9 25. always27. 15 29. 0 31. 15 33. 17 35. 11 37. 9 39. 3 41. 443. Let h � the number; h � 10 � 27; 37 45. Let w � thenumber; 9 � w � 36; 27 47. Let x � the number; 3x � 45; 15 49. $8 51. Symmetric Property of Equality53. Symmetric Property of Equality 55. 3 57. Sampleanswer: Once the variable(s) are replaced in the opensentence, the order of operations is used to find the value ofthe expression. Answers should include the following. • To evaluate an expression, replace the variable(s) with

the given values, and then find the value of theexpression.

• To solve an open sentence, find the value of the variablethat makes the sentence true.

59. B 61. 23 � d 63. 10 � n 65. 11 67. 42 69. 1871. 50 73. 90

Page 32 Practice Quiz 21. Identity (�) 3. 24h 5. 8

Pages 36–38 Lesson 1-61. Sample answer: (3, 5); the x-coordinate is 3 and the y-coordinate is 5. 3. The domain of a relation is the set ofx-coordinates. The range is the set of y-coordinates.5. 7. (6, 5)y

xOD

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9.

11.

13. 15.

17. 19. (7, 3) 21. (6, 6)23. (3, 4) 25. on the x-axis;on the y-axis

27.

29.

31.

domain � {4, 5, 1};range � {5, 2, 6}

33.

domain � {7, 3, 4, 5};range � {0, 2, 4, 1}

35.

domain � {0, 2};range � {1, 3, 5, 0}

37. (0, 14.7), (1, 10.2), (2, 6.4), (3, 4.3), (4, 2.7), (5, 1.6)39. domain � {0, 1, 2, 3, 4, 5}; range � {14.7, 10.2, 6.4, 4.3,2.7, 1.6} 41. {(0, 100), (1, 95), (2, 90), (3, 85), (4, 80), (5, 75)}43. about 93°C; about 96°C 45. Ordered pairs can be usedto graph real-life data by expressing the data as orderedpairs and then graphing the ordered pairs. Answers shouldinclude the following.• The x- and y-coordinate of an ordered pair specifies the

point on the graph.• longitude and latitude lines.

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4 5

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5 1

x y

0 1

0 3

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domain � {1, 6, 0, 3};range � {6, 4, 2, 1}

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47. D 49a. 49b. triangle49c. (4, 2), (4, 8),(10, 2)49d. triangle49e. The figureshave the sameshape but not thesame size.

51. 6 53. Multiplicative Identity 55. 7 57. 10 · 30 59. 1261. 28 63. 7 65. 9

Pages 42–44 Lesson 1-71. Sample answer: make predictions, draw conclusions,spot trends 3. negative, positive, and none 5. No; haircolor is not related to height. 7. Since the points appear tobe random, there is no relationship. 9. The number ofsongs on a CD usually does not affect the cost of the CD;no. 11. As speed increases, distance traveled increases;positive. 13. The size of a television screen and thenumber of channels it receives are not related; no. 15. Thenumber decreases.17.

19. about 800 21. Sample answer: Yes; as more emphasis isplaced on standardized tests, students will become morecomfortable taking the tests, and the scores will increase.23. C25. 27.

29. (0, 4) 31. domain � {0, 4, 2, 6}; range � {9, 8, 3, 1}33. 7 35. b � 18 37. 31

Pages 47–50 Chapter 1 Study Guide and Review1. d 3. e 5. c 7. 20 9. 22 11. 22 13. 16 15. 1217. 14 19. 10 21. 25 23. Commutative Property of

Addition 25. Multiplicative Property of Zero 27. 1029. 17 31. 633.

domain: {2, 6, 7}; range: {3, 1, 5}

35. Positive; as the height increases, the circumferenceincreases.

Chapter 2 Integers

Page 55 Chapter 2 Getting Started1. 22 3. 42 5. 8 7. 4 9. T 11. V 13. Q

Pages 59–61 Lesson 2-11. Draw a number line. Draw a dot at �4. 3. The absolutevalue of a number is its distance from 0 on a number line.5. �15

7. �4 � 2; 2 � �4 9. � 11. � 13. 10 15. 21 17. 319. �54, �52, �45, �37, �36, �34, �27, �27, �221. �6

23. �9

25. �5

27.

29.

31. �5 � �10; �10 � �5 33. 248 � 425; 425 � 24835. 212 � 32; 32 � 212 37. � 39. � 41. � 43. �45. {�15, �4, �2, �1} 47. {�60, �57, 38, 98, 188} 49. 4651. �5 53. 7 55. 2 57. 9 59. –20 61. 4 63. 40 65. 367.

69. �54 � �70 71. 7 73. Sometimes; if A and B are bothpositive, both negative, or one is 0, it is true. If one numberis negative and the other is positive, it is false. 75. B77. Positive; as height increases, so does arm length.79. {(3, 2), (3, 4), (2, 1), (2, 4)}

81. Commutative Property of Multiplication83. Commutative Property of Multiplication 85. 38887. 17 89. 1049

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Pages 67–68 Lesson 2-21a. Negative; both addends are negative. 1b. Positive;12 � �2. 1c. Negative; �11 � 9. 1d. Positive;both addends are positive. 3. �6 5. 5 7. 3 9. 411. 4 � (�5) � �1 13. �7 15. �11 17. �16 19. �2121. �66 23. 2 25. �2 27. 6 29. �26 31. 21 33. �235. �6 37. �3 39. 0 41. �5 43. 8 45. 4047. �107,68049. To add integers on a number line, start at 0. Move rightto show positive integers and left to show negativeintegers. Answers should include the following.• Sample answer:

• Sample answer:

51. D 53. {�12, �9, �8, 0, 3, 14} 55. no relationship57. 6 59. 20 61. 25 63. 42 65. 65

Pages 72–74 Lesson 2-31. Sample answer: 5, �5; �9, 9 3. �3 5. 9 7. �2 9. 2011. 21 13. Utah, Washington, Wisconsin, or Wyoming15. �1 17. �3 19. �9 21. �12 23. 10 25. 12 27. 329. �9 31. �14 33. �28 35. 239 37. 1300 39. 14,776 ft41. 24 43. �36 45. �9 47. �20 49. �23 51. �1753. �10,822 55a. False; 3 � 4 � 4 � 3 55b. False; (5 � 2) � 1 � 5 � (2 � 1) 57. A 59. �2450 61. 3 63. 7

65. �x5

� 67. �8b6� 69. 20 71. 75 73. 120

Page 74 Practice Quiz 11. �80, �70, �69 3. 6 5. �7 7. 32 9. �9

Pages 77–79 Lesson 2-41. 3(�5) � �15 3. Sample answer: (�4)(9)(2) 5. �407. 28 9. �540 11. �21y 13. 120 15. A 17. �4219. �72 21. �70 23. 128 25. 45 27. 130 29. �30831. 528 33. �1344 35. �56°F 37. �96y 39. �55b41. 108mn 43. �135xy 45. �88bc 47. –90jk 49. �9951. 80 53. �216 55. 248 ft 57a. True; 3(�5) � �5(3)57b. True; �2(3 � 5) � (�2 � 3)(5) 59. B 61. �16 63. 465. 10 67. 126°F 69. �14 71. (6, 2) 73. (1, 5) 75. (5, 5)77. 480 79. 550 81. 6 83. 15 85. 4

Pages 83–84 Lesson 2-51. Sample answer: �16 � 4 � �4 3. 11 5. �3 7. �109. �13 11. 0 13. 9 15. 8 17. 10 19. �50 21. �1123. �11 25. 19 27. �12 29. �13 31. 16 33. 49 points35. 61 37. Sample answer: x � �144; y � 12; z � �1239. When the signs of the integers are the same, both aproduct and a quotient are positive; when the signs aredifferent, the product and quotient are negative. Answersshould include the following.• Sample answer: 4 � (�6) � �24 and �24 � 4 � �6;

�3 � 2 � �6 and �6 � (�3) � 2• Sample answers: same sign: �30 � (�5) � 6, 30 � 5 � 6;

different signs: �24 � 8 � �3, 24 � (�8) � �341. B 43. �39 45. �50cd 47. B 49. D

Page 84 Practice Quiz 21. �84 3. �126 5. �31 7. �25 9. �20xy

Pages 87–89 Lesson 2-61. Sample answer: (3, 6) represents a point 3 units to theright and 6 units up from the origin. (6, 3) represents apoint 6 units to the right and 3 units up from the origin.3. Keisha; a point in Quadrant I has two positivecoordinates. Interchanging the coordinates will still result in two positive coordinates, and the point will be inQuadrant I. 5. (1, 3) 7. (5, �4) 9. II 11. III 13. (�2, 4)15. (4, �2) 17. (2, 2) 19. (0, �2) 21. (�3, �5)

23–34.

23. I 25. IV 27. IV 29. none 31. none 33. none

35. Sample answer:The points arealong a lineslanting down tothe right,crossing the y-axis at 5 andthe x-axis at 5.

37. Sample answer:The points arealong a lineslanting up,through theorigin.

39. Sample answer:The points arealong a lineslanting up,crossing the y-axis at 2 andthe x-axis at �2.

y

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K (�5, 1)

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H (0, �3)

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41. 5-point star

43. Sample answer:The graph can include anyinteger pairs where x � 3 orx � �3.

45. The new triangle is 47. The new triangle is twice the size of the original translated right 2 units andtriangle, and is moved to up 2 units; it is the samethe right and up. size as the original triangle.

51. Sample answer: The points lie outside arhombus defined by (0, 4), (4, 0), (0, �4), and (�4, 0).

53. D 55. �3 57. 8 59. �96 61. 13°F 63. 24h 65. 45b67. 0

Pages 90–92 Chapter 2 Study Guide and Review1. negative number 3. coordinate 5. integers7. inequality 9. � 11. � 13. 25 15. 22 17. �5 19. �421. �10 23. �8 25. 5 27. �4 29. 9 31. �66 33. 4835. 7 37. �4 39. 2

40–43. 41. III 43. None

Chapter 3 Equations

Page 97 Chapter 3 Getting Started1. �6 3. 10 5. 5 � (�7) 7. �5 � (�9) 9. �3 11. 013. 5 � 2n 15. n � 3

Pages 100–102 Lesson 3-11. Sample answer: 2(3 � 4) � 2 � 3 � 2 � 4 3. 5 � 7 � 5 � 8,75 5. 2 � 6 � 4 � 6, 36 7. 3n � 6 9. �6x � 30 11. $56.2513. 5 � 7 � 5 � 3, 50 15. 4 � 3 � 3 � 3, 21 17. 8 � 2 � 8 � 2, 3219. 6 � 8 � 6(�5), 18 21. �3 � 9 � (�3)(�2), �2123. 10(�5) � 3(�5), �35 25. 12($15 � $10 � $8), 12($15) � 12($10) � 12($8); $396 27. 5y � 30 29. 7y � 5631. 10y � 20 33. 10 � 5x 35. 9m � 18 37. 15s � 4539. 12x � 36 41. 2w � 20 43. �5a � 50 45. �5w � 4047. �5a � 30 49. 3a � 3b 51. $9918 53. No; 3 � (4 � 5) � 23, (3 � 4)(3 � 5) � 56 55. C57. 8(20 � 3) � 184 59. 16(10 � 1) � 17661. 9(100 � 3) � 927 63. 12(1000 � 4) � 12,048 65. 667. 4 69. 21, 25, 29 71. 80, 160, 320 73. �8 � (�4)75. 3 � (�9) 77. �7 � (�10)

Pages 105–107 Lesson 3-21. terms that contain the same variable or are constants3. Koko; 5x � x � 6x, not 5x. 5. terms: 2m, �1n, 6m; liketerms: 2m, 6m; coefficients: 2, �1, 6: constant: none 7. 8a9. 7c � 12 11. 9y 13. �3y � 16 15. 4x � 12y 17. terms:3, 7x, 3x, x; like terms: 7x, 3x, x; coefficients: 7, 3, 1; constant: 3 19. terms 2a, 5c, �1a, 6a; like terms: 2a, �1a, 6a;coefficients: 2, 5, �1, 6; constant: none 21. terms: 6m, �2n,7; like terms: none; coefficients: 6, �2; constant: 7 23. 7x25. 11y 27. 7a � 3 29. 7y � 9 31. 2x 33. �y35. �4x � 8 37. 8y 39. �x � 12 41. 5b � 6 43. �4a � 645. �8 47. 16m � 2n 49. �9c � 2d 51. 3s � 8053. 5d � 2 55. 6x � 2 57a. Distributive Property57b. Commutative Property 57c. Substitution Property ofEquality 57d. Distributive Property 59. C 61. �2y � 1663. III 65. 17 67. 2 69. �11 71. �5 73. �13

Page 107 Practice Quiz 11. 6x � 12 3. 7y � 4 5. 2m � 15

Pages 113–114 Lesson 3-31. Addition Property of Equality 3. 11 5. �4 7. 559.

11. C 13. 13 15. �8 17. �15 19. �1 21. 15 23. 2425. 36 27. �4 29. �31 31. 118 33. n � 9 � �2; �1135. n � 3 � �6; �337.

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39.

41.

43. 12 � x � 20; 32 47. 17 million 49. When you solve anequation, you perform the same operation on each side sothat the two sides remain equal. Answers should includethe following.• In an equation, both sides are equal. In a balance scale,

the weight of the items on both sides are equal.• The Addition and Subtraction Properties of Equality

allow you to add or subtract the same number from eachside of an equation. The two sides of the equation remainequal.

51. C 53. 3t � 12 55. �4z � 4 57. �4m � 159. Additive Inverse Property 61. 84 63. �25 65. �967. �4

Pages 117–119 Lesson 3-41. Multiplication Property of Equality 3. Sampleanswer: �5x � �20 5. �5 7. 27 9. 66 11. 7 13. �815. 8 17. 24 19. 14 21. �33 23. 9 25. �43 27. �13529. 130 31. 29 33. �168 35. 6x � �42; �7

37. ��x4� � 8; �32

39.

41.

43.

45. 12,000 � 5x; 2400 mi2 47. 6p � 24, 4 painters49a. True; one pyramid balances two cubes, so this is thesame as adding one cube to each side. 49b. True; onepyramid and one cube balance three cubes, which balanceone cylinder. 49c. False; one cylinder and one pyramidbalance five cubes. 51. B 53. 13 55. �28 57. 7y � 659. �36 61. 10 63. �2 65. 2 67. �19 69. �27

Pages 122–124 Lesson 3-51. You undo the operations in reverse order. 3. 8 5. �27. �40 9. �4 11. 10 13. 2 15. 4 17. 8 19. 13 21. 323. 28 25. 64 27. 65 29. 21 31. 11 33. 30 35. 3337. �13 39. 5 41. 5 43. –2 45. 10 47. 3 h 49. 131 bikes51. 5x � 2 � 8 53. C 55. �7 57. �2 59. �261. �5y � 15 63. �9y � 36 65. �8r � 40 67. (2, �3)69. (�3, �4) 71. x � 15 73. 2x � 10

Pages 128–130 Lesson 3-61. is, equals, is equal to 3. Ben; Three less than means thatthree is subtracted from a number. 5. 2n � 4 � �2, 17. 2x � 5 � 37, 21 yr 9. 3n � 20 � �4, �8

11. 10n � 8 � 82, 9 13. ��n4� � 8 � �42, 136

15. 3n � 8 � �2, 2 17. 17 � 2n � 5, 619. 4n � 3n � 5 � 47, 6 21. 8 � 5x � �7, 3 h 23. 2x � 2 �12. 5 million people 25. Sample answer: By 2020, Texas isexpected to have 10 thousand more people age 85 or olderthan New York will have. Together, they are expected tohave 846 thousand people age 85 or older. Find theexpected number of people age 85 or older in New York by2020. 27. Two-step equations can be used when you start

with a certain amount and increase or decrease at a certainrate. Answers should include the following.• You’ve been running 15 minutes each day as part of a

fitness program. You plan to increase your time by 5minutes each week. After how many weeks do you planto run 30 minutes each day? (5w � 15 � 30, 3 weeks)

• You are three years older than your sister is. Together thesum of your ages is 21. How old is your sister? (2x � 3 � 21, 9 years old)

29. D 31. 4 33. 5 35. �11 37. �4 39. �5 41. 6

Page 130 Practice Quiz 21. �13 3. �18 5. 3n � 20 � 32, 4

Pages 133–136 Lesson 3-71. d � rt 3. Sample answer:

5. 34 km, 30 km2 7. 4 in. 9. 8 h 11. 15 mph 13. 54 cm,162 cm2 15. 136 in., 900 in2 17. 48 m, 144 m2 19. 20 m,25 m2 21. 11 yd 23. 5 m 25. 39 ft 27. 19 yd 29. 390 yd,9000 yd2 31. d � 2r 33. 4300 ft2 35. � 23.5 mph37. 39.

41. Sometimes; a 3-inch by 4-inch rectangle has a perimeterof 14 inches and an area of 12 square inches; a 6-inch by 8-inch rectangle has a perimeter of 28 inches and an area of48 square inches. 43. Formulas are important in math andscience because they summarize the relationships amongquantities. Answers should include the following.• Sample answer: The formula to find acceleration is

a � �vf �

t

vi� where vf is the final velocity and vi is the

initial velocity.• You can find the acceleration of an automobile with this

formula.45. C 47. �9 49. �8 51. �4x � 9 53a. {(1870, 14),(1881, 600), (1910, 1000), (2000, 1500)} 53b. domain: {1870, 1881, 1910, 2000}, range: {14, 600, 1000, 1500}

Pages 138–140 Chapter 3 Study Guide and Review1. like terms 3. Multiplication Property of Equality5. Distributive Property 7. coordinate 9. constant11. 3h � 18 13. �5k � 5 15. 9t � 45 17. �2b � 819. 9a 21. �2n � 8 23. 3 25. 5 27. 8 29. �1831. 1 33. �6 35. 2n � 3 � 53; 25 37. 34 ft, 72 ft2

Chapter 4 Factors and Fractions

Page 147 Chapter 4 Getting Started1. 2x � 2 3. �2k � 16 5. 12c � 24 7. 7a � 7b 9. 1411. 28 13. 63 15. 30 17. 45 19. 78 21. 0.39 23. 0.005

Pages 150–152 Lesson 4-11. Use the rules for divisibility to determine whether 18,450is divisible by both 2 and 3. If it is, then the number is alsodivisible by 6 and there is no remainder. 3a. Sample

4 cm

4 cm4 ft

3 ft

5 in.

4 in.

30 31 32 33 34 35 36 37

�3 �2 �1 0 1 2 3 4

�3 �2�6 �5 �4�9 �8 �7

�3�4 �2 �1 0 1 2 3

8 9 10 11 125 6 7


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answer: 102 3b. Sample answer: 1035 3c. Sample answer:343 5. 2 7. 2, 5, 10 9. 1, 2, 4, 5, 8, 10, 16, 20, 40, 8011. yes; a number 13. No; two terms are added. 15. 2000,2004, and 2032 are leap years. 17. 3, 5 19. 2, 3, 5, 6, 1021. 2 23. 5 25. 2, 3, 6 27. 2, 5, 10 29. 1, 2, 3, 6, 19, 38, 57, 114 31. 1, 5, 13, 65 33. 1, 2, 4, 31, 62, 124 35. 1, 3, 5, 9,15, 27, 45, 135 37. yes; a number 39. No; one term issubtracted from another term. 41. No; two terms areadded. 43. No; one term is subtracted from another term.45. yes; the product of a number and a variable 47. yes;the product of numbers and variables 49. 6 ways; 1 � 72,2 � 36, 3 � 24, 4 � 18, 6 � 12, 8 � 9 51. Alternating rowsof a flag contain 6 stars and 5 stars, respectively. Fifty is notdivisible by a number that would make the arrangement ofstars in an appropriate-sized rectangle. 53. Never; anumber that has 10 as a factor is divisible by 2 � 5, so it isalways divisible by 5. 55a. 24 cases 55b. 36 bags55c. Sample answer: 12 cases, 18 bags; 14 cases, 15 bags; 16 cases, 12 bags 57. The side lengths or dimensions of arectangle are factors of the number that is the area of therectangle. Answers should include the following.• A rectangle with dimensions and area labeled; for

example, a 4 � 5 rectangle would have length 5 units,width 4 units, and area 20 square units.

• Factors are numbers that are multiplied to form aproduct. The dimensions of a rectangle are factor pairs ofthe area since they are multiplied to form the area.

59. C 61. 34 in., 60 in2 63. 5n � 2 � 3; 1 65. 2 67. 6469. �27 71. 2304

Pages 155–157 Lesson 4-21. Sample answer: 25, x5 3. When n is even, 1n � (�1)n � 1. When n is odd, 1n � 1 and (�1)n � �1.5. 72 7. (2 � 103) � (6 � 102) � (9 � 101) � (5 � 100)9. �11 11. 132 13. 61 15. (�8)4 17. (�t)3 19. m4

21. 2x2y2 23. 9(p � 1)2 25. (8 � 102) � (0 � 101) � (3 � 100)27. (2 � 104) � (3 � 103) � (7 � 102) � (8 � 101) � (1 � 100)29. 1000 31. �32 33. 81 35. �54 37. 13 39. 9 41. 24343. 64 � 82 or 43 or 26, 49 � 72 45. (�8)3;(�8)(�8)(�8); �512 47. Always; the product of twonegative numbers is always positive. 49. 21, 22, 23, 24, 25

51. After 10 folds, the noodles are 5(210) � 5(1024) or 5120feet long, which is slightly less than a mile. So, after 11folds the length of the noodles will be greater than a mile.53. � 55. 6 � 32 cm2 57. No; the surface area is multipliedby 4. The volume is multiplied by 8.59. As the capacity of computer memory increases, thefactors of 2 in the number of megabytes increases. Answersshould include the following.• Computer data are measured in small units that are

based on factors of 2.• In describing the amount of memory in modern

computers, it would be impractical to list all the factorsof 2. Using exponents is a more efficient way to describeand compare computer data.

61. B 63. 2, 5, 10 65. 150 mph 67. 4 69. 3y � 8 71. 1, 573. 1, 2, 4, 8, 16 75. 1, 5, 7, 35

Pages 161–163 Lesson 4-31. A prime number has exactly two factors: 1 and itself. Acomposite number has more than two factors.3. Francisca; 4 is not prime. 5. prime 7. 2 � 32 9. 2 � 52

11. 5 � a � a � b 13. 3 and 5, 5 and 7, 11 and 13, 17 and 19, 29and 31, 41 and 43 15. composite 17. composite19. composite 21. prime 23. 34 25. 32 � 7 27. 22 � 52

29. 2 � 5 � 11 31. 3 � 3 � t � t 33. �1 � 5 � 5 � z � z � z35. �1 � 2 � 19 � m � n � p 37. 3 � 7 � g � h � h � h39. 2 � 2 � 2 � 2 � 2 � 2 � n � n � n41. �1 � 2 � 2 � 2 � 3 � 5 � r � r � s � t � t � t 43. Sampleanswer: �25x45. The number of rectangles that can be modeled torepresent a number indicate whether the number is primeor composite. Answers should include the following.• If a number is prime, then only one rectangle can be

drawn to represent the number. If a number iscomposite, then more than one rectangle can be drawn torepresent the number.

• If a model has a length or width of 1, then the numbermay be prime or composite. If a model does not have alength or width of 1, then the number must becomposite.

47. C 49. (�5)3h2k 51. yes 53. no 55. �9 57. �2859. 5x � 35 61. 10a � 60 63. 72 � 8y

Page 163 Practice Quiz 11. 3, 5 3. none 5. 37 7. 7 � 11 � x 9. �1 � 23 � n � n � n

Pages 166–168 Lesson 4-41. Sample answer: Find the prime factorization of eachnumber. Multiply the factors that are common to both.3. Jack; the common prime factors of the expressions are 2and 11, so the GCF is 2 � 11 or 22. 5. 3 7. 14 9. 3611. 14n 13. 3(n � 3) 15. 5(3 � 4x) 17. 4 19. 8 21. 1023. 9 25. 8 27. 5 29. 4 31. 3 33. 4 35. 4x 37. 2s39. 14b 41. 4n 43. Sample answer: 2x, 6x2 45. 3(r � 4)47. 3(2 � y) 49. 7(2 � 3c) 51. 4(y � 4)53a. 7; Sample answer:

7 14 21 28 35↓ ↓ ↓ ↓ ↓7(1) 7(2) 7(3) 7(4) 7(5)

The terms increase by a factor of 7.53b. 42, 49 55a. 6-in. squares 55b. 20 tiles 57. Yes; theGCF of 2 and 8 is 2. 59. D 61. yes 63. no 65. yes67. 3 � 3 � n 69. �1 � 5 � j � k 71. 92 73. �6 75. �1077. 36 79. 24 81. 1000

Pages 171–173 Lesson 4-51. The GCF of the numerator and denominator is 1. 3. �

17

�

5. simplified 7. �11

67� 9. �

2a

� 11. simplified 13. B 15. �56

�

17. �29

� 19. �292� 21. simplified 23. �

13

� 25. �152� 27. �

1290�

29. �932� 31. �

y1

2� or y2 33. �

22

01� 35. �

81t� 37. �

74z2� 39. simplified

41. �g3h� 43. �

22

45� 45a. yes; �34

34

00

� � �34

� 45b. No; �2394

49

� cannot

be simplified. 45c. yes; �2562

48

� � �12

� 47. �35

10� 49. �

170�

51. Fractions represent parts of a whole. So, measurementsthat contain parts of units can be represented usingfractions. Answers should include the following.• Measurements can be given as parts of a whole because

smaller units make up larger units. For example, inchesmake up feet.

• Twelve inches equals 1 foot. So, 3 inches equals �132� or

�14

� foot.

53. A 55. 2 57. 5 59. composite 61. prime 63. 2765. (6 � 7)(k3) 67. (3 � �5)(x4 � x2)


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Pages 177–179 Lesson 4-61. Neither; the factors have different bases. 3. Sampleanswer: 5 � 52 � 53 5. a6 7. �12x5 9. 102 11. a4 13. 35

15. d10 17. n9 19. 99 21. 18y5 23. 8a3b10 25. 53 27. b3

29. m12 31. (�2)1 or �2 33. n6 35. k2m 37. 97 39. 79

41. 102 or 100 times 43. 3 45. 2 times 47. 8 49. 551. Each level on the Richter scale is 10 times greater thanthe previous level. So, powers of 10 can be used to compareearthquake magnitudes. Answers should include thefollowing.• On the Richter scale, each whole-number increase

represents a 10-fold increase in the magnitude of seismicwaves.

• An earthquake of magnitude 7 is 105 times greater thanan earthquake of magnitude 2 because 107 � 102 � 107 � 2

or 105.

53. B 55. simplified 57. �32

xy� 59. 2 61. a 63. Positive; as

the high temperature increases, the amount of electricity

that is used also increases. 65. ��110� 67. ��

210� 69. �

614�

Pages 183–185 Lesson 4-71. To get each successive power, divide the previous power

by 3. Therefore, 30 � 3 � 3 or 1. 3. �512� 5. �

t16� 7. 3�4

9. 7�2 11. �312� 13. 10�3 15. �

513� 17. �

(�13)3� 19. �

1104�

21. �a110� 23. �

q14� 25. x2 27. �

514� ; 0.0016 29. 5�5 31. 13�2

33. 9�2 35. 2�4 or 4�2 37. 10�2 or 100�1 39. 10�5

41. ��1128� 43. �

7129� 45. 128 times 47. x�5 49. x�3

51. a3b�2 or �ba3

2�

53. Yes; (x3)�2 � �(x

13)2�

� �x3

1� x3� or �

x16�

(x�2)3 � (x�2)(x�2)(x�2)

� x�6 or �x16�

55. C 57. 9 � 10�1 59. (1 � 10�1) � (7 � 10�2) � (3 �10�3) 61. 37 63. 53 65. 8y � 48 67. 5n � 15 69. 72071. 40.5 73. 0.0005

Page 185 Practice Quiz 2

1. 5 3. 2a 5. �25

� 7. �2n7 9. �b16�

Pages 188–190 Lesson 4-81. Sample answer: Numbers that are greater than 1 can beexpressed as the product of a factor and a positive power of10. So, these numbers are written in scientific notationusing positive exponents. Numbers between 0 and 1 cannotbe expressed as the product of a factor and a whole numberpower of 10, so they are written in scientific notation usingnegative exponents. 3. 0.000308 5. 849,500 7. 6.97 � 105

9. 1.0 � 10�3 11. Mars, Venus, Earth 13. 57,20015. 0.005689 17. 0.0901 19. 2505 21. 2.0 � 106

23. 6.0 � 10�3 25. 5.0 � 107 27. 5.894 � 106

29. 4.25 � 10�4 31. 6.25 � 106 33. 7.53 � 10�7

35. � 37. 39. Arctic, Indian, Atlantic, Pacific 41. 6.1 �10�5, 0.0061, 6.1 � 10�2, 6100, 6.1 � 104

43. 48,396 45. 2.52 � 105; 252,000 47. Bezymianny; SantaMaria; Agung; Mount St. Helens tied with Hekla 1947;

Hekla, 1970; Ngauruhoe 49. 3.14 51. B 53. �811� 55. �

419�

57. 15a4 59. c � $2.50

Pages 191–194 Chapter 4 Study Guide and Review1. true 3. true 5. true 7. true 9. 3 11. 5 13. 2, 3, 615. 2, 5, 10 17. 27 19. 25 21. 90 23. 112 25. 32 � 527. 22 � 17 29. 7 � 7 � k 31. 2 � 13 � p � p � p 33. 6 35. n

37. 2(t � 10) 39. 2(15 � 2n) 41. �35

� 43. �11

07� 45. simplified

47. �58cb

2� 49. c4 51. r2 53. �

712� 55. �

b14� 57. �

(�14)3�

59. 0.0029 61. 70,450 63. 8.0 � 10�3 65. 4.571 � 107

Chapter 5 Rational Numbers

Page 199 Chapter 5 Getting Started1. 0.6 3. 34 5. 0.2 7. �75 9. �1.7 11. �

35

� 13. �12

85� 15. 6

17. �13 19. 15 21. 9

Pages 202–204 Lesson 5-11. Sample answer: write the fractions as decimals and thencompare. 3. Sample answer: 0.1�4� 5. 2.08 7. 0.26� 9. 11. � 13. 0.2 15. 0.32 17. 7.3 19. 5.125 21. 0.1�23. �0.4�5� 25. 0.16� 27. 0.3125 29. 0.83 31. �

79

� , 0.8, �78

�

33. 35. 37. � 39. � 41. � 43. � 45. Sample

answer: 0.7 and 0.7�; �16

� � 0.16� and �89

� � 0.8�; 0.7 and 0.7� are

both greater than 0.16� and less than 0.8�. 47. This is greater

than those who chose English in the survey because �17

� � 0.14, and 0.14 � 0.13. 49. All coins were made with a

fraction of silver that was contained in a silver dollar.Answers should include the following.• A quarter had one-fourth the amount of silver as a silver

dollar, a dime had one-tenth the amount, and a nickelhad one-twentieth the amount.

• It is easier to perform arithmetic operations usingdecimals rather than using fractions.

51. D 53. 7.7 � 10�2 55. 9.25 � 105 57. �(�

12)7� 59. �

y13�

61. 29 63. �32 65. 56 67. �113� 69. �

23

� 71. �47

� 73. �18

�

Pages 207–209 Lesson 5-21. any number that can be written as a fraction 3. ��

73

�

5. �45

� 7. ��79

� 9. I, Q 11. �1,00309,000� 13. ��

171� 15. �

610�

17. �1

900� 19. 1�

12

75� 21. 8�

2150� 23. ��

13

� 25. 5�23

� 27. 2�2959�

29. �530� 31. �

25090

� 33. �245� 35. I, Q 37. N, W, I, Q 39. Q

41. not rational 43. 200�11090

� 45. Sometimes; �12

� and 2 are

both rational numbers, but only 2 is an integer. 47. �12

150� in.

49. Yes; 2�38

� � 2.375 and 2.375 � 2.37. 51. The set of rational

numbers includes the set of natural numbers, wholenumbers, and integers. In the same way, natural numbersare part of the set of whole numbers and the set of wholenumbers is part of the set of integers. Answers shouldinclude the following.• The number 5 belongs to the set of natural numbers,

whole numbers integers, and rational numbers.

• The number �12

� belongs only to the set of rationalnumbers.

53. C 55. �7.8 57. 2.5� 59. 3,050,000 61. 0.0168163. (4 � 102) � (8 � 101) � (3 � 100) 65. 24 cm; 27 cm2


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67. 8 � 2 � 1 � 2 69. 7x � 28 71. Sample answer: �5 � 4 � �20 73. Sample answer: 7 � 2 � 14 75. Sampleanswer: 16 � 2 � 32

Pages 212–214 Lesson 5-3

1. Sample answer: �12

�, �13

� 3. �230� 5. �

59

� 7. �12

32� 9. �

67

� 11. �8t�

13. �14

29� 15. ��

410� 17. �

485� 19. �

13

� 21. ��14

� 23. �38

� 25. 1�16

�

27. 3�13

� 29. 14�23

� 31. 10 33. �4�49

� 35. 6 37. 27 39. 27

41. �181c� 43. �

x3z2� 45. �

295� 47. �

6101� 49. 12.7 51. 10.257

53a. Sample answer: �84

� � �35

� 53b. Sample answer: �34

� � �56

�

55. A 57. �58

� 59. �13

32� 61. ��

15

� 63. �79

� 65. 0.16� 67. �4.875

69. 8n 71. 2t 73. 9

Pages 217–219 Lesson 5-41. Dividing by a fraction is the same as multiplying by its

reciprocal. 3. �54

� 5. �285� 7. �

45

� 9. 1�175� 11. �1�

23

96� 13. �

32a�

15. 6 boards 17. ��51

� or �5 19. �214� 21. ��

299� 23. �

89

�

25. ��12

52� 27. �

11

56� 29. �1 31. 1�

12

� 33. �10 35. 1�13

� 37. 2

39. �6�14

� 41. �43

� 43. �65r� 45. �

1t56� 47. 6 ribbons 49. �

28516

�

51. 8 days 53. Dividing by a fraction is the same asmultiplying by its reciprocal. Answers should include thefollowing.• For example, a model of two circles, each divided into

four sections, represents 2 � �14

�. Since there are 8 sections,

2 � �14

� � 8.

• Division of fractions and multiplication of fractions are

inverse operations. So, 2 � �14

� equals 2 � 4 or 8.

55. C 57. �254� 59. ��

12

01� 61. Q 63. not rational 65. 7

67. 1�17

� 69. 6�14

� 71. 3�23

� 73. 1�23

�

Pages 222–224 Lesson 5-51.

3. Kayla; Ethan incorrectly left out the negative sign on the

first term. 5. �47

� 7. ��34

� 9. 8�12

� 11. �181r� 13. ��

31x� 15. �

35

�

17. �23

� 19. ��12

� 21. �1�12

� 23. ��29

� 25. 11�45

� 27. 9�13

� 29. �34

�

31. 4�67

� 33. 8�18

� 35. 2�35

� 37. �15

� 39. �58x� 41. �

m3� 43. 2�

37

�c

45. 5�38

� in. 47. 38 ft 49. When you use a ruler or a tape

measure, measurements are usually a fraction of an inch.Answers should include the following.

• The marks on a ruler represent �116� of an inch, �

18

� of an

inch, �14

� of an inch, and �12

� of an inch.

• Fractional measures are used in sewing and construction.

51. A 53. �1�78

� 55. �130� 57. 1�

13

� 59. 42 cm; 90 cm2

61. 52 � 7 63. 22 � 3 � n 65. 2 � 3 � 7 � a2 � b


1. 0.16 3. 3.125 5. �235� 7. �

227� 9. �

152�

Pages 228–230 Lesson 5-61. The LCM involves the common multiples of a set ofnumbers; the LCD is the LCM of the denominators of twoor more fractions. 3. 24 5. 70 7. 48 9. 8 11. 100x13. � 15. front gear: 5; back gear: 13 17. 60 19. 4821. 84 23. 100 25. 96 27. 84 29. 630 31. 112a2b33. 75n4 35. 15 37. 35 39. 24 41. 16c2d 43. 60 s 45. �47. 49. � 51. 53. amphibians 55. 12 and 1857. Never; sample answer: 5 and 6 do not contain anyfactors in common, and the LCM of 5 and 6 is 30. 59a. Iftwo numbers are relatively prime, then their LCM is theproduct of the two numbers. For example, the LCM of 4and 5 is 22 � 5 or 20; the LCM of 6 and 25 is 2 � 3 � 52 or 150.59b. Always; the LCM contains all of the factors of bothnumbers. Therefore, it must contain any common factors.

61. B 63. �12

� 65. 1�17

� 67. 3 69. �a5d� 71. 7 � 2n � 11; 2

73. �20 75. Sample answer: 0 � 1 � 1 77. Sampleanswer: 1 � 2 � 3 79. Sample answer: 8 � 7 � 15

Pages 234–236 Lesson 5-71. Find the least common denominator. 3. José; he finds acommon denominator by multiplying the denominators.Daniel incorrectly adds the numerators and the

denominators of unlike fractions. 5. �29

� 7. ��56

� 9. �4�14

�

11. �190� 13. �

258� 15. 1�

116� 17. �

18

� 19. ��18

� 21. 1�115� 23. �7�

59

�

25. �11�79

� 27. �14�58

� 29. 3�3161� 31. 5�

35

� lb 33. 8�34

� in.

35. Sample answer: Fill the �12

�-cup. From the �12

�-cup, fill the

�13

�-cup. �16

� cup will be left in the �12

�-cup because �12

� � �13

� � �16

�.

37. Find the LCM of the denominators. Then rename thefractions as like fractions with the LCM as thedenominators. Answers should include the following.• For example, the LCM of 4 and 6 is 12. So,

�14

� � �56

� � �132� � �

11

02� � �

11

32� or 1�

112�.

• Writing the prime factorization of the denominators isthe first step in finding the LCM of the denominators,which is the LCD. Then the fractions can be added orsubtracted.

39. B 41. Sample answer: �12

� � �110� 43. 36 45. 6n3 47. 9�

12

�

49. 2�45

� 51. 1�45

� 53. 27 55. �9

Pages 241–242 Lesson 5-81. Mean; when an extreme value is added to the other data,it can raise or lower the sum, and therefore the mean.3. 12.4; 8; none 5. 3.6; 3.5; 4 7. Sample answer: 13 couldbe an extreme value because it is 12 less than the nextvalue. It lowers the mean by 2.1. 9. 98 11. 8.9; 8; 813. 7.6; 7.5; 7.1 and 7.4 15. 4.3; 4.2; 4.1 and 4.2 17. Sampleanswer: the median, 95, or the modes, 95 and 97, becausemost students scored higher than mean, which is 91.19. Sample answer: The median home price would beuseful because it is not affected by the cost of the veryexpensive homes. The cost of half the homes in the countywould be greater than the median cost and half would

be less. 21. C 23. 9�56

� 25. �3�78

� 27. 29. 18 31. �5

33. 7.9 35. 3

27

47

67


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Pages 246–248 Lesson 5-91. Subtraction Property of Equality 3. Ling; dividing 0.3by 3 does not isolate the variable on one side. 5. 18.7

7. 1�13

30� 9. �2�

112� 11. –90 13. 29.15 in. 15. �2.4 17. 12.24

19. 5.9 21. ��33

16� 23. 6�

79

� 25. ��125� 27. �2�

130� 29. 4

31. 5 33. �32 35. 1�14

� 37. 5�34

� 39. 2�78

� 41. 13�12

� in. by

21�12

� in. 43. $16.66 45. 2�14

� ft 47. Equations with fractions

can be written to represent the number of vibrations persecond for different notes. To solve, multiply each side ofthe equation by the reciprocal of the fraction. Answersshould include the following.• For example, if n vibrations per second produce middle

C, then �54

�n vibrations per second produce the note E

above middle C.

• The equation �53

�n � 440 represents the number of

vibrations per second to produce middle C. To solve,

multiply each side by the reciprocal of �53

�, �35

�.

49. D 51. 13; 12; 11 and 12 53. 70.8; 66; 60 55. �12

74� 57. �

13

76�

59. 7�1151� 61. �

38

� 63. �6 65. �6 67. 5 69. ��13

�


1. 72 3. 10 5. �11

36� 7. 1�

23

� 9. 32.4; 30.5; 29

Pages 251–252 Lesson 5-101. Arithmetic sequences have a common difference and theterms can be found by adding or subtracting. Geometricsequences have a common ratio and the terms can be foundby multiplying or dividing. 3. A; 4; 19, 23, 27

5. neither 7. A; ��13

�; �53

�, �43

�, 1 9. $11,027.36 11. A; 11; 38,

49, 60 13. G; 3; 162, 486, 1458 15. A; �3; 13, 10, 7

17. G; ��15

�; ��1125�, �6

125�, ��

31125� 19. A; �

16

�; �23

�, �56

�, 1 21. A; �0.5,

2.5, 2, 1.5 23. neither 25. G; ��13

�; �29

�, ��227�, �

821�

27. G; �12

�; �312�, �

614�, �1

128� 29a. Arithmetic; the common

difference is $3. 29b. $48 31. Find the pattern, continuethe sequence, and use the new values to make predictions.Answers should include the following.• The difference between any two consecutive terms in an

arithmetic sequence is the common difference. To findthe next value in such a sequence, add the commondifference to the last term. The ratio of any twoconsecutive terms in a geometric sequence is thecommon ratio. So, to find the next value in such asequence, multiply the last term by the common ratio.

• Sequences occurring in nature include geysers spoutingevery few minutes, the arrangement of geese inmigration patterns, and ocean tides.

33. A 35. 56 37. �5.28 39. 10 41. 3.3; 3.3; 3.6

43. 102�78

� in. 45. b3 47. 6 49. 15

Pages 254–258 Chapter 5 Study Guide and Review1. rational 3. algebraic fraction 5. LCD 7. reciprocal

9. arithmetic 11. 0.45 13. �0.46� 15. 6.3�6� 17. �35

� 19. �18

�

21. 4�2151� 23. �

59

� 25. 1�79

� 27. 3�141� 29. ��

277� 31. 6�

25

� 33. 1�13

�

35. �3 37. 9�49

� 39. x 41. �6 43. �3�34

� 45. �4�15

� 47. �2

41x�

49. �59

� 51. 1�13

� 53. 2�35

� 55. �34x� 57. 120 59. 21c2 61. �

63. � 65. 1�23

� 67. 2�56

� 69. 1�1151� 71. 3�

16

� 73. 6.0; 6.5; 3.6

and 7.2 75. 3.25 77. �2�12

� 79. G; 3; 81, 243, 72981. neither

Chapter 6 Ratio, Proportion, andPercent

Page 263 Chapter 6 Getting Started1. 24 3. 10,560 5. 480 7. 4000 9. 6 11. 58013. 50 15. 15,000 17. 48.8 19. 13.44 21. 0.18

23. 3.04 25. �13

� 27. simplified 29. simplified 31. �34

�


1. Sample answer:

3. Sample answer: $12 per person 5. �58

� 7. �13

�

9. 0.75 inch/hour 11. 24.2 miles/gallon 13. 576

15. No; the ratio will be 2 to 3. 17. �25

� 19. �37

� 21. �32,

9000�

23. �17

160� 25. �

11178

� 27. �31

� 29. 0.10 cents/pencil

31. 4.5 m/sec 33. 7.8 ft/h 35. 39 pages/week 37. The 6-pack of soda costs $0.37 per can. The 12-pack of sodacosts $0.35 per can. So, the 12-pack is less expensive.39. 26.4 41. 19.2 43. � 45. � 47. about 579 mi/h 49.$9 51. C 53b. The ratios should be close in value. 53c.Sample answer: Pyramid of Khufu in Giza, Egypt; The Taj Mahal in India; The Lincoln Memorial inWashington, D.C. 55. arithmetic; 0.3; 13.3, 13.6, 13.9

57. ��112� 59. 13�

13

� 61. 5.2 � 107 63. 3.8 � 10�2 65. 30

67. 40 69. 13

Pages 272–274 Lesson 6-21. A statement of equality of two ratios. 3. Yes 5. 157. 4.2 9. yes 11. no 13. yes 15. 4 17. 20 19. 1521. 1.4 23. 7.5 25. 0.94 27. 0.8 29. 15 31. 26

33. �132� � �

7m2�; 18 35. �

6.525� � �

8.d75�; 7 37. about 360.8 ft

39. $22.47 41. chocolate pieces: 3 c; peanuts: 1�12

� c

43. �ac

� � �db

�, �ba

� � �dc

�, or �ac

� � �db

� 45. C 47. 57.3 mph

49. 4 51. �74y� 53. 102 55. 6.5


1. 3. 40 mi 5. 1 in. � 5 ft

7. 9. 12 ft 11. 24.6 ft 13. 11.4 ft

15. 49�12

� ft 17. �23

�

19. 1 cm � 0.25 cm

21. A scale factor less than 1 means that the drawing ormodel is drawn smaller than actual size. A scale factor of 1means that the drawing or model is drawn actual size. A

15 ft

10 ft

0.5 in. � 10 ft

1 unit 3 units


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scale factor greater than 1 means the drawing or model is

drawn larger than actual size. 23. B 25a. �12

� 25b. �14

�

25c. The perimeter of a 3-inch by 5-inch rectangle is 16 inches. The area is 15 square inches. For a 6-inch by 10-inch rectangle, the perimeter should be double the 3-inch by 5-inch rectangle. That is, 16 � 2 or 32 inches. Thearea should be 4 times the area of the 3-inch by 5-inchrectangle. That is, 4 � 15 or 60 square inches. Since theperimeter of the 6-inch by 10-inch rectangle is 32 and itsarea is 60, the conjecture is true. 27. 3.5 29. 21.6 31. 6�

112�

33. 18t5 35. �4m

33

� 37. �210� 39. �

25

� 41. �35

90� 43. �

45

10�

Pages 283–285 Lesson 6-41. Sample answer: write an equivalent fraction with adenominator of 100 or express the fraction as a decimal andthen express the decimal as a percent. A fraction is greaterthan 100% if it is greater than 1. It is less than 1% if it is less

than �1100�. 3. �

130�, 0.3 5. 1�

14

�, 1.25 7. 1�270�, 1.35 9. 45%

11. 0.8% 13. 133.3% 15. daily newspaper 17. �22

25�, 0.88

19. �78

�, 0.875 21. 3�12

�, 3.5 23. �16010

�, 0.61 25. 2�12030

�, 2.23

27. �10

5,0300

�, 0.0053 29. 9% 31. 270% 33. 0.06% 35. 22.5%

37. 175% 39. 1.7% 41. �1

30

700� 43. 0.45 45. 19%

47. 61%, �23

�, 0.69 49. 0.4 51. There are only two

possibilities that satisfy the conditions, �14

� and �25

�.

53. Percents are related to fractions and decimals becausethey can be expressed as them. Answers should include thefollowing.•

• 25% � �14

� � 0.25; 30% � �130� � 0.3; 40% � �

25

� � 0.4;

65% � �12

30� � 0.65 55. A 57. �

112� 59. �

2111� 61. 1�

133�

63. composite 65. composite 67. 800 69. 0.94 71. 320


1. �numbe5r0correct��

1%00� 3. 40% 5. 104 7. 60% 9. 45%

11. 50 13. 77 15. 36% 17. 112 19. 0.2% 21. 16%23. about 70% 25. 26.8 lbs27. In real-world situations, percents are important becausethey show how something compares to the whole. Answersshould include the following.

• For example, the outer layer of the new state quarters isan alloy of 3 parts copper to 1 part nickel.

• Thus, there are 4 parts to the outer layer (copper, copper,

copper, nickel). The outer layer is �34

� or 75% copper and �14

�

or 25% nickel.

29. �25

10� 31. 1�

15

� 33. �79

� 35. 3�12

� 37. 8 39. 6 41. 25

Page 292 Practice Quiz 11. $0.14 per can 3. 1 ft � 3069 ft 5. 19.5


1. 18% is about 20% or �15

�. 216 is about 220. �15

� of 220 is 44.

So, 18% of 216 is about 44. 5. Sample answer: 13

7. Sample answer: 72 9. Sample answer: 8; fraction

method: �13

� � 24 or 8 11. Sample answer: 21; meaning of

percent method: 152% means about 150 for every 100 orabout 15 for every 10. 14 has 1 tens. 1 � 15 � 15. So, 152%of 14 is about 21. 13. Sample answer: 14 15. Sampleanswer: 33 17. Sample answer: 49 19. Sample answer: 421. Sample answer: 90 23. Sample answer: 375

25. Sample answer: �14

� � 8 or 2 billion 27. Sample answer:

27; fraction method: �130� � 90 or 27 29. Sample answer: 36;

fraction method: �25

� � 90 or 36 31. Sample answer: 2; 1%

method: Since 1% of 806 is about 8, �14

�% of 806 is about �14

� of

8 or 2. 33. Sample answer: 78; meaning of percent: 127%means about 130 for every 100 or about 13 for every 10. 64 has 6 tens. 6 � 13 � 78. So, 127% of 64 is about 78.35. Sample answer: 450; meaning of percent: 295% meansabout 300 for every 100 or about 30 for every 10. 145 hasone 100 and about 5 tens. (300 � 1) � (30 � 5) � 300 � 150or 450. 37. Sample answer: Pluto and Mars, or Neptune

and Jupiter 39. Sample answer: �13

� � 90,000 or 30,000 miles

41. about 10% 43. 7 to 8 45. C 47. 21 49. Maine: 31,813 sq mi; New Hampshire: 8238 sq mi; West Virginia:18,779 sq mi; Vermont: 7279 sq mi; Alabama: 35,071 sq mi51. 160% 53. 0.77 55. 4.21 57. 8.9 59. �21 61. 0.563. 0.25 65. 0.07

Pages 300–302 Lesson 6-71. Use the percent equation in any situation where the rateand base are known. 3. I � interest; p � principal; r � annual interest rate; t � time in years 5. 50 7. 3%9. $1680 11. 1.5 years 13. 95% 15. 50 17. 63 19. 37.5%21. 14.52 23. 218% 25. 0.9% 27. 13.2 29. $25.4931. $17 33. $18.50 35. $1113.75 37. $244.76 39. 1641. $1.20 43. If you know two of the three values, you canuse the percent proportion to solve for the missing value.Answers should include the following.• To find the amount of tax on an item, you can use the

percent proportion or the percent equation.• For example, the following methods can be used to find

6% tax on $24.99.Method 1: Percent Proportion

�24

x.99� � �1

600�

Method 2: Percent Equationn � 0.06(24.99)

Using either method, x � 1.50. The amount of tax is $1.50. 45. B 47. Sample answer: 250; meaning of percent method:126% means about 125 for every 100 and 12.5 for every 10.

65%

40%

30%25%


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198 has about 2 one-hundreds. 125 � 2 � 250. So, 126% of198 is about 250. 49. 121 51. 41 53. 38 cm 55. 8w � 2457. 89% 59. 156% 61. 22.4%

Pages 306–308 Lesson 6-81. If the amount increases, it is a percent of increase. If theamount decreases, it is a percent of decrease. 3. Mark; hedivided the difference of the new amount and the originalamount by the original amount. 5. �60%; D 7. 10.1%; I9. A 11. 170%; I 13. �12%; D 15. �5.4%; D 17. 164%; I19. 10.1% 21. �14.3% 23. 150%25. The amount by which a rectangle is increased ordecreased can be represented by a percent. Answers shouldinclude the following.• If the size of the new rectangle is greater than the size of

the original rectangle, the percent of increase is greaterthan 100%.

•

27. D 29. $149.85 31. $13.46 33. Sample answer: 63;

fraction method: �190� � 70 or 63 35. integer, rational

37. rational 39. 20% 41. 83�13

�%


1. Sample answer: 28; fraction method: �25

� � 70 or 28

3. $14.50 5. 158%

Pages 312–314 Lesson 6-91. The event will not happen.3. Sample answer: Spinning the spinner shown and having it land on 4.

5. �12

�; 50% 7. �25

�; 40% 9. 1; 100% 11. 75 13. �14

�; 25%

15. �12

�; 50% 17. 0; 0% 19. �78

�; 87.5% 21. �29

�; 22.2%

23. �1181�; 61.1% 25. �

13

�; 33�13

�% 27. 1; 100% 29. �16

� 31. �116�

33. �14

� 35. 0.05; 5% 37. 1140

39. Once the probability or likeliness of somethinghappening is known, then you can use the probability tomake a prediction. For example, in football, if you know thenumber of field goals a player has made in the past, youcan use the information to predict the number of field goalshe/she will make in upcoming games. Answers shouldinclude the following.

• E: �11020

� or 12%; A, I: �1900� or 9%; O: �1

800� or 8%; N, R, T: �1

600�

or 6%; D, L, S, U: �1400� or 4%; G: �1

300� or 3%; B, C, F, H, M,

P, V, W, Y, blank: �1200� or 2%; J, K, Q, X, Z: �1

100� or 1%

41. 146.9% 43. 23.9 45. 2x5 47. �18

7n2�

Pages 316–320 Chapter 6 Study Guide and Review1. proportion 3. scale factor 5. experimental probability

7. �34

� 9. �14

� 11. �290� 13. 30 15. 0.9 17. 45.6 ft 19. �

270�; 0.35

21. �225�; 0.08 23. 1�

15

�; 1.2 25. �58

�; 0.625 27. 24% 29. 45.2%

31. 40% 33. 7.5% 35. 40% 37. 25 39. 50 41. 43 43. 9

45. 8 47. Sample answer: 16; fraction method: �12

� � 32 or 16

49. Sample answer: 10; fraction method: �15

� � 50 or 10

51. Sample answer: 1; 1% method: Since 1% of 304 is about

3, �13

�% of 304 is about �13

� of 3 or 1. 53. 48% 55. 94.5

57. 200 59. D; �70% 61. I; 86.2% 63. �13

� 65. �23

� 67. 0

Chapter 7 Equations and Inequalities

Page 327 Chapter 7 Getting Started1. 4 3. 24 5. �44 7. 11 9. �17 11. 16 13. �1415. �15 17. 72 19. �5 21. 1

Pages 332–333 Lesson 7-11. Subtraction Property of Equality 3. �8 5. 3 7. 0.3

9. 75 miles 11. 13 13. �7 15. �0.5 17. �6 19. �43

�

21. 3 23. 4.2 25. 0.3 27. 3.4 29. 3y � 14 � y; 7 31. �1633. 72 35. 70 min 37. 29 39. A 41. �40° 43. 12.5%

45. 6.48 47. 70 49. 6a � 27 51. 2.4c � 28 53. �12

�n � �92

�

Pages 336–338 Lesson 7-21. Multiply 4 times (x � 1). Subtract 2x from each side. Add4 to each side. Divide each side by 2. 3. 11 5. 13 7. �9. � � 7 ft; w � 3 ft; A � 21 ft2 11. 6 13. 2.5 15. 18 17. 319. 35 21. � 23. all numbers 25. 6 27. all numbers29. 0 31. 70 yd by 150 yd 33. w: 3 ft; �: 13 ft; A: 39 ft2

35. triangle: 7, 8, 9; rectangle, 4, 8; perimeter: 24 37. 2 gal39. Many equations include grouping symbols. You mustuse the Distributive Property to correctly solve theequation. Answers should include the following.• The Distributive Property states that a(b � c) � ab � ac.• You use the Distributive Property to remove the

grouping symbols when you are solving equations.41. D 43. 0.4 45. 40% 47. 0.375 49. 3.24 51. �753. �24 55. �8

Page 338 Practice Quiz 11. 2x � 5x � 150; 50 3. 3.1� 5. all numbers

Pages 342–344 Lesson 7-31. An inequality represents all numbers greater or less thana given number. A number line graph can represent allthose numbers. 3. n � 14 � 25 5. true7.

9.

11. x � �20 13. f � 18,000 15. 86 � 2w 17. true19. false 21. true

9873 4 5 61 2

6540 1 2 3�2 �1

1 2

4 3

Greater than 100%

Less than 100%Original Rectangle


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23.

25.

27.

29.

31.

33.

35. x � 13 37. x � �3 39. x � �32 41. m � 6.443. b � 14,600 � 30,000; b � 15,400 45. Symmetric: If a � b, then b � a; not true. Sample counterexample: 4 � 5,but 5 �� 4. Transitive: If a � b and b � c, then a � c; true.47. B49a.

49b.

51. 5 53. 4n � 6 � 3n � 2; 8 55. G: �16, 32, �64 57. 1359. �7 61. 19.8

Pages 347–349 Lesson 7-41. Use addition to undo subtraction; use subtraction toundo addition. 3. Sample answer: Joanna works part-timeat a clothing store. Part-time workers must work fewer than30 hours a week. If Joanna has already worked 8 hours thisweek, how many hours can she still work? 5. y � �77. a � 11 9. t � �311. x � 10

13. p � 2 15. b � �22 17. y � 5 19. r � 7 21. j � �4

23. w � 6 25. y � 1.4 27. f � 5.4 29. b � 314

31. n � 5

33. p � 2

35. x � �5

37. m � 27

39. b � 134

41. s � 423

43. 980 lb 45. 42 � x � 74; x � 32; at least 32 mph47. Always; subtracting x gives �1 � 0, which is alwaystrue. 49. C 51. F 53. F 55. 3 cm, 9 cm 57. 8 � 3259. 5x � 17.5 61. �3 63. �15 65. �2 67. �4 69. �48

Pages 353–354 Lesson 7-51. Multiply each side by �12 and reverse the inequalitysymbol. 3. Tamika is correct. She divided each side of theinequality by 9. Since 9 is a positive number, she did notreverse the inequality symbol.

5. x � �2

7. a � 50

9. m � �8.4

11. y � �72

13. C

15. y � 9

17. b � �3

19. t � 5

21. h � 98

23. z � 3

25. w � 2

27. r � 4

29. k � �18

31. t � �16

33. n � 4

35. y � 5.7

37. b � 72

39a. 40m � 2000 39b. at least 50 min 41. Inequalities canbe used to compare the weights of objects on differentplanets. Answers should include the following.• Comparing the weight of an astronaut in a space suit on

Mars to the same astronaut on the moon: 113 � 50.• If you multiply or divide the astronaut’s weight by the

same number, the inequality comparing the weights ondifferent planets would still be true.

43. 40 45. c � �20 47. 2n � 14 49. �251 51.

2ca 53. 4

55. �9 57. 32

70 8674 78 82

5 5.85.2 5.4 5.6

1 9832 64 5 7

�20 �12�18 �16 �14

�12�14�18 �16�20

9873 4 5 61 2

�2 �1�3 1 20 43�4

9873 4 5 61 2

10610294 9890

9873 4 5 61 2

�2 �1�3 1 20 43�4

8 976 12 1311105

�80 �76 �72 �68 �64

�7.4�7.8�8.6 �8.2�9

907030 5010

�2 �1�3 1 20 43�4

3 4 5

0 1 1 212

12

23 25 27 29 31

0�7�6 �5�4�3�2 �1 1

9873 4 5 61 2

9873 4 5 61 2

9 1087 13 14 151211

�1�2 1 20 4 53�3

�1�2 1 20 4 53�3

0�8�7�6 �5�4 �3�2 �1

�3�2�4�5 1 20�1�6

6540 1 2 3�2 �1

9 1087 13 1412116

6 754 10 11 1298

6 7540 1 2 3�1


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1.

3. a � 40 5. n � 124 7. r � �225 9. g � 7

Pages 357–359 Lesson 7-61. Check the solution by replacing the variable with anumber in the solution. If the inequality is true, the solutionchecks. 3. Jerome is correct. By the Distributive Property2(2y � 3) � 4y � 6 not 4y � 3.

5. n � 2

7. c � 1

9. x � 8

11. d � �9�12

�

13. x � 8

15. c � �4

17. x � 3

19. k � �5

21. n � �5

23. b � 2

25. y � 30

27. c � �4

29. n � 7

31. n � 4.5

33. t � �1

35. c � �4

37. 0.55c � 0.35 � 2; 3 candy bars 39. 2s � 10 � 40, 15 subscriptions 41. x � 200; Sample explanation: Theinequality finds at what mileage Able’s charge is greaterthan Baker’s charge. 43. more than 100 minutes 45. k � 3and k � �3, or k � {�2, �1, 0, 1, 2} 47. D 49. �5 � x � 151. y � 37 53. n � 5 55. a � �18.6 57. 0.5%59. 16.6� mpg 61. $1.25 an issue 63. 6 m

Pages 360–362 Chapter 7 Study Guide and Review1. true 3. false; identity 5. false; inequality 7. true9. false; is greater than or equal to 11. 3 13. 4 15. 117. �1 19. �1.2 21. 9 23. 16 25. all numbers 27. true29. b � 17

31. t � 3�12

�

33. k � 5.1

35. y � �7

37. a � �2�25

�

39. n � 4 41. t � �12 43. b � �4�14

�

Chapter 8 Functions and GraphingPage 367 Chapter 8 Getting Started1. domain � {0, �3}; range � {4, 3}

3. domain � {6, 7, 8}; range � {8, 10, 12}

5. domain � {�8, 7, 6, 1}; range � {5, �1, 1, �2}

7. E 9. A 11. F 13. true 15. true 17. true

Pages 371–373 Lesson 8-11. Sample answer: a set of ordered pairs: {(1, 2), (4, 3), (�2, �1), (�3, 3)}a table: a graph:

3. Sample answer: This graph does notrepresent a functionbecause when x equals 1,there are two y values, 0and 2.

y

xO

y

xO

(4, 3)

(1, 2)

(�3, 3)

(�2, �1)

40�2�4 2 6

�4�8�10�12 �6

�1 8 9543210 6 7

4 5210 3

22 24181614 20

�10 �2�8 �6 �4

�4 4�2 0�3 �1 1 32

1 9832 64 5 7

�10 �2�8 �6 �4

10 9030 50 70

�4 4�2 0�3 �1 1 32

�7 1�5 �3�6 �4 �2 0�1

�7 1�5 �3�6 �4 �2 0�1

�4 4�2 0�3 �1 1 32

�4 4�2 0�3 �1 1 32

1 93 52 4 6 87

�10 �6�9 �8 �7

1 93 52 4 6 87

�4 4�2 0�3 �1 1 32

1 93 52 4 6 87

�4 4�2 0�3 �1 1 32


6 8

7 10

8 12

x y

0 4

�3 3

x y

�8 5

7 �1

6 1

1 �2

x y

1 2

4 3

�2 �1

�3 3

x y

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5. Yes; each x value is paired with only one y value. 7. No;5 is paired with 4 and 14. 9. Yes; any vertical line passesthrough no more than one point of the graph. 11. As windspeed increases, the windchill temperature decreases.13. Yes; each x value is paired with only one y value.15. No; 5 in the domain is paired with �4 and �1 in therange. 17. No; �2 in the domain is paired with 5 and 1 inthe range. 19. Yes; each x value is paired with only one y value. 21. No; a vertical line passes through more thanone point. 23. Yes; any vertical line passes through nomore than one point of the graph. 25. Generally, as theyears progress, the number of farms decreases. Anexception is in the year 2000. 27. Generally, as the yearsprogress, the size of farms increases. An exception is in theyear 2000. 29. Generally, as foot length increases, heightincreases. 31. Sometimes; a relation that has a member ofthe domain paired with more than one member in therange is not a function.33. For a given wind speed, there is only one windchilltemperature for each actual temperature. So, therelationship between actual temperatures and windchilltemperatures is a function. Answers should include thefollowing.• For a given wind speed, as the actual temperature

increases, the windchill temperature increases. • Since the relationship between actual temperatures and

windchill temperatures is a function, there cannot be twodifferent windchill temperatures for the same actualtemperature when the wind speed remains the same.

35. A 37. a � �21 39. x � 6 41. � 43. 18 45. 7547. 13 49. 5 51. 0

Pages 377–379 Lesson 8-21. Sample answer: Infinitely many values can be substitutedfor x, or the domain.3. (�3, 2), (�1, 4),

(0, 5), (1, 6)

5. Sample answer: (�1, �4), (0, 0), (1, 4), (2, 8) 7. Sampleanswer: (�1, 1), (0, 6), (1, 11), (2, 16)9.

11. Sample answer: (1, 186,000) means that light travels186,000 miles in 1 second. (2, 372,000) means that lighttravels 372,000 miles in 2 seconds.13. (�4, �2), (0, 6),

(2, 10), (4, 14)

15. Sample answer: (�1, �8), (0, �7), (1, �6), (2, �5)17. Sample answer: (�1, 5), (0, 0), (1, �5), (2, �10)19. Sample answer: (�1, �2), (0, 1), (1, 4), (2, 7)21. Sample answer: (�1, �5), (0, �6), (1, �7), (2, �8)23. Sample answer: (�1, �13), (0, �10), (1, �7), (2, �4)25. Sample answer: (�1, 0), (�1, 1), (�1, 2), (�1, 3)27. 6.2 mi 29. Quadrant I; a person cannot have a negative age or heart rate.31. 33.

35. 37.

39. 41.

43.

45. Yes; the points lie on a straight line. 47. Yes; the pointslie on a straight line. 49. No; the exponent of x is not 1.51. Sample answer: In the first table, as the x valuesincrease by 1, the y values increase by 2. In the secondtable, as the x values increase by 1, the y values do notchange by a constant amount. 53. B 55. Yes; each x valueis paired with only one y value. 57. No; 11 in the domainis paired with 8 and 21 in the range.59. x � 4;

61. �67

� 63. 3 65. 4

5 6 74321

P

s

1412108642

10 2 3 4 5 6 7

(1, 4)

(2, 8)

(3, 12)

y

xOy � �3

y

xO

3x � y � 7

y

xO

x � y � 6

y

xO

y � 3x � 4

y

xO

y � �x � 6

y

xO

y � x � 5

y

xO

y � 2x � 1


�3 �3 � 5 2

�1 �1 � 5 4

0 0 � 5 5

1 1 � 5 6

x x � 5 y

�4 2(�4) � 6 �2

0 2(0) � 6 6

2 2(2) � 6 10

4 2(4) � 6 14

x 2x � 6 y

R19-R50 C1-13 SA-870424 12/10/04 3:42 AM Page R33

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Pages 384–385 Lesson 8-31. To find the x-intercept, let y � 0 and solve for x. To findthe y-intercept, let x � 0 and solve for y. 3. �1; �35. �4; 4 7. 3; 2

9.

11. The y-intercept 3represents the base fee of $3.

13. 1; 1 15. none; �5 17. �5; 5 19. none; �4 21. 8; �423. 5; 4

25. 27.

29. 31.

33.

35.

The x-intercept 6 represents the number of books that shecan buy with no money left over. The y-intercept 18represents the money she has before she buys any books.37. The x- and y-intercept are both 0. Therefore, the linepasses through the origin. Since two points are needed tograph a line, y � 2x cannot be graphed using only the intercepts.

39. B 41. Sample answer:(�1, 5), (0, 7), (1, 9), (2, 11)43. Sample answer: (�1, 1),(0, 5), (1, 9), (2, 13) 45. no47. n � 12 49. 2.8%51. �16 53. 25

Pages 389–391 Lesson 8-41. Sample answer: horizontals do not rise, so

slope � �rriusne

� � �ru

0n� or 0. 3. Mike; Chloe should have

subtracted �2 from 11 in the denominator. 5. ��23

� 7. 2

9. 0 11. B 13. 4 15. ��34

� 17. 0 19. 1 21. ��32

�

23. undefined 25. ��34

� 27. It decreased; negative slope.

29. Slope can be used to describe the steepness of rollercoaster hills. Answers should include the following.• Slope is the steepness of a line or incline. It is the ratio of

the rise to the run.• An increase in rise with no change in run makes a roller

coaster hill steeper. An increase in run with no change inrise makes a roller coaster less steep.

31. A 33. 2; 6 35. Sample answer: (�1, 3), (0, 5), (1, 7), (2, 9) 37. Sample answer: (�1, 8), (0, 7), (1, 6), (2, 5)

39. y � �2x 41. y � �13

�x

Pages 395–397 Lesson 8-51. The slope is 60, the rate of change is 60 units for every 1 unit, and the constant of variation is 60. 3. Justin; anylinear function, including direct variations, has a rate ofchange. 5. increase of $12 per hour 7. y � 6x 9. increaseof 12 in./ft 11. decrease of 2°F/min13. Sample answer: The population of wild condorsdecreased from 1966 to 1990. Then the population increasedfrom 1990 to 1996. The population of condors in captivity

y

xO

y � 2x(1, 2)

(�1, �2)

y

x

y � 18 � 3x

Number of Books

Mo

ney

($)

2

0 1 2 3 4 5 6 7 8 9

468

1012141618

y

xO

3x � 6y � 18

(6, 0)

(0, 3)

y

x(0, �2)

O

y � �2

y

xO

y � �2x � 4

(2, 0)

(0, 4)

y

xO

x � y � 4

(4, 0)

(0, 4)

y

xO

y � x � 2

(0, 2)(�2, 0)

y

xO

y � 6x � 3

(0, 3)

(�0.5, 0)

y

xO

x � 2y � 6 (0, �3)

(6, 0)


R19-R50 C1-13 SA-870424 12/10/04 3:42 AM Page R34

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increased slowly from 1966 to 1982, then increased morerapidly from 1982 to 1996.

15. y � �5x 17. y � 0.75x 19. y � 2.54x 21. A linerepresenting the relationship between time and distancehas a slope that is equal to the speed. Answers shouldinclude the following.• Sample drawing:

• As speed increases, the slope of the graph becomessteeper.

23. B 25. 227.

29. 14 31. y � 1 � 3x


1. No; 1 is paired with 2 and �3.3.

5. �9; 9 7. 5; �4 9. �2

Pages 400–401 Lesson 8-61. a 3. Alex; the equation in slope-intercept form is

y � ��12

�x � 4. 5. �1; 0

7. 9.

11. The y-intercept 25 represents the charge for a basic cake.Slope 1.5 represents the cost per additional slice.13. 2; �4 15. �2; �3 17. 0; 4

19. 21.

23. 25.

27. 29.

31.

33. slope � �50, the descent in feet per minute;

y-intercept � 300, initial altitude 35. ��mb�. Replace y with 0

y

xOy � �3

y

xO

2x � 3y � 12

y

xO

5x � y � �3

y

xO

x � y � 0

y

xO

y � x � 234

y

xO

y � �x � 6

y

xO

y

xOx � 2y � 4

y

xO

y � x � 114

y

xO

y � x � 4

y

xO

(0, 1) (1, 0)

y � �x � 1

y

x

Time (h)

Dis

tan

ce (

mi)

10 2 3 4 5 6

100

200

300


1966–1982 �2.25 0.1875

1982–1990 �3 4.625

1990–1992 0 8

1992–1994 1.5 14.5

1994–1996 12.5 3.5

Interval Condors in Condors inthe Wild Captivity

Rate of Change(number per year)

R19-R50 C1-13 SA-870424 12/10/04 3:43 AM Page R35

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in y � mx � b and solve for x. 37. B 39. y � �4x 41. 2

43. 4 45. 6x � 2x � 28; 7 47. ��35

� 49. 29 51. 11

Pages 407–408 Lesson 8-71. Sample answer: Find the y-intercept b and another pointon the line. Use the points to determine the slope m. Thensubstitute these values in y � mx � b and write theequation.

3. y � �12

�x � 1 5. y � �2x � 3 7. y � �12

�x � 1

9. y � �34

�x � 1 11. y � 2x � 6 13. y � 5 15. y � ��13

�x � 8

17. y � 2x � 3 19. y � �2.5 21. y � ��12

�x 23. y � x � 1

25. y � �x 27. y � 7 29. y � 4x � 3 31. y � 1088x; The speed of sound is 1088 feet per second.33a. d � 0.5(0.7c � 1.06) or d � 0.371c 33b. $18.55 35. C37. 6; 7 39. 3; �2 41. positive

Pages 410–413 Lesson 8-81. Sample answer: Use a ruler to extend the line so that itpasses through the x value for which you want to predict.Locate the x value on the line and determine thecorresponding y value. Or, write an equation for the best-fitline and substitute the desired value of x to find thecorresponding value of y.3. Sample answer:

5. y � 20x � 3207. Sample answer:

9. Sample answer:

11. No, the equation gives a negative value for barometricpressure, which is not possible. Also, the data in the scatterplot do not appear to be linear. 13. Sample answer: 238 in.15. As latitude increases, temperature decreases.17. Sample answer: 61.3°F 19. The data describing the lifeexpectancy for past generations can be displayed using ascatter plot. Then a line is drawn as close to as many of thepoints as possible. Then the line can be extended and usedto predict the life expectancy for future generations.Answers should include the following.• A best-fit line is a line drawn as close to as many of the

data points as possible. • Although the points may not be exactly linear, a best-fit

line can be used to approximate the data set.21. A 23. y � �2x � 2 25. y � �4

27.

29. n � 7 31. d � ��32

� 33. 2 35. 4.5 37. 3 39. �141. �2

Pages 416–418 Lesson 8-91. Sample answer: A group of two or more equations form asystem of equations. The solution is the ordered pair thatsatisfies all the equations in the system. If the equations aregraphed, the solution is the coordinates of the point wherethe graphs intersect. The system has infinitely manysolutions if the equations are the same and the graphs coincide. 3. (�5, �4)

5. no solution

7. (2, 6) 9. (3, �2) 11. infinitely many

13. (3, 3) 15. infinitely many y

xO

2x � 3y � 0

y � x 23

y

xO

(3, 3)

x � y � 6

y � x

y

xO

x � y � 2

x � y � 4

y

xO

y � �x � 3

Bar

om

etri

c Pr

essu

re(i

n. m

ercu

ry)

5

0

15

25

35

10

20

30

Altitude(1000s ft)

10 30 50 7020 40 60 x

y

Att

end

ance

(m

illio

ns)

1200

1150

0

125013001350

14001450

1500

Year’93 ’94 ’95’96 ’97 ’98 ’99

y

x

y

x

510

15

2025

3035

40

’95 ’96 ’97 ’98 ’99 ’00 ’01 ’020

Year

Nu

mb

er o

f H

ou

seh

old

s(m

illio

ns)


R19-R50 C1-13 SA-870424 12/10/04 3:43 AM Page R36

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17. (�2, 4)

19. (�2, 0) 21. (�4, 10) 23. (3, 6) 25. (6, 11); an order of6 pounds will cost the same, $11.00, for both sites.27a. Sample answer: No; since sloperepresents rate, the slopes of thegraphs are the same. Therefore, the runners willnever meet.

27b. Sample answer: The line representingrunner B has asteeper slope thanthe line representingrunner A. Theintersection pointrepresents the timeand distance atwhich runner Bcatches up to runner A.

29. C 31. positive slope 33. y � �3x 35. yes 37. no39. yes


1. �1; 8 3. ��12

�; 3 5. y � 1

7. Sample answer:

9. (0, 5)

Pages 421–422 Lesson 8-101. y � �x � 3 3a. Sample answer: (0, �1), (1, 0), (2, 1)3b. Sample answer: (0, 0), (1, 1), (2, 2)

5. 7.

9. Sample answer: 5 adults, 30 children; 10 adults, 22 children;15 adults, 15 children

11. 13.

15. 17.

19. 21.y

xO

y � � x � 1 13

y

xO

y � 2x � 4

y

xO

y � 0

y

xOy � x � 4

y

xOy � �3

y

xO

y � x

Ch

ildre

n

10

15

5

0

20

25

30

35

40

45

Adults15105 25 3520 30

25x � 15y � 630

y

x

y

xO

y � �3x � 2

y

xO

y � x � 1

y

x

Ag

e

25

27

29

24

26

23

0

28

30

Year’84 ’00 ’04 ’08’92’88 ’96

0

25

50

75

Time (s)

BA

y

x

Dis

tan

ce (

m)

1 2 3 4 5 6 7

Dis

tan

ce (

m)

0

25

50

75

Time (s)

B

Ay

x1 2 3 4 5 6 7

y

xO

y � � x � 312

y � �2x

(�2, 4)


R19-R50 C1-13 SA-870424 12/10/04 3:44 AM Page R37

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23.

25. No; the number of sales and the costs cannot benegative. 27. 10x � 25y � 1440 29. Sample answer: 25 small, 45 large; 50 small, 30 large; 100 small, 10 large

31.

33a. y � x � 1, y � ��32

�x � 2

33b. Sample answers: (0, 2), (�1, 2), (�3, �2) 35. C

37. (0, 3) 39. (2, �5)

41. 0.4 43. �0.5�

Pages 424–428 Chapter 8 Study Guide and Review1. d 3. h 5. a 7. f 9. c 11. Yes; each x value is pairedwith only one y value. 13. Yes; each x value is paired withonly one y value.

15. 17.

19. 21.

23. 25.

27. 29.

31. 1 33. �78

� 35. undefined 37. increase of 8 m/s

39. 41.

43. y � �x � 3

45. Sample answer:

Att

end

ance

2500

2400

0

260027002800

29003000

Year2000 20022001 2003

y

x

y

xO

y � x � 2 13

y

xO

y � x � 4

y

xO

x � y � �2

(0, �2)

(�2, 0)

y

xO

(�4, 0)x � �4

y

xO

y � �x � 3

(0, �3)

(�3, 0)

y

xO

(�2, 0)

(0, 2)

y � x � 2

y

xO

x � y � 4

y

xO

y � 3x � 2

y

xO

y � �x

y

xO

y � x � 4

y

xOy � �2x � 1

y � �x � 3(2, �5)

y

xO

y � x � 3

x � 0

(0, 3)

Eco

no

Raf

ts

10

0

20

30

Super Rafts5 10 15

100x � 40y � 1500

y

x

2000

3000

1000

0

4000

5000

6000

3000 6000

y

x

Sale

s ($

)

Costs ($)

y � x � 3000


R19-R50 C1-13 SA-870424 12/10/04 3:45 AM Page R38

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47. (3, 3)

49. no solution

51. (4, 4)53. 55.

Chapter 9 Real Numbers and Right Triangles

Page 435 Chapter 9 Getting Started1. � 3. � 5. � 7. � 9. 8 11. 60 13. 9 15. 11 17. 819. 34 21. 97

Pages 438–440 Lesson 9-11. A positive number squared results in a positive number,and a negative number squared results in a positive number. 3. Sample answer: ��1.69�

5. �8a 7. 3.9 9. 8 11. 44.9 mi 13. 6 15. �5a 17. notpossible 19. 14y 21. 18, �18 23. 1.5 25. 7.5 27. �9.329. 15.8 31. �1.7 33. 70.7 35. 9 37. �7 39. 1441. �17 43. �2 45. 6 47. 14.8 mi 49. 9; Since 64 � 65 � 81, �64� � �65� � �81�. Thus it follows that 8 � �65� � 9. So, 9 is greater than �65�. 51a. 10.4 in.; 41.6 in. 51b. 14.2 cm; 56.8 cm 51c. 8.4 m; 33.6 m53. 10 55. 2 57. Sample answer: A number that has arational square root will have an ending digit of 0, 1, 4, 5, 6,or 9. The last digit is the ending digit in one of the squaresfrom 1–100. There are just six ending digits. 59. D61. Sample answer: addition and subtraction 63. a

65. 67. (5, 7) 69. (�4, �3)

71. �23

� 73. 9 75. It can

be written as a fraction.

77. It can be written as �34

�.

79. It can be written as �61

�.

Pages 443–445 Lesson 9-21. Whereas rational numbers can be expressed in the form �ba

�, where a and b are integers and b does not equal 0,

irrational numbers cannot. 3. N, W, Z, Q 5. Q 7. �

9. �130�, 3�

35

�, �13�, 3.7� 11. 8.6, �8.6 13. N, W, Z, Q 15. Q

17. Q 19. I 21. I 23. Z, Q 25. Q 27. Z, Q 29. always

31. always 33. � 35. � 37. � 39. �65

�, �4�, 2.1�, 5�14

�

41. �10�12

�, ��105�, �10, �1.05 43. Sample answer: �4�and �49� 45. 7, �7 47. 4.7, �4.7 49. 12, �12 51. 11.3,�11.3 53. 1.3, �1.3 55. 1.9, �1.9 57. 12 or –1259. 4 or –4 61. 3663. If a square has an area that is not a perfect square, thelengths of the sides will be irrational. Answers shouldinclude the following.•

65. B 67. 2621.2 ft2 69. 7 71. 3 73. Sample answer: (0, 5), (1, 6), (�6, 2) 75. x � 5 77. $0.53/cupcake

79. 81. 83.


1. N; NM��, NP��; �1, �MNP, �PNM, �N 3. 20°; acute5. 70°; acute 7. acute 9. straight angle

11. 15°; acute 13. 85°; acute 15. 135°; obtuse17. 60°; acute 19. 90°

21.acute

23.acute

25.obtuse

27. obtuse155˚

95˚

65˚40˚

55˚

7:4510:003:00

Area �64 in2

Area �56 in2

y

xO

�10 �9 �8 �7 �6 �5 �4 �3 �2 �1

�1.69�

y

xO

y � �x � 4y

xO

y � 3x � 1

y

xO

3x � y � 1

y � �3x � 5

y

xO

(3, 3)

y � xy � 3


R19-R50 C1-13 SA-870424 1/5/05 1:47 PM Page R39

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29.acute

31a. obtuse 31b. right 31c. acute33. better self-image: about 95°;better health: about 101°; more alert:about 79°; more relaxed: about 56°;other: about 29° 35. 24

37. C 39. Z, Q 41. I 43. 4 45. x � 7 � 22 47. 9949. 60 51. 18

Page 451 Practice Quiz 2 1. 6 3. 8.2, �8.2 5. obtuse

Pages 455–457 Lesson 9-41. Whereas an isosceles triangle has at least two sidescongruent, an equilateral triangle has three sides congruent. 3. Sample answer:

5. 90; right 7. right isosceles 9. acute isosceles11. 27; right 13. 112; obtuse 15. 90; right 17. 20°, 60°, 100°19. acute equilateral 21. right scalene 23. acute scalene25. always 27. obtuse 29. acute 31. not possible33. not possible 35. 45°; 50°; 85° 37. 10, 15, 21 39. B41. 180°; straight 43. 145°; obtuse 45. 9, �9 47. 9.2, �9.249. 144 51. 324 53. 729

Pages 462–464 Lesson 9-51. Sample answer: 8, 15, 17 3. 25 5. 15 7. no 9. B11. 26 13. 12.5 15. 18.9 17. 23 in. 19. 12 21. 12.123. 37.3 25. 28 27. 33.5 29. yes 31. no 33. no35. 32 in.37. There is enough information to find the lengths of thelegs. Since the right triangle is an isosceles right triangle,we know that the lengths of the legs are equal. So, in thePythagorean Theorem, we can say that a � b. In addition,we know that c � 8.

c2 � a2 � b2 Pythagorean Theorem82 � a2 � a2 a � b and c � 882 � 2a2 Add a2 and a2.64 � 2a2 Evaluate 82.

�624� � �

22a2� Divide each side by 2.

32 � a2 Simplify.�32� � a Take the square root of each side.39. D 41. 17 units 45. 90; right 49. n � �9 51. 5

Pages 468–470 Lesson 9-61. the point halfway between two endpoints3. Sample answer:

; The coordinates of the midpoint of A�B� are ��

12

�, 0�. 5. 11.2 7. (2, �5) 9. 9.211. 10.2 13. 16.6 15. 4.817. 19.2 19. (1, 3) 21. (4, �2)23. (2, 2) 25. (3, �4)

27. �11�12

�, �5�

29. Yes; P�M� and M�N� have equal measures. 31. (�2, 3)33. C 35. 9.2 37. 35.1 39. 2, 1 41. –4, �6 43. 2845. 21 47. 59

Page 470 Practice Quiz 21. obtuse isosceles 3. Yes; 342 � 302 � 162 5. (�1, 5)


1. Sample answer: corresponding sides:

�XA

YB� � �

YBC

Z� � �

AX

CZ�

3. �1x5� � �

69

�; 10 5. 6 km 7. �x4

� � �150�; 8 9. �

1x8� � �

21

05�; 24

11. �x3

� � �47.2�; 5 13. always 15. 68 yd 17. 6 ft

19. No, triangles ABC and DEF are not similar since thecorresponding sides are not proportional. 21. A 23. 3.625. 7.1 27. 77.4 29. �

14

� 31. 1�12

� 33. 0.7143 35. 0.225

Pages 479–481 Lesson 9-81. The sine ratio compares the measure of the leg oppositethe angle to the measure of the hypotenuse. The cosineratio compares the measure of the leg adjacent to the angleto the measure of the hypotenuse. The tangent ratiocompares the measure of the leg opposite the angle to themeasure of the leg adjacent to the angle. 3. 0.88245. 1.875 7. 0.9455 9. 25.6 11. 7.8 13. 0.9231 15. 0.724117. 2.4 19. 0.8944; 0.4472; 2.0 21. 0.1045 23. 0.857225. 0.2126 27. 6.8 29. 24.9 31. 97.6 33. about 21 m35. about 44 m 37. 24.0 39. 40.4 41. sin 45° � cos 45°;sin 60° � cos 30°; sin 30° � cos 60° 43. To find heights ofbuildings. Answers should include the following.• If two of the three measures of the sides of a right triangle

are known, you can use the Pythagorean Theorem to findthe measure of the third side. If the measure of an acuteangle and the length of one side of a right triangle areknown, trigonometric ratios can be used to find themissing measures.

•

The height of the ramp is about 2 feet.

45. C 47. �1�12

�, �12

�� 49. (�3, �4) 51. a � �6

Pages 483–486 Chapter 9 Study Guide and Review1. real numbers 3. obtuse 5. hypotenuse7. trigonometric ratio 9. 6 11. –9 13. not possible15. 9, �9 17. 1.2, �1.2 19. 90°; right 21. 35°; acute23. obtuse isosceles 25. 13.7 27. 15.9 29. 9.4 31. (3, 5)

33. (0, �2) 35. �AH

BJ

� � �BJKC�; 10 37. 1.3333

Chapter 10 Two-Dimensional Figures

Page 491 Chapter 10 Getting Started1. 44 3. 51 5. 28 7. 39 9. 44 11. 71.8 13. 12.5

15. 10.7 17. 10�16

� 19. 3�78

� 21. 5�38

� 23. 6�29

�

Pages 495–497 Lesson 10-11. Complementary angles have a sum of 90° andsupplementary angles have a sum of 180°. 3. 56° 5. 124°7. 28 9. D 11. 127° 13. 53° 15. 127° 17. 148 19. 175

sin 6° � �1x9�

19(sin 6°) � x2.0 � x

6˚ x ft19 ft

B C

A X

Y Z

y

xO

(�3, 1)

(2, �1)

( , 0)Midpoint

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A 12 �

30˚ 120˚30˚

38˚


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21. 9 23. 41° 25. 73° 27. 112° 29. 5 31. 9 33. Theyare supplementary. 35. A 37. Sample answer: Bothgraphs intersect to form right angles. 39. Sample answer:The slopes of the graphs of perpendicular lines are negativereciprocals of each other. 41. 0.8910 43. 7.5 45. �9m47. 49.

Pages 502–504 Lesson 10-21. They have the same size and shape. 3. �J � �C, �K � �B, �M � �G, K�M� � B�G�, M�J� � G�C�, K�J� � B�C�; �BGC5. �M 7. M�N� 9. 15 ft 11. �K � �N, �J � �P, �M � �M, K�J� � N�P�, J�M� � P�M�, K�M� � N�M�; �NPM13. �Z � �S, �W � �T, �Y � �R, Z�W� � S�T�, W�Y� � T�R�, Z�Y� � S�R�; �STR 15. sometimes 17. 30° 19. �F 21. �A23. H�F� 25. D�C� 27. 20 29. 6 31. Sample answer: �ZQN33. Sample answer: �WQO 35. Congruent triangles canbe found on objects in nature like leaves and animals.Answers should include the following.• Congruent triangles are triangles with the same angle

measures and the same side lengths. • Sample answer: A bird’s wings when extended are an

example of congruent angles. Another example ofcongruent angles would be the wings of a butterfly.

37. D 39. 0.1219 41. 1.1585 43. �645–49.

Pages 509–511 Lesson 10-31. The figure is moved 5 units to the right and 2 units down.3. 5.

7. A�(�2, 5), B�(1, 3), 9. D��1, 3�12

��, E��3, 4�12

��, C�(�2, 0);

G��1, �1�12

��, F��3, ��12

��;

11. R�(�4, �3), S�(0, �3), 13. M�(�1, �2), N�(4, �4), T�(�4, 1); O�(3, �2), P�(3, 0),

Q�(0, 0);

15. 17.

19. translation

21. Sample answer: ; The image of the figure�s

reflection is the same as theimage of its translation to theright 6 units.

23. reflection 25. Since many of the movements used inrecreational activities involve rotating, sliding, and flipping,they are examples of transformations. Answers shouldinclude the following.• a translation is a slide, a reflection is a mirror-image, and

a rotation is a turn.• sample answer: the swing represents a rotation, the

scooter represents a translation, and the skateboardrepresents reflection.

27. C 29. D�F� 31. 110°33. x � 9.6;

35. 113 37. 47 39. 106

Pages 515–517 Lesson 10-41. Sample answer: A textbook is an example of aquadrilateral; the tiles in a shuffleboard scoring region areexamples of parallelograms; a “dead end” road sign is anexample of a rhombus; and a floppy disk is an example of a square. 3. 110; 110° 5. rectangle 7. trapezoids,parallelograms 9. 102; 102° 11. 60; 60°; 60°; 120° 13. 70;70°; 80°; 120° 15. Sample answer: A chessboard; it is asquare because it is a parallelogram with 4 congruent sidesand 4 right angles. 17. square 19. parallelogram21. rhombus 23. always 25. sometimes 27. quadrilateral

7.0 8.0 9.0 10.0

y

xO

y

xO A

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29a. Yes; a rhombus is equilateral but may not be equiangular.

29b. Yes; a rectangle is equiangular but may not be equilateral.

31. B 33. 35. M�A� 37. 14.439. 28.52

Page 517 Practice Quiz 11. 35° 3. Q�(3, �3), R�(5, �6), S�(7, �3) 5. 60; 60°; 120°


1. Sample answer:

3. 8 ft2 5. 60 m2 7. 11 m2 9. 90 cm2 11. 43.99 cm2

13. 28 in2 15. 22.8 yd2 17. 36.75 m2 19. about 95,284 mi2

21. 147 km2 23. 57 ft2 25. 5 bags 27. 16 in. 29. 24.5%31. The area of a parallelogram is found by multiplying thebase and the height of the parallelogram. The area of arectangle is found by multiplying the length and the widthof the rectangle. Since in a parallelogram, the base is thelength of the parallelogram, and the height is the width ofthe parallelogram, both areas are found by multiplying thelength and the width. Answers should include the following.• Parallelograms and rectangles are similar in that they are

quadrilaterals with opposite sides parallel and oppositesides congruent. They are different in that rectanglesalways have 4 right angles.

•

33. B 35. 24; 24°; 96° 37. 30 39. 26 41. 900 43. 1260


1. 3. The number of triangles is 2 less than the number of sides. 5. octagon;regular 7. 128.6° 9. hexagon; regular11. nonagon; not regular 13. decagon,not regular 15. 540° 17. 1440°

19. 2880° 21. Sample answer: hexagon, triangle, decagon,quadrilateral, and pentagon 23. 140° 25. 135° 27. 150°29. octagons, squares 31. 180 cm 33. 58.5 in.35. In tessellations, polygons are fit together to create apattern such that there are no gaps or spaces.Answers should include the following.• Sample answer:

• Sample answer:

37. B 39. 120° 41. 60° 43. 30° 45. 18 cm2

47. quadrilateral 49. 16.4x 51. 33.9 53. 18.1

Pages 536–538 Lesson 10-71. Multiply 2 times � times the radius. 3. Mark; since thediameter of the circle is 7 units, its radius is 3.5 units. Thus,the area of the circle is � · (3.5)2 or 38.5 square units.5. 50.3 m; 201.1 m2 7. 8.2 km; 5.3 km2 9. about 9.1 mi2

11. 40.8 in.; 132.7 in2 13. 131.9 km; 1385.4 km2 15. 79.8 m;506.7 m2 17. 22.9 cm; 41.9 cm2 19. 96.6 in; 742.6 in2

21. 1.5 m 23. 13 cm 25. about 3979 mi 27. d 29. a31. about 26 times 33. are safe: 30.5 in2; are unsafe: 13.3 in2;unsure: 19.7 in2 35. 4 37. C 39. 125° 41. 235°43. 125° 45. 62.5° 47. Sample answer: S�P�, S�Q��, R�P��49. 144° 51. 38 m2 53. x � �7 55. 150.5

Page 538 Practice Quiz 21. 112.86 cm2 3. 32 m2 5. 29.5 in.; 69.4 in2


1. Sample answer:

3. 49.5 yd2 5. 2 7. 72 ft2 9. 56.1 cm2 11. 18.3 in2

13. 45 ft2 15. 86.8 yd2 17. 85 units2 19. 6963.5 yd2

21. Sample answer: Separate the area into a rectangle and atrapezoid. 23. 68,679 mi2 25. You can use polygons tofind the area of an irregular figure by finding the area ofeach individual polygon and then finding the total area ofthe irregular figure. Answers should include the following.•

• To find the area of the irregular figure shown above, thefigure can be separated into two rectangles and a triangle.

27. C 29. 44.0 cm, 153.9 cm2 31. 540° 33. 1080°35. �24xy

Pages 544–548 Chapter 10 Study Guide and Review1. supplementary 3. corresponding angles 5. equilateral7. 109° 9. 71° 11. �H 13. R�S� 15. G�F�

8 in.

3 in.

y

xO

G

E

D

F

D'

F'

G'

E'


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17. 19. 112; 112° 21. 70; 70°;70° 23. 11 yd2

25. hexagon; 720°27. decagon; 1440°29. 13.2 m; 13.9 m2

31. 118 in2 33. 863.4 cm2

Chapter 11 Three-Dimensional Figures

Page 553 Chapter 11 Getting Started1. yes; triangle 3. no 5. 17 7. 7 9. 155 11. yes 13. yes15. yes

Pages 559–561 Lesson 11-11. Five planes form a square pyramid because the solid hasfive faces. An edge is formed when two planes intersect; avertex is formed when three or four planes intersect.3. triangular pyramid; any one of the following faces can be considered a base: RST, QRS, QST, QRT; Q�R�, Q�S�, Q�T�, R�T�, R�S�, S�T�; Q, R, S, T 5. intersecting7.

9. rectangular prism; LMNP, QRST or LPTQ, MNSR orPNST, LMRQ; LMNP, QRST, LPTQ, MNSR, PNST, LMRQ; L�M�, M�N�, N�P�, P�L�, L�Q�, M�R�, N�S�, P�T�, Q�R�, R�S�, S�T�, T�Q�; L, M, N,P, Q, R, S, T 11. triangular pyramid; any one of thefollowing faces can be considered a base: WXY, WYZ,WZX, XYZ; W�X�, W�Y�, W�Z�, X�Z�, X�Y�, Y�Z�; W, X, Y, Z 13. W�R�15. skew 17. top 19. rectangular and pentagonal prisms23. Never; only three or more planes can intersect in asingle point. 25. Sometimes; three planes may intersect ina line. Or, the planes may be parallel and not intersect at all.27. Two-dimensional figures form three-dimensionalfigures. Answers should include the following.• Two-dimensional figures have length and width and

therefore lie in a single plane. Three-dimensional figureshave length, width, and depth.

• Two-dimensional figures form the faces of three-dimensional figures.

29. D 31. 37.7 cm; 113.1 cm2 33. 0.5000 35. c � 8

37. n � �11 39. y � 1�34

� 41. 14 in2 43. 6.5 cm2

Pages 565–567 Lesson 11-21. Sample answer: Finding how much sand is needed to filla child’s rectangular sandbox; measure the length, width,and height, and then multiply to find the volume.3. 183.6 cm3 5. 1608.5 ft3 7. 282.7 yd3 9. 198.9 ft11. 512 cm3 13. 748 in3 15. 88.0 ft3 17. 225 mm3

19. 18.6 m3 21. 6.2 m 23. 1728 25. 1,000,000 27. 11.5 in.

29. The volume will be greater if the height is 8�12

� inches.

By using the formula for circumference, you can find theradius and volume of each cylinder. If the height is

8�12

� inches, the volume is 86.5 in3; if the height is 11 inches,

the volume is 67.7 in3. 31. C 33. Sample answer: Q�T� and Y�Z� 35. x � �8 37. 25 39. 4 41. 28

Pages 570–572 Lesson 11-31. The base is a circle.3. Sample answer: V � 134.0 cm3

5. 37.7 cm3 7. 378 ft3 9. 91,636,272 ft3

11. 412 cm3 13. 150 in3 15. 78.5 m3

17. 270.8 cm3 19. 565.5 m3 21. 44.0 m3

23a. 2.4 ft3 23b. 314.4 lb

25. The volume of a pyramid is one-third the volume of aprism with the same base and height. Answers shouldinclude the following.• The height of the pyramid and prism are equal. The

bases of the pyramid and prism are squares with equalside lengths. Therefore, their base areas are equal.

• The formula for the volume of a pyramid is one-thirdtimes the formula for the volume of a prism.

27. B 29. 904.8 cm3 31. 107.5 mm3 33. 10.1 in3

35. 7.8 37. 36

Page 572 Practice Quiz 11. triangular prism 3. 12.6 cm3 5. �11,545,353 ft3

Pages 575–577 Lesson 11-41. Sample answer: The surface of a solid is two-dimensional. Its area is the sum of the face areas, which aregiven in square units. 3. 150 ft2 5. 571.8 in2 7. 140.7 mm2

9. 282 in2 11. 264 m2 13. 1885.0 ft2 15. 294 ft2

17. 628.3 in2 19. 264.0 in2 21. 754 ft2 23. The surfacearea is 4 times greater. 25. D 27. square or rectangle

29. rectangle 31. 565.5 in3 33. 15.21 35. 1.3 37. 3�14

�

Pages 580–582 Lesson 11-51. Slant height is the altitude of a triangular face of apyramid; it is the length from the vertex of a cone to theedge of its base. Height of a pyramid or cone is the altitudeof the whole solid. 3. Sample answer: An architect mightuse the formulas to calculate the amount of materialsneeded for parts of a structure. 5. 42.9 m2 7. 336 ft2

9. 96.3 in2 11. 62.4 in2 13. 339.3 in2 15. 311.9 m2

17. 506.6 mm2 19. Style 8M has 29 in2 more plastic.21. 339 ft2; 4 squares 23. Many building materials arepriced and purchased by square footage. Architects usesurface area when designing buildings. Answers shouldinclude the following.• Surface area is used in covering building exteriors and in

designing interiors. • It is important to know surface areas so the amounts and

costs of building materials can be estimated.25. C 27. 5541.8 mm2 29. 7 ft2 31. 25.1 in3 33. infinitelymany solutions 35. 3 37. 3 39. 3.15

Pages 586–588 Lesson 11-61. Sample answer: The cones are similarbecause the ratioscomparing their radiiand slant heights are

equal: �23

� � �75.5�.

5 m 7.5 m

2 m3 m

8 cm

4 cm

sidefronttop

y

xO

H H'

J J'I I'


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3. no 5. x � 33�13

� ft 7. 525 m 9. 2,976,750 m3 11. yes

13. yes 15. x � 7 m, y � 18 m 17. Sometimes; bases mustbe the same polygon and the corresponding side lengthsmust be proportional. 19. always; same shape, diametersor radii are proportional 21. 2003 or 8,000,000 timesgreater 23. If the ratios of corresponding lineardimensions are equal, the solids are similar. Answersshould include the following.• For example, if the ratio comparing the heights of two

cylinders equals the ratio comparing their radii, then thecylinders are similar.

• A cone and a prism are not similar.

25. C 27. 184 ft2 29. 65° 31. ��59

� 33. 19.3 35. 6.0

37. 9.4

Page 588 Practice Quiz 21. 166 mm2 3. 9.4 m2 5. Yes; their correspondingdimensions are proportional.

Pages 592–594 Lesson 11-71. Josh; the first two 0s are not significant because they areplaceholders for the decimal point. The 0 between 2 and 5is significant because it is between two significant digitsand shows the actual value in the thousandths place.3. Sample answer: 0.012 or 2500 5. 3 7. 3 9. 7.1 L

11. 544.5 in2 13. �312� in. 15. 3 17. 2 19. 1 21. 4

23. 45 in. 25. 2 ft2 27. 84.47 m 29. 49.5 cm 31. 26 m2

33. b; The precision unit of ruler a is �18

� inch. The precision

unit of ruler b is �116� inch. 35. No, the numbers are

estimated to the nearest 0.1 million. 37. 46,700,000; 339. Not necessarily, because the actual size of the 2.0 mmwrench can range from 1.95 mm to 2.05 mm and the actualsize of the 2 mm bolt can range from 1.5 mm to 2.5 mm. So,the bolts could be larger than the corresponding wrenches.41. A 43. 0.05 mi; between 132.75 mi and 132.85 mi45. 26.5 cm2 47. 14.8 m2

Pages 595–598 Chapter 11 Study Guide and Review1. false; lateral area 3. false; slant height 5. false; cylinder7. true 9. rectangular prism; QRST, UVWX or QTXU,RSWV or QRVU, TSWX; QRST, UVWX, QTXU, RSWV, QRVU, TSWX; Q�R�, R�S�, S�T�, T�Z�, U�V�, V�W�, W�X�, X�U�, Q�U�, T�X�, S�W�, R�V�; Q, R, S, T, U, V, W, X 11. rectangular pyramid; YNPZ; AYZ, AZP, ANP, ANY, YNPZ; A�Y�, A�Z�, A�P�, A�N�, Y�Z�, Z�P�, P�N�, N�Y�; A, Y, Z, P, N 13. 0.8 mm3 15. 4 ft3

17. 1721.9 cm3 19. 548.7 mm2 21. 45 in2 23. 37.1 in2

25. yes 27. 19.0 cm 29. 0.9 m 31. 973 ft2

Chapter 12 More Statistics andProbability

Page 605 Chapter 12 Getting Started

1. 16; 15; none 3. 5.3, 5.8, 6.5 5. �13

� 7. �12

� 9. �12

� 11. �12

�

13. �18

� 15. �16

� 17. �16

�

Pages 608–611 Lesson 12-11. Sample answer: The age of the youngest President at thetime of his inauguration was 42 and the age of the oldestPresident to be inaugurated was 69. However, most of thePresidents were 50 to 59 years old at the time of theirinauguration.

3. Stem Leaf

0 6 71 2 5 52 03 54 0 1 20 � 20

11. 13.

15.

29c. Sample answer: It would be easier to find the mode ina stem-and-leaf plot because the value or values that occurmost often are grouped together. 31. C 33. no35. 62.8 ft; 314.2 ft2 37. 247% 39. 0.65% 41. 57.1%43. 1.6% 45. 6 47. 1.1

Pages 614–616 Lesson 12-21. The range describes how the entire set of data isdistributed, while the interquartile range describes how themiddle half of the data is distributed. 3. Sample answer:{8, 9, 13, 25, 26, 26, 26, 27, 28, 30, 35, 40} 5. 27; 6 7. 24 h9. 77; 39 11. 50; 10 13. 25; 15.5 15. 22 17. Feb.: 13.5;July: 8 19. National League: 42, 44, 48, 38, 10; AmericanLeague: 39, 44, 49, 39, 10 21a. Sample answer: {43, 49, 50,50, 58, 60, 60, 66, 70, 70, 71, 78} 21b. Sample answer: {15, 18, 20, 20, 44, 60, 60, 64, 70, 70, 75, 79} 21c. Sampleanswer: The first set of data has a smaller interquartilerange, thus the data in the first set are more tightlyclustered around the median and the data in the second aremore spread out over the range. 23. C

25. Stem Leaf

0 91 2 4 5 82 1 73 7 37 � $37


5. 50, 99 7. Sample answer: Thelowest score was 50. The highestscore was 99. Most of the scoreswere in the 70–79 interval.9. Chicken; whereas chickensandwiches have 8–20 grams offat, burgers have 10–36 grams offat.

Stem Leaf

1 32 6 8 3 4 945 2 36 2 2 77 7 98 4 77 � 77

Stem Leaf

40 0 0 54142 5434445 0 6464748 0 4 7495051 052 0...62 5...76 47778 9 764 � 764

Stem Leaf

0 6 6 81 0 1 4 6 82 0 2 53 2 745 0 37 � 37

17. never 19. 73 21. Sampleanswer: In this 10-year period,most of the leaders hit between40 and 50 home runs. 23. 525. The average number of gameswon by the teams in the Big EastConference is less than theaverage number of games wonby the teams in the Big TenConference. 29a. Sampleanswer: It would be easier to findthe median in a stem-and-leafplot because the data arearranged in order from least togreatest. 29b. Sample answer: Itwould be easier to find the meanin a table because once you findthe sum, it may be easier to countthe number of items in a table.

27. 461.8 cm3 29. 1.6 ft31. {0.2, 0.3, 0.6, 0.8, 1.2, 1.4, 1.5}33. {9.8, 9.9, 10.5, 10.9, 11.2, 11.4}

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Pages 619–621 Lesson 12-31. lower quartile, least value; upper quartile, greatest value3. Sample answer: {28, 30, 52, 68, 90, 92}

5.

7. Sample answer: The length of the box-and-whisker plotshows that the winning times of the men’s marathons arenot concentrated around a certain time. 9. The most fuel-efficient SUV and the least fuel-efficient sedan both average22 miles per gallon.

11.

13.

15.

17. 50% 19. Sample answer: The least number of gameswon for NFC is 3 and the least number of games won forthe AFC is 1. The most number of games won for the NFCis 12 and the most number of games won for the AFC is 13.In addition, for both conferences, the median number ofgames won is about 9. 21. A box-and-whisker plot wouldclearly display any upper and lower extreme temperaturesand the median temperature. Answers should include thefollowing.•

• Sample answer: Tampa has a median temperature of 73and Caribou has a median temperature of 40.5. Whereasthe highest average temperature for Tampa is 82, thehighest average temperature for Caribou is 66.

• Sample answer: You can easily see how the temperaturesvary.

23. C 25. 4

27. Stem Leaf

1 42 1 4 73 94 8 24 � 24

Pages 625–628 Lesson 12-41. Sample answer: Because the intervals are continuous.

3.

5. the number of states that have a certain number of rollercoasters 7. The numbers between 10 and 34 are omitted. 9. 2 or more national monuments

11.

13.

15. 13 17. 37.5% 19. Dallas 21. true 23. false 25. true27. A 29. absolute frequency: 2, 9, 17, 12, 7, 2; relative

frequency: �429�, �

499�, �

14

79�, �

14

29�, �

17

�, �429�; cumulative frequency:

2, 11, 28, 40, 47, 49

Touchdowns in a Season

4

6

2

0

8

Nu

mb

er o

f Pl

ayer

s

10

Number of Touchdowns

114–130

148–164

97–113

131–147

165–181

80–96

Weekly Study Time

0

87654321

Nu

mb

er o

f St

ud

ents

12

109

11

Time (hr)

10–127–94–60–3 13–15

Pet Survey

10–127–94–61–3

468

10

20

18161412

20

Nu

mb

er o

f Pa

rtic

ipan

ts

22

13–15Number of Pets

Caribou, ME

Tampa, FL

10 20 30 40 50 60 70 80 900

26.0 28.0 30.0 32.0 34.0 36.0

50 70 90 110 130 150 170

60 70 80 90 100 110 120 130

14 18 22 26 30 34 38 42 46 50


29. 14

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31.

33. 44; 15 35. Sample answer: Brand B costs one-thirdmore than brand C.


1. Stem Leaf

1 6 8 9 92 0 2 6 8 8 83 0 24 0 2 3 5 5678 6 9 55 � 55

3.

5.

Pages 631–633 Lesson 12-51. Sample answer: inconsistent vertical scale and break invertical scale 3. Graph A has a break in the vertical scale.5. From the vertical scale, you can see that the number of

area codes in 1999 is about 1.5 times the number of areacodes in 1996. The graph is misleading because the drawingof the phone for 1999 is about 3 times the size of the phonefor 1996. Also, there is a break in the vertical scale.7. Graph B 9. Graph B; the vertical scale used makes thedecrease in the unemployment rates appear more drastic.11a. Sample answer:

11b. Sample answer:

13. B15.

17. 20.3 m2 19. �16

� or 16�23

�% 21. �56

� or 83�13

�%

23. �56

� or 83.3�%

Pages 637–639 Lesson 12-61. Sample answer: Both methods find the number ofoutcomes. Using the Fundamental Counting Principle isfaster and uses less space; using a tree diagram shows whateach outcome is. 3. First find the number of outcomespossible. The possible outcomes are taco-chicken, taco-beef,

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Commuter Train Passengers

Am

ou

nt

(mill

ion

s)

450

46

47

48

49

50

51

5352

54

5556

57

5859

Year’96 ’97 ’98 ’99

Commuter Train Passengers

Am

ou

nt

(mill

ion

s)

50

10

15

20

25

30

35

4540

50

5560

Year’96 ’97 ’98 ’99

60–6950–59

40–4930–39

20–29

10–19

0–9

Freq

uen

cy

70–79

80–89

Cost ($)

4

6

2

0

3

5

1

7

9

10

8

Costs

0 10 20 30 40 50 60 70 80 90 100

Average Lengthof U.S. States

900–1199

600–899

300–599

1–299

Nu

mb

er o

f St

ates

1200–1499

Length (mi)

8

12

4

0

16

24

20

10

14

6

2

18

26

22

3032

28

Source: The World Almanac


R19-R50 C1-13 SA-870424 12/10/04 3:49 AM Page R46

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taco-bean, burrito-chicken, burrito-beef, and burrito-bean,for a total of 6 outcomes. Two of the outcomes have chicken

filling, so the probability of chicken filling is �26

� or �13

�. 5. �116�

7. �14

� 9. 9

11.

8 outcomes13.

15. 36 outcomes 17. 24 outcomes19. 1024 outcomes 21. �

158� 23. �100

1,000�

25. Either; the probability of rollingeither odd or even is one-half.27. Sample answer: any two lettersfollowed by any four digits 29. D31. Sample answer: Vertical scale thatdoes not start at zero. 33. 11–20

35. 37.

39. 15 41. 28

Pages 643–645 Lesson 12-71. Sample answer: How many 3-digit numbers can be madefrom the digits 1, 2, 3, and 4 if no digit is repeated?3. Sarah; five CDs from a collection of 30 is a combinationbecause order is not important. 5. P; 120 ways 7. C; 84 ways 9. 220 pizzas 11. P; 24 flags 13. C; 105 ways15. P; 1320 ways 17. C; 364 ways 19. 40,32021. 39,916,800 23. 36 handshakes 25. 3003 ways

27. 10 combinations 29. �25

� 31. When order is not

important, duplicate arrangements are not included in thenumber of arrangements. Answers should include thefollowing.• When order was not important there were half as many

pairs. • Order is important when you arrange things in a line;

order is not important when you choose a group ofthings.

33. C 35. Yes; the vertical axis does not include zero.37. Q 39. I 41. 1:8 43. 11:2

Page 645 Practice Quiz 21. Sample answer: Bars are different widths.3. 256 outcomes 5. 15 segments

Pages 648–649 Lesson 12-81. Write a ratio comparing the ways the event can occur tothe ways the event cannot occur. 3. Hoshi; the probabilityof rolling a 2 is 1 out of 6. The odds of rolling a 2 are 1 in 5.5. 1:2 7. 5:1 9. 1:2 11. 2:1 13. 1:1 15. 1:3 17. 5:7

19. 31:5 21. 1:17 23. 5:4 25. 9:4 27. �81

192� 29. 47:53

31. No; 512 is the total number of possible outcomes, so itcould not be a number in the odds of winning. 33. A35. 6 ways37. ; a � 6

39. ; y � �3

41. �13

� 43. �516�

Pages 653–655 Lesson 12-91. Independent and dependent events are similar becauseboth are a connection of two or more simple events and theprobability of the compound event is found by multiplyingthe probabilities of each simple event. They are differentbecause the second event in a dependent event isinfluenced by the outcome of the first event. Therefore, the probability of the second event used in calculating theprobability of the compound event is dependent on theoutcome of the first event. 3. The result of the 1st event

must be taken into account. 5. �112� 7. �

134� 9. �

34

� 11. �310�

13. �15

� 15. �911� 17. �

19

01� 19. �

3564� 21. �

58

� 23. �37

� 25. 1 27. �29

�

29. 0.16 31a. Sample answer: 3 red, 2 white, and 4 blue31b. Sample answer: The numerator must be 24. Any

combination of 3, 2, and 4 will have a probability of �211�.

33. B 35. �23

� 37. 3:10 39. 17,576,000 41. 65° 43. 65°

45. 90° 47. 40.6 49. 16

Pages 658–662 Chapter 12 Study Guide and Review1. b 3. c 5. d 7.

9. 23; 7 11. 22; 10 13. 80°F 15. 50% 17. Graph A

19. 16 outcomes 21. C; 364 ways 23. C; 21 ways 25. 3:5

27. 1:3 29. �310�

Chapter 13 Polynomials and Nonlinear Functions

Page 667 Chapter 13 Getting Started1. 1 3. 2 5. 0 7. 5a � 20 9. �4 � 32n 11. 27b � 27c13. yes 15. yes

�3 �2 �1 0 21�5 �4�6

108 96 74 53

y

xO

y

xO

S

B

SB

N

SN

T

ST

W

B

WB

N

WN

T

WT

Y

B

YB

N

YN

T

YT

B

B

BB

N

BN

T

BT

H

THH

T

THT

H

TTH

T

TTT

T

H T

H

HHH

T

HHT

H

HTH

T

HTT

H

H T


12 outcomes

Stem Leaf

4 5 55 0 0 5 5 6 0 0 0 0 07 5 5 58 5 5 75 � 75¢

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Pages 670–672 Lesson 13-11. The degree of a monomial is the sum of the exponents ofits variables. The degree of a polynomial is the same as thedegree of the term with the greatest degree. 3. Tanisha; the degree of a binomial is the degree of the term with thegreater degree. 5. yes; monomial 7. yes; binomial9. yes; trinomial 11. 0 13. 1 15. 4 17. 2 19. yes;binomial 21. yes; monomial 23. no 25. yes; trinomial27. no 29. yes; trinomial 31. 0 33. 3 35. 5 37. 5 39. 341. 5 43. Always; any number is a monomial.45. 2x � 2y � z � xy 49. Polynomials approximate real-world data by using variables to represent quantities thatare related. Answers should include the following.• Heat index is found by using a polynomial in which one

variable represents the percent humidity and anothervariable represents the temperature.

• Heat index cannot be approximated using a linearequation because the values do not change at a constantrate.

51. C 53. mutually exclusive; �23

� 55. 70 in3

57. (x � 2x) � 4 59. (6n � 3n) � (2 � 5)61. (s � 5s) � (t � 3t)

Pages 676–677 Lesson 13-21. x2 and 2x2; 5x and �4x; 2 and 7 3. Hai; the terms havethe same variables in a different order. 5. 7a2 � 9a � 47. 13x � 4y 9. 4x2 � 3x � 2 11. 3x � 313. 11x2 � 5xy � 4y2 15. 4x � 14 17. 8y � 2r19. 5x2 � xy � y 21. 7x2 � 9x � 5 23. 5a � 4b; �3125. 4a � 6b � c; 14 27. 56 29. 23x � 12 31. 42x � 2233. Use algebra tiles to model each polynomial andcombine the tiles that have the same size and shape.Answers should include the following.• Algebra tiles that represent like terms have the same size

and shape. • When adding polynomials, a red tile and a white tile that

have the same size and shape are zero pairs and may beremoved. The result is the sum of the polynomials.

35. B 37. 2 39. �123� 41. �

236� 43. 15c � (�26)

45. 1 � (�2x) 47. (n � rt) � (�r2)

Pages 680–681 Lesson 13-31. Subtracting one polynomial from another is the same asadding the additive inverse. 3. 4r 5. 5x � 27. 3x2 � 3x � 8 9. 7x � 5 units 11. �2n2 � 6n13. y2 � 7y � 10 15. 15w2 � 2w � 10 17. 4x � 319. �2t � 2 21. 3a2 � 2b2 23. 9n2 � n � 1225. 2x2 � 2xy � 3y2 27. x � y � 68 � (x � y); �34°F29. In subtracting polynomials and in subtractingmeasurements, like parts are subtracted. Answers shouldinclude the following.• To subtract measurements with two or more units,

subtract the like units. To subtract polynomials with twoor more terms, subtract the like terms.

• For example, to subtract 1 foot 5 inches from 3 feet 8 inches, subtract the feet 3 � 1 and subtract the inches 8 � 5. The difference is 2 feet 3 inches.

31. B 33. 12x � 3y 35. �t2 � 12t � 2 37. yes; binomial39. Stem Leaf

5 4 96 4 6 87 0 1 1 28 5 99 1 54 � 54

Page 681 Practice Quiz 11. 4 3. 3 5. 2x � 2 7. 8r � 3s 9. �3x � 5y

Pages 684–686 Lesson 13-41. False; the order in which numbers or terms aremultiplied does not change the product, by theCommutative Property of Multiplication; x(2x � 3) � 2x2 � 3x and (2x � 3)x � 2x2 � 3x. 3. Sampleanswer: 2x(x � 1) � 2x2 � 2x 5. a2 � 4a 7. 12x2 � 28x9. �15x2 � 35x � 45 11. 14n � 35 13. t2 � 9t15. �7a2 � 6a 17. 40n � 8n2 19. 3y3 � 6y 21. 5x2 � 5xy23. �14x2 � 35x � 77 25. 4c4 � 28c2 � 40c 27. –129. high school, 84 ft by 50 ft; college, 94 ft by 50 ft

31. 33. D 35. 7x � 137. 4y2 � 2y � 1439. 8x � 11y

(a � b)(c � d) � ac � ad � bc � bd41. Sample answer: The scales are labeled inconsistently or the bars on a bar graph are different widths.43. reflection

45.

Pages 689–691 Lesson 13-51. Sample answer: Determine whether an equation can bewritten in the form y � mx � b or look for a constant rate ofchange in a table of values. 3. Sample answer: populationgrowth 5. Nonlinear; graph is a curve. 7. Nonlinear;equation cannot be written as y � mx � b. 9. Linear; rateof change is constant. 11. Nonlinear; graph is a curve.13. Linear; graph is a straight line. 15. Nonlinear; graph isa curve. 17. Linear; equation can be written as y � 0.9x � 0. 19. Linear; equation can be written as

y � �34

�x � 0. 21. Nonlinear; equation cannot be written as

y � mx � b. 23. Linear; rate of change is constant.25. Nonlinear; rate of change is not constant.27. Nonlinear; the points (year, subscribers) would lie on acurved line, not on a straight line. Or, the rate of change isnot constant. 29. No, the difference between the yearsvaries, so the change is not constant. 31. A 33. 4t � 9t2

35. a2b � 2ab2 37. �x 39. acute

41. 43.

x

y

O

y � � x � 312

x

y

O

y � x � 4

a

�b

adac

bdbc

c � d


41. 8y2 43. 4m3 45. 10r5

0 �3 (0, �3)

1 �1 (1, �1)

2 5 (2, 5)

3 15 (3, 15)

x 2x2 � 3 (x, y)

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Page 691 Practice Quiz 21. 2c3 � 8c 3. 5a2 � a3 � 2a4 5. Nonlinear; equationcannot be written as y � mx � b.

Pages 694–696 Lesson 13-61. Sample answer: The graph of y � nx2 has line symmetryand the graph of y � nx3 does not. 3. Sample answer: y � x2 � 3; make a table of values and plot the points.

5. 7.

9. 11.

13. 15.

17. 19.

21.

23.

Both equations are functions because every value of x ispaired with a unique value of y.25. (0, 7)27. Similar shape; y � 3x2 is

more narrow.

29. Same shape; y � �2x2

is y � 2x2 reflected over thex-axis.

31. A � 50x � x2 33. 25 ft by 25 ft35. V � 0.2�r2 or V � 0.6r2

37. Formulas, tables, and graphs are interchangeable waysto represent functions. Answers should include thefollowing. • To make a graph, use a rule to make a table of values.

Then plot the points and connect them to make a graph. • To write a rule, find points that lie on a graph and make

a table of values using the coordinates. Look for apattern and write a rule that describes the pattern.

39. C 41. Sample answer: 18 units2 43. 10x � 2045. 24y � 21y2 47. y � 4x � 3

Pages 698–700 Chapter 13 Study Guide and Review1. trinomial 3. cubic 5. like terms 7. curve 9. yes;binomial 11. yes; monomial 13. yes; trinomial 15. no

r

V

V � 0.6r 2

1110987654321

0 3 5 761 2 4

y

xO

y � �2x 2

y � 2x 2

y

xO

y � x 2y � 3x 2

y

xO

y � �4x 3

y

xO

y � x 2 � 4

y

xO

12y � x 2 � 1

y

xO

y � x 3 � 1

y

xO

y � 2x 3

y

xO

y � �2x 3

y

xO

y � �x 2

y

xO

y � 3x 2

y

xO

y � x 3� 2

y

xO

y � �x 3

y

xO

y � �2x 2


R19-R50 C1-13 SA-870424 12/10/04 3:51 AM Page R49

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17. 1 19. 3 21. 6 23. 5 25. 8b � 3 27. 5y2 � 2y � 429. y2 � y � 1 31. 3x2 � 4x � 7 33. �x � 1 35. 20t � 1037. 6k2 � 3k 39. �18a � 2a3 41. Linear; graph is a straightline. 43. Nonlinear; rate of change is not constant. 45. 47.

49. y

xO

y � 2x 2 � 4

y

xO

y � x 3 � 1

y

xO

y � �3x 2


R19-R50 C1-13 SA-870424 12/10/04 3:51 AM Page R50

Photo Credits R51

Photo CreditsP

hoto

Cre

dits

About the CoverThe Great Bear at Hersheypark in Hershey, Pennsylvania, is an inverted coaster – that is, you ridebelow it, not above it. With four inversions, including loops, twists, and rolls, this ride reaches aspeed of almost 60 miles per hour and at one point falls 124 feet. Roller coasters use math in theirdesign and operation from beginning to end. Their designers want to make the tallest, fastest,most exciting coasters ever!

Cover Alan Schein/CORBIS Stock Market; ix Tom Pidgeon/Getty Images, x Roy Ooms/Masterfile; xi David Young-Wolff/PhotoEdit; xii Robert Fried/Stock Boston; xiii KayChernush/Getty Images; xiv Tony Demin/ InternationalStock; xv Douglas Faulkner/Photo Researchers; xvi ChrisCole/DUOMO; xvii Adam Jones/ Photo Researchers; xviii SuperStock; xix Georgette Douwma/Getty Images; xx Matt Meadows; xxi Antonio M. Rosario/Getty Images; 1 Laura Sifferlin; 2-3 Ken Chernus/Getty Images, (bkgd)CORBIS; 4-5 ZSSD/SuperStock; 10 Doug Martin; 15 TomPidgeon/Getty Images, 19 TempSport/CORBIS; 27 KenEward/Photo Researchers; 31 Erik Dreyer/Getty Images;35 Michael Boys/CORBIS; 37 Rhoda Sidney/Stock Boston;42 Galen Rowell/CORBIS; 54–55 Jeff Hunter/GettyImages; 57 Jonathan Daniel/Getty Images; 66 NASA; 73Doug Martin; 78 Mike Mazzaschi/ Stock Boston; 96–97 JanButchofsky-Houser/CORBIS; 99 AP/Wide World Photos;105 Kit Kittle/CORBIS; 106 Mary Kate Denny/PhotoEdit;112 file photo; 116 Stuart Westmorland/CORBIS; 123 IndexStock/Eric Kamp; 127 David Young-Wolff/PhotoEdit; 129Dwayne Newton/ PhotoEdit; 131 PhotoDisc; 134AFP/CORBIS; 144-145 Getty Images, (bkgd) CORBIS;146–147 Thomas Mangelsen/ Minden Pictures; 149Elizabeth Whiting & Associates/ CORBIS; 151 AaronHaupt; 156 Christophe Loviny/ CORBIS; 165 AP/WideWorld Photos; 172 Geoff Butler; 178 Laura Sifferlin; 180Latent Image; 182 Ralph A. Clevenger/CORBIS; 184VCG/Getty Images; 189 Robert Fried/Stock Boston;198–199 SuperStock; 208 Lester Lefkowitz/CORBIS StockMarket; 214 JPL/ NASA; 217 Tony Anderson/GettyImages; 219 David Barnes/CORBIS Stock Market; 220 JohnCancalosi/Stock Boston; 223 Tony Freeman/PhotoEdit; 229NASA; 231 237 Geoff Butler; 247 Andy Caulfield/GettyImages; 253 (t)Kay Chernush/Getty Images, (b)GeoffButler; 262–263 SuperStock; 267 Chuck Pefley/ StockBoston; 272 Louisville Slugger Museum, Louisville, KY; 275Matt Meadows; 276 (t)Landscape plans provided byGreenscapes Landscape Architects and Contractors,Columbus, OH, (bl)Matt Meadows, (br)Ron Kimball/RonKimball Stock; 277 Kunio Owaki/CORBIS Stock Market;278 Jeff Greenberg/Southern Stock/ PictureQuest; 284Gary White Photography/StockFood; 288 Geoff Butler; 296Frans Lanting/Minden Pictures; 299 TonyDemin/International Stock; 306 Michael Paras/International Stock; 324-325 Mark Richards/PhotoEdit,(bkgd) Jon Arnold Images/Alamy; 326–327 MichaelMelford/Getty Images; 331 SW Productions/IndexStock/Picturequest; 337 Matt Meadows; 344 BobDaemmrich/Stock Boston; 347 Bob Daemmrich; 348Douglas Faulkner/Photo Researchers; 356 SuperStock; 358

Doug Martin; 366-367 Paul J. Sutton/Duomo/CORBIS; 370Peter/Stef Lamberti/Getty Images; 383 DavidKeaton/CORBIS Stock Market; 386 Matt Meadows; 387Tony Freeman/PhotoEdit; 392 Doug Martin; 395NASA/JSC; 399 Cris Haigh/Getty Images; 401 DUOMO;408 Gail Shumway/Getty Images; 412 MichaelSteele/Allsport; 417 Chris Cole/DUOMO; 422 RoyOoms/Masterfile; 432-433 Jeff Hunter/Getty Images,(bkgd) Ken Biggs/Getty Images; 434-435 RichardCummins/CORBIS; 438 Kunio Owaki/CORBIS StockMarket; 444 Kennan Ward/CORBIS Stock Market; 456Garry Gay/ImageBank; 463 Steven E. Sutton/DUOMO; 472Geoff Butler; 474 Adam Jones/Photo Researchers; 480David Young-Wolff/ PhotoEdit; 490–491 J. DavidAndrews/Masterfile; 500 SuperStock; 503 ChuckSzymanski/International Stock; 511 Pete Saloutos/CORBISStock Market; 513 Richard Hamilton Smith/CORBIS; 515(l)Pat LaCroix/Getty Images, (r)Irene Rica Pereira. Untitled,1951. Oil on board, 101.5 � 61 cm (40 � 24 in.). Solomon R.Guggenheim Museum, New York, NY. Gift of Jerome B.Lurie, 1981; 516 Elizabeth Murray. Museum of Modern Art,New York, NY. Acquired through the Bernhill Fund. Gift ofAgnes Gund; 524 SuperStock; 529 Papilio/CORBIS; 530Roy Lichtenstein. Modern Painting with Clef, 1967. Oil onsynthetic polymer and pencil on canvas.

252.4 � 458.2 (100�18

� � 180�38

� in.)Hirshhorn Museum and

Sculpture Garden, Smithsonian Institution; 537 Charles E.Rotkin/ CORBIS; 552–553 Rohan/Getty Images; 556EyeWire, Yann Arthus-Bertrand/CORBIS; 558 WalterBibikow/Getty Images; 560 (t)SHOE 8/31/94 ©TribuneMedia Services. All Rights Reserved. Reprinted bypermission, (bl)Roberto Otero/Black Star/PictureQuest,(br)Hermitage Museum, St. Petersburg, Russia/SuperStock;575 Bob Mullenix; 578 SuperStock; 579 Bob Daemmrich;581 (l)John Elk III/ Stock Boston, (r)John Elk III/StockBoston; 583 Matt Meadows; 584 Aaron Haupt; 586 NASA;602-603 Getty Images, (bkgd) Richard Price/Getty Images;604-605 Mike Dobel/Masterfile; 607 610 CORBIS; 614Eastcott/Momatiuk/Getty Images; 634 David Young-Wolff/PhotoEdit; 638 Michael Zito/ SportsChrome USA;640 Aaron Haupt; 644 Mark Burnett; 649 Aaron Haupt; 651Matt Meadows; 654 CORBIS; 656 Aaron Haupt; 666–667(bkgd)Digital Stock, David Madison Sports Images; 670Raymond Gehman/CORBIS; 675 Antonio M.Rosario/Getty Images; 683 Dallas & John Heaton/CORBIS;685 Bettmann/CORBIS; 693 Photri/Tom Sanders/CORBISStock Market; 793 William Floyd Holdman/Index StockImagery.

R51_Photo Credits-870424 12/10/04 5:36 AM Page R51

IndexIn

dex

R52 Index

Absolute frequencies, 627

Absolute value, 58, 59, 61, 63, 64, 65, 66, 91algebraic expressions, 58integers, 90

Accuracy, 589

Activity. See Algebra Activity;Geometry Activity

Acute angles, 449, 450, 451, 457,484, 745

Acute triangles, 454, 456, 746

Addends, 63, 64, 66

Addition, 11, 16, 726, 734, 735, 756algebraic fractions, 221Associative Property, 24, 26, 49,

63, 66, 130, 725Commutative Property, 23, 26,

32, 49, 63, 66, 107, 114, 725decimals, 5, 538, 712, 713fractions, 220, 233, 716integers, 62–63, 64–66, 74, 82, 84,

91, 97, 107, 199, 327like fractions, 220–224, 256measurements, 591–592mixed numbers, 220, 233, 491,

716polynomials, 674–677, 699properties, 672solving equations, 111–112, 113,

139, 244solving inequalities, 345–349unlike fractions, 232–236, 257

Addition expressions, 97, 102, 677

Addition Property of Equality, 111,360

Addition table, 63

Additive identity, 24, 48, 49, 66

Additive inverse, 66, 67, 70, 71, 72,91, 112, 114, 677, 679, 681, 699

Adjacent angles, 476, 493, 495

Algebra ActivityAnalyzing Data, 237Area and Geoboards, 518–519Base 2, 158Capture-recapture, 275Constructions, 498–499Dilations, 512Equations with Variables on Each

Side, 328–329

Fibonacci Sequence, 253Graphing Irrational Numbers,

465Half-Life Simulation, 180Input and Output, 367It’s All Downhill, 386Juniper Green, 231Modeling Multiplication, 682Modeling Polynomials with

Algebra Tiles, 673Probability and Pascal’s Triangle,

640Pythagorean Theorem, 458–459Ratios in Right Triangles, 476Scatter Plots, 39Simulations, 656–657Slope and Rate of Change, 392Solving Equations using Algebra

Tiles, 108–109Symmetry, 505Taking a Survey, 309Tessellation, 532Using a Percent Model, 286–287

Algebra Connection, 25, 35, 58, 77,150, 161, 166, 170, 176, 181, 211,217, 221, 227

Algebraic equations, solving, 30,31, 118, 130, 136, 152, 157, 163,219, 230, 235, 242, 246, 248, 252,328–329, 330–333, 338, 344, 349,443, 444, 457, 484, 685

Algebraic expressions, 17, 19, 69,99, 667absolute value, 58evaluating, 17, 19, 20, 27, 32, 38,

44, 48, 51, 55, 59, 60, 68, 72, 73,74, 77, 78, 79, 82, 83, 84, 89, 93,118, 147, 155, 156, 168, 170, 182,185, 190, 213, 218, 222, 223, 235,338, 373

factoring, 166, 167, 193finding value, 27, 32, 48, 74, 457identify parts, 104simplifying, 25, 26, 27, 32, 44, 48,

51, 77, 78, 84, 89, 100, 103–107,118, 139, 147, 157, 213, 224, 439

translating verbal phrases into,18, 19, 20, 32, 74, 105, 724

writing, 20, 97, 124, 125

Algebraic fractions, 211addition, 221division, 217lowest common denominator, 227multiplication, 211simplifying, 169–173, 185, 193

Algebraic relationships, graphing,87

Algebra tiles. See also Modelingadding integers, 62–63algebraic expressions, 103, 106Distributive Property, 99equations with variables on each

side, 328–329multiplication, 682multiplication, polynomials by

monomial, 683polynomials, 673, 674, 677properties of equality, 120, 123representing expressions, 103solving equations, 108–109solving two-step equations, 120

Alternate exterior angles, 492, 493

Alternate interior angles, 492, 493

Altitude, 520

Angles, 447–451, 484acute, 449, 450, 451, 457, 484, 745adjacent, 476, 493, 495alternate exterior, 492, 493alternate interior, 492, 493central, 452, 538complementary, 493, 494, 495,

496, 517, 544congruent, 493corresponding, 474, 492, 493, 500,

544of elevation, 480exterior, 492, 531inscribed, 538interior, 492, 528, 530, 538, 543measurement, 447, 448measures, 448, 454obtuse, 449, 450, 451, 457, 484,

745quadrilateral, 514right, 449, 450, 451, 457, 484, 745straight, 447, 449, 450, 451, 457,

484, 745supplementary, 494, 495, 496vertical, 493, 495

Applications. See also Cross-Curriculum Connections; More Aboutaccounting, 67aerospace, 759ages, 128aircraft, 172air pressure, 37animals, 172, 184, 229, 266, 306,

619, 639

A

R52-R67-Index-870424 12/10/04 4:09 AM Page R52

Index

Index R53

aquariums, 576architecture, 277, 479, 558, 579,

580, 581, 587, 626, 769, 770art, 463, 509, 515, 516, 530astronauts, 606astronomy, 759, 761auto racing, 229aviation, 765, 766baking, 768ballooning, 134banking, 300, 301baseball, 450, 615–616, 766baseball cards, 739basketball, 83, 241, 337, 761batteries, 567bicycles, 536bicycling, 135birds, 291, 758birthdays, 106blood types, 655books, 291, 766boxes, 685brand names, 763breakfast, 202bridges, 767buildings, 480, 559business, 16, 21, 73, 123, 190, 247,

301, 307, 384, 399, 400, 421, 760,761, 763, 765, 769

calculators, 301calendars, 151camping, 768candy, 10, 358, 763carpentry, 167, 218, 390car rental, 332, 358, 765cars, 251car sales, 764catering, 385celebrations, 290, 291census, 764city planning, 767codes, 761college, 762comics, 560communication, 10, 185, 631community service, 134computers, 177, 203, 638construction, 589, 695, 766, 770consumerism, 769cooking, 218, 247, 516, 763crafts, 421, 576cruises, 107currency, 273cycling, 228decorating, 768design, 277, 279–280, 321driving, 313earnings, 353earthquakes, 177, 761ecology, 670

economics, 761, 769education, 618elections, 113electricity, 761employment, 758, 762energy, 83, 179engineering, 566entertainment, 36, 141, 391, 411,

415, 421, 760, 769environment, 289farming, 372fast food, 763fencing, 760ferris wheel, 763finance, 677, 765fish, 291fitness, 450flags, 523floods, 78flooring, 444flowers, 644food, 21, 48, 219, 284, 296, 301,

608, 626, 643, 758, 762food costs, 397food service, 129, 637football, 64, 67forestry, 297fuel, 765fund-raising, 358, 581furniture, 762games, 516, 638, 653, 726, 759gardening, 15, 213, 223, 429gardens, 279golf, 67grilling, 235grocery shopping, 764handshakes, 644health, 9, 248, 610, 762, 763height, 31, 141highway maintenance, 570hiking, 358hobbies, 312home improvement, 540home repair, 252, 390homework, 343, 769hourly pay, 240houses, 234insects, 279interior design, 761Internet, 764, 770kites, 765landmarks, 473landscape design, 540landscaping, 135, 502, 672lawn care, 524license plates, 644light bulbs, 136literature, 163lunchtime, 761machinery, 209magazines, 267

maintenance, 766manufacturing, 208, 767, 768, 770maps, 88, 292, 472, 473, 759masonry, 592measurement, 118, 171, 172, 183,

189, 207, 213, 222, 372, 378, 593,762

measurement error, 593media, 283medicine, 10, 122, 184, 671metals, 566meteorology, 128, 157, 246, 759microwaves, 567military, 133mining, 572mirrors, 511models, 768money, 9, 10, 51, 100, 105, 152,

173, 295, 296, 357, 385, 409, 754, 759, 762, 763

monuments, 537, 768movies, 101, 632moving, 767music, 151, 536Native Americans, 129newspapers, 758nutrition, 239, 341, 762, 763, 765oceanography, 74oil production, 762olympics, 128, 273, 619, 624online service, 762paint, 274painting, 118parades, 167parks, 474patterns, 758, 761pet care, 768pets, 73, 763phone calling cards, 123phone services, 358photography, 272, 273picnics, 407pools, 123, 577, 684population, 68, 114, 129, 302, 307,

735, 770postal service, 7, 724presents, 768presidents, 629pressure, 411production, 770public safety, 767publishing, 15, 235, 246, 762purchasing, 760quilts, 504racing, 449reading, 631real estate, 301, 525recreation, 479, 766remodeling, 762rides, 475roller coasters, 279, 439, 625

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R54 Index

running, 135safety, 343, 480, 495, 496sailing, 766salaries, 242sales, 21, 121, 135, 358, 363, 418,

758savings, 303, 347school, 42, 107, 185, 203, 213, 307,

358, 413, 420, 537, 608, 631, 764school colors, 642school concert, 765school supplies, 106sewing, 218, 223, 235, 259shadows, 473, 480shapes, 767shipping, 679, 768shipping rates, 765shoes, 283shopping, 26, 101, 106, 265, 267,

300, 363, 376, 760, 763, 764signs, 767skyscrapers, 438snacks, 274soccer, 353sound, 155space, 187, 188, 189, 296, 758space exploration, 758space shuttle, 16, 19space travel, 212spending, 411sports, 93, 101, 238, 301, 515, 542,

759, 760, 764statistics, 83, 686, 764statues, 279submarines, 759surveying, 766surveys, 243swimming, 410, 641technology, 393, 411, 744telecommunications, 690telephone rates, 251telephones, 229television, 463, 769temperature, 78tennis, 685tepees, 768tessellations, 529tests, 241test scores, 40time, 9, 449towers, 502toys, 117traffic laws, 614trains, 247transportation, 10, 14, 204, 348,

760, 761, 767travel, 8, 15, 16, 134, 156, 212,

219, 259, 267, 594, 620, 630, 632,760, 766

trees, 534, 758trucks, 202

utilities, 766vacations, 241, 625volleyball, 753, 758, 769voting, 235walkways, 542water parks, 623weather, 59, 60, 71, 72, 73, 83, 89,

93, 113, 248, 307, 333, 348, 371,608, 615–616

weather records, 79white house, 208wildlife, 129working, 760world cultures, 769write a problem, 130

Approximations, 594, 672

Area, 132, 137, 518–519. See alsoSurface areacircles, 533–538, 548, 749irregular figures, 539–543, 548parallelograms, 520, 547rectangles, 132, 133, 134, 135, 140,

141, 152, 214, 224, 349, 671, 730,767

square, 523trapezoids, 521, 522–523, 547triangles, 521, 522, 523, 547

Arithmetic sequences, 249–252, 258,259, 268, 344, 736

AssessmentExtended Response, 53, 95, 143,

197, 261, 323, 365, 431, 489, 551,601, 665, 703

Multiple Choice, 52, 94, 142, 196,260, 322, 364, 430, 488, 550, 600,664, 702

Open Ended, See ExtendedResponse

Practice Chapter Test, 51, 93, 141,195, 259, 321, 363, 429, 487, 549,599, 663, 701

Practice Quiz, 21, 32, 74, 84, 107,130, 163, 185, 224, 248, 292, 308,338, 354, 397, 418, 451, 470, 517,538, 572, 588, 628, 645, 681, 691

Prerequisite Skills, 5, 10, 16, 21,27, 32, 38, 55, 61, 68, 74, 79, 84,97, 102, 107, 114, 119, 124, 130,147, 152, 157, 163, 168, 173, 179,185, 199, 204, 209, 213, 219, 224,230, 236, 242, 248, 263, 268, 274,280, 285, 292, 297, 302, 308, 327,333, 338, 344, 349, 354, 367, 373,379, 385, 391, 397, 401, 408, 413,418, 435, 440, 445, 451, 457, 464,470, 475, 491, 497, 504, 511, 517,525, 531, 538, 553, 561, 567, 572,577, 582, 588, 605, 611, 616, 621,628, 633, 639, 645, 649, 667, 672,677, 681, 686, 691, 706–723

Short Response/Grid In, 53, 95,124, 143, 197, 261, 323, 354, 365,431, 489, 517, 531, 537, 551, 601,665, 703

Standardized Test Practice, 10,16, 21, 29, 30, 32, 39, 44, 51, 61,68, 74, 76, 77, 79, 84, 89, 93, 102,107, 112, 113, 114, 119, 124, 130,136, 141, 152, 157, 163, 168, 171,173, 179, 184, 190, 204, 209, 213,219, 224, 230, 236, 240, 241, 242,247, 252, 259, 268, 274, 280, 285,292, 297, 302, 305, 306, 308, 314,321, 333, 338, 344, 349, 351, 353,354, 359, 363, 373, 379, 385, 389,390, 391, 397, 401, 408, 413, 418,422, 429, 440, 445, 451, 457, 461,462, 464, 470, 475, 481, 487, 494,495, 497, 504, 511, 517, 525, 531,537, 543, 549, 561, 564, 566, 567,572, 577, 582, 588, 594, 599, 611,616, 621, 627, 633, 639, 645, 647,648, 649, 655, 663, 672, 677, 681,686, 689, 691, 695, 701

Test-Taking Tips, 29, 52, 76, 95,143, 171, 196, 240, 305, 322, 351,364, 389, 430, 461, 488, 494, 550,564, 600, 647, 664, 689, 702. Seealso Preparing for StandardizedTests

Associative Property ofMultiplication, 24, 26, 49, 51, 76,78, 114, 522, 725

Average (mean), 82, 92

Backsolving, 29, 112

Back-to-back stem-and-leaf plots,607–608, 609, 611

Bar graphs, 722–723

double, 722–723

misleading, 631

Bar notation, 201

Base 2 numbers, 158

Base 10 numbers, 158

Bases, 153, 290, 299, 520, 557, 559,570, 595, 599

Best-fit lines, 409–413, 427, 429

Bias, 634

Bilateral symmetry, 505

Binary numbers, 158

Binomials, 669, 671, 676, 681, 698,755

Box-and-whisker plots, 617–621,622, 633, 659, 753

B

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Index R55

double, 619drawing, 619, 620interpretation, 618–619

Brackets [ ], as grouping symbol, 12

Cake method, 161

Calculator skills, 437, 438, 439, 478,479, 480, 497, 504, 531, 534, 561.See also Graphing CalculatorInvestigation

Career Choicesarchitect, 579artist, 515biologist, 42business owner, 399carpenter, 223cartographer, 472civil engineer, 480ecologist, 670interior designer, 278marine biologist, 348meteorologist, 129musician, 172real estate agent, 358statistician, 649veterinarian, 73

Center, circles, 533

Central angles, 452, 538

Challenge. See Critical Thinking:Extend the Activity; Extendingthe Lesson

Change, rate of, 393–397, 426

Checking reasonableness, 82, 586,684

Checking solutions, 99, 111, 113,116, 117, 118, 121, 122, 123, 124,130, 136, 141, 152, 157, 163, 176,201, 204, 212, 217, 230, 242, 245,246, 248, 252, 258, 297, 330, 331,332, 334, 335, 336, 338, 346, 347,351, 352, 353, 354, 355, 356, 359,360, 373, 377, 379, 382, 406, 413,414, 420, 437, 438, 454, 514, 561,588, 689, 729, 736, 739, 740, 741

Chords, 538

Circle graphs, 451, 452

Circlesarea, 535–538, 548, 749center, 533circumference, 533–538, 548, 749diameter, 533, 536, 749pi, 208, 533, 534radius, 533, 536, 749

Cicumferencecircles, 533–538, 548, 749

Closure Property, 27

Coefficients, 103, 104, 105, 106negative, 122, 161

Columns, 705

Combinations, 642–643, 644, 661, 754notation, 643

Commission, 301

Common Misconceptions, 58, 132,154, 175, 355, 420, 449, 467, 507,557, 591, 617. See also Find theError

Common multiples, 226

Common ratios, 250, 251, 258

Commulative, 23

Communicationchoose, 592classify, 529compare and contrast, 228, 251,

312, 455, 549, 637, 643, 653, 674define, 19, 36, 59, 105, 207, 272,

300, 468, 523, 614describe, 202, 234, 283, 371, 389,

395, 429, 515, 559, 580, 589, 599,653, 680, 689, 694

determine, 150, 272, 684display, 608draw, 222, 266, 549estimate, 295explain, 59, 83, 87, 117, 122, 133,

141, 150, 155, 161, 166, 171, 177,188, 202, 217, 241, 266, 295, 300,306, 342, 347, 377, 384, 407, 410,416, 421, 438, 443, 468, 495, 502,529, 570, 575, 580, 586, 614, 619,625, 637, 648, 670, 684, 689, 694

find, 228, 241, 540identify, 207, 608list, 42, 51, 128, 336, 353, 421, 438,

570name, 36, 42, 246, 332, 449, 455,

631, 676replace, 228state, 67, 77, 117, 141, 177, 251,

400, 429tell, 9, 14, 26, 30, 113, 312, 529,

535, 619write, 19, 51, 77, 133, 207, 357,

421, 509, 540

Commutative Property of Addition,23, 26, 32, 49, 63, 66, 107, 114, 725

Commutative Property ofMultiplication, 23, 26, 49, 61, 75,78, 522, 725

Compare and orderdecimals, 710fractions, 228integers, 57, 59numbers in scientific notation,

188percents, 283, 284real numbers, 442

Complementary angles, 493, 494,495, 496, 517, 544

Complex solids, volume, 564

Composite numbers, 159, 161, 162,192, 229, 285, 731

Compound events, 650–655, 662

Compound interest, 303

Computation, choosing method, 8

Concept Summary, 41, 47, 48, 49,50, 82, 90, 91, 92, 138, 139, 140,148, 154, 191, 192, 193, 194, 207,254, 255, 256, 257, 258, 289, 293,298, 316, 317, 318, 319, 320, 341,360, 361, 362, 377, 416, 424, 425,426, 427, 428, 442, 483, 484, 485,486, 495, 544, 545, 546, 547, 548,595, 596, 597, 598, 658, 659, 660,661, 662, 688, 698, 699, 700

Cones, 569diameter, 571radius, 571surface area, 578–582, 597volume, 568–572, 596, 616

Congruence statements, 501, 502,503, 511, 517, 545, 549

Congruent angles, 493

Conjectures, 7, 12, 22, 25, 26, 32, 38,39, 63, 137, 155, 162, 175, 180, 204,215, 253, 275, 303, 368, 386, 392,393, 445, 453, 476, 512, 563, 583,584, 640, 697

Constants, 103, 104, 105, 106proportionality, 394variation, 394, 395

Constructed Response. SeePreparing for Standardized Tests

Constructions, 498–499

Converting measurements, 397, 566

Coordinate plane, 45, 57, 87, 88, 89,92, 93, 124, 728reflections, 508rotations, 509transformations, 506–511, 545–546translations, 507

C

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R56 Index

Coordinates, 69, 468, 486

Coordinate system, 33–34, 36, 38,39, 44, 50, 51, 79, 85–89, 92, 367,475, 504, 725

Corresponding parts, 471, 500, 501,502, 503

Cosine, 477–481, 486, 747

Counterexamples, 25, 26, 27, 73,208, 444, 510, 684

Counting outcomes, 661, 635, 639

Critical Thinking, 10, 16, 21, 27, 32,37, 44, 60, 61, 68, 73, 78, 84, 89,102, 107, 114, 119, 124, 130, 135,152, 157, 163, 168, 173, 179, 184,190, 204, 209, 213, 219, 223, 230,236, 242, 247, 251, 268, 274, 280,284, 285, 292, 297, 302, 307, 314,333, 338, 344, 348, 354, 358, 373,379, 385, 391, 397, 401, 408, 412,417, 422, 440, 445, 450, 457, 464,469, 475, 481, 497, 504, 511, 517,525, 531, 537, 543, 560, 567, 572,577, 581, 587, 593, 610, 616, 621,627, 633, 639, 644, 649, 654, 672,677, 680, 685, 690, 695

Cross-Curriculum Connections. Seealso Applications; More Aboutbiology, 42, 156, 761chemistry, 68, 178, 768earth science, 235, 383geography, 60, 73, 208, 284, 296,

332, 524, 543, 617, 759, 767geology, 571, 758, 759history, 151, 156, 168, 537, 570,

587, 766, 768life science, 178, 291physical science, 184, 190, 251, 396physics, 765, 766science, 20, 27, 36, 37, 45, 131,

291, 378, 438, 536, 571, 614, 696,760, 761

Cross products, 270, 271, 272

Cubes, 584surface area, 157, 694volume, 157

Cubic functions, 688graphing, 692–696, 700

Cubic units, 575

Cumulative frequencies, 627

Customary system, 118converting measurements,720–721, 734

Cylinderssurface area, 573–577, 597volume, 563–567, 596

Dataanalysis, 39, 180, 237, 240, 253, 275,

386, 392, 562, 583, 640, 656, 657box-and-whisker plots, 633, 659,

753collecting, 39, 180, 237, 253, 275,

369, 386, 392, 562, 583, 640, 656,657

comparisons, 269display, 606, 722–723frequency tables, 627histograms, 623–628, 629, 633,

660, 753line plot, 239matrices, 414, 669, 705mean, 82, 92, 238–239, 240, 248,

252, 258, 605, 618, 735median, 238–239, 240, 248, 252,

258, 605, 611, 615, 618, 735mode, 238–239, 240, 248, 252, 258,

605, 735modeling, 657patterns, 22scatter plots, 39, 40–42, 43, 45–46,

50, 61, 68, 107, 408, 410, 411,412, 422, 427, 429, 726

stem-and-leaf plots, 606–611, 658,681, 752

Decimal numbers, 158

Decimals, 206, 281–285, 318, 435addition, 5, 538, 712, 713comparison with fractions, 202division, 242, 714, 715estimating, 5multiplication, 263, 491, 714, 715with negative exponents, 183ordering, 616, 710repeating, 201, 202, 203, 206, 214,

224, 254, 338, 733rounding, 588, 711subtraction, 5, 712, 713terminating, 200, 203, 206writing as fractions or mixed

numbers, 207, 208, 224, 254, 422,733

writing as percents, 282–283, 297,302

writing fractions as, 200–209, 214,338, 475

writing mixed numbers as, 209,214

Decision making. See CriticalThinking; Problem solving

Deductive reasoning, 25, 107

Degrees, 448

Density, 566

Dependent events, 652

Dependent variable, 375

Diagonals, 528, 558

Diametercircles, 533, 536cones, 571

Differences, 13, 21, 61, 70, 71, 72,73, 74, 84, 91, 93, 118, 230, 235,242, 256, 257, 327, 349, 605, 712,716, 727, 734, 735, 756. See alsoSubtraction

Dilations, 512

Dimensional analysis, 212, 213,217, 266, 267, 280

Dimensions, 705

Direct variation, 394

Discounts, 299, 308, 738

Distance, 746

Distance Formula, 131, 212,466–470, 485–486

Distributive Property, 98–102, 104,107, 138, 147, 163, 164, 166, 185,193, 209, 333, 334, 338, 349, 361,667, 683, 686, 699, 728

Divisibility Rules, 148, 149, 150,151, 157, 191, 730

Division, 11decimals, 242, 714, 715integers, 80–84, 92, 114, 199, 327negative numbers, 351–352notation, 13positive numbers, 350–351rational numbers, 215–219, 256solving equations, 115–119, 139,

245, 435solving inequalities, 350–354

Division expressions, 117

Division Property of Equality, 115

Division sentence, 80

Divisor, 69

Domain, 35, 36, 37, 38, 44, 50, 51,136, 367, 725

Double bar graphs, 722–723

Double box-and-whisker plots, 619

Double line graphs, 722–723

Edges, 556, 557, 559, 595, 599

Element, 705

Endpoints, 468, 469, 481, 486, 527, 746

Enrichment. See Critical Thinking;Extend the Activity; Extendingthe Lesson

D

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Index R57

Equals sign, 126

Equations, 28, 49, 96–143, 126, 326.See also Algebraic equations;Linear equations; Percentequations; Systems of equations;Two-step equationsgraphing, 691identifying functions, 687–688negative coefficients, 122solving, 28–29, 49, 68, 113, 118,

121, 122, 123, 124, 141, 157, 443,491, 511, 588, 725, 729, 730, 736,739, 740, 744, 745addition, 111–112, 139division, 115–119, 139, 435with grouping symbols,334–338, 361by multiplication, 115–119, 139rational numbers, 244–248, 258subtraction, 110–111, 139variables on each side, 330–333,360

solving systems, 414–418, 428solving two-step, 120–122, 140,

327, 354, 451translating verbal sentences into,

30, 125writing inequalities, 340–342writing linear, 404–408, 427writing two-step, 126–130

Equilateral figures, 517

Equivalent equations, 104, 111

Equivalent expressions, 98

Error Analysis. See Find the Error;Common Misconceptions

Estimation, 5, 9, 121, 209, 220, 230,233, 294, 295, 296, 297, 298, 302,308, 319, 321, 397, 437, 438, 439,445, 456, 564, 567, 586, 712, 714,716, 717, 738, 745

Evaluating expressions. SeeExpressions

Even numbers, 148

Eventscompound, 650–655, 662dependent, 652inclusive, 672independent, 650–651mutually exclusive, 652, 672simple, 310

Expanded form, 154, 156, 185, 192

Experimental probability, 311

Exponents, 153–157, 190, 192, 252,435, 464, 731, 732

negative, 181–185, 187, 194positive, 182, 183, 185, 187, 194

Expressions, 12–13. See alsoAddition expressions; Algebraic expressions; Binomial expressions; Division expressions; Equivalent expressions;Numerical expressions;Subtraction expressions; Verbal expressionsevaluating, 12, 107, 154, 155, 724,

726, 727, 731, 732with exponents, 154, 155factoring, 731finding value, 14, 21, 724simplifying, 104, 114, 497, 525,

725, 727, 728translating, into words, 11

Extend the Activity, 39, 158, 253,368, 386, 392, 640, 656, 657, 682

Extended Response. See Preparingfor Standardized Tests

Extending the Lesson, 32, 102, 168,185, 214, 236, 252, 268, 280, 333,344, 359, 392, 440, 445, 464, 497,531, 538, 572, 577, 582, 594, 621,627, 655, 696

Extra Practice, 724–757

Extreme value, 239

Faces, 557, 559, 595, 599

Factor expressions, 166

Factorial notation, 642

Factoring, 157

Factor monomials, 161

Factors, 69, 79, 148–152, 151, 191, 730

Factor tree, 160

Families of quadratic functions, 697

Family of graphs, 402–403

Find the Error, 14, 26, 72, 87, 100,105, 128, 161, 166, 212, 222, 234,246, 278, 291, 306, 347, 353, 357,389, 395, 400, 462, 479, 536, 565,592, 643, 648, 671, 676. See alsoCommon Misconceptions

Foldables™ Study Organizer, iv, 1,5, 55, 97, 147, 199, 263, 327, 367,435, 491, 553, 605, 667

Formulas, 131–133, 140, 300distance, 466–470, 485–486midpoint, 466–470, 485–486

Four-step problem-solving plan,5, 6–8, 9, 10, 47–48, 51

Fraction bars as grouping symbol,12, 13, 224, 264

Fractions, 281, 318. See alsoAlgebraic fractionsaddition, 220, 233, 716comparison, 202, 228computations, 605division, 216, 717multiplication, 567, 649, 717percents as, 281–282, 283simplifying, 171, 172, 173, 179,

185, 199, 732subtraction, 221, 716unit, 236writing decimals, 200–209, 214,

224, 254, 338, 422, 475, 733writing rational numbers, 205writing ratios, 264–265writing repeating decimals, 206writing simplest form, 263writing terminating decimals, 206

Free Response. See Preparing forStandardized Tests

Frequenciesabsolute, 627cumulative, 627relative, 627

Frequency distribution, 623

Frequency polygon, 628

Frequency tables, comparison tohistograms, 627

Functional notation, 380

Functions, 369–373, 424, 537, 741graphing, 370, 757quadratic and cubic, 692–696,700

linear, 687–691, 700nonlinear, 687–691, 700

Fundamental Counting Principle,636, 661

Geometric sequences, 249–252, 258, 259, 268, 344, 736

Geometryangles, 447–451, 484

acute, 449, 450, 451, 457, 484,745

F

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R58 Index

adjacent, 476, 493, 495alternate exterior, 492, 493alternate interior, 492, 493central, 452, 538complementary, 493, 494, 495,496, 517, 544congruent, 493corresponding, 474, 492, 493,500, 544of elevation, 480exterior, 492, 531inscribed, 538interior, 492, 528, 530, 538, 543measures, 447, 448, 454obtuse, 449, 450, 451, 457, 484,745quadrilateral, 514right, 449, 450, 451, 457, 484, 745straight, 447, 449, 450, 451, 457,484, 745supplementary, 494, 495, 496vertical, 493, 495

areacircles, 533–538, 548, 561, 749irregular figures, 539–543, 548parallelograms, 520–521, 547rectangles, 132, 133, 134, 135,140, 141, 152, 214, 224, 349, 671,730, 767shaded region, 770squares, 439, 523triangles, 445, 561

circumference of circle, 561, 749diameter of circle, 533, 749inequality involving acute angle,

764isosceles triangle, 469length of hypotenuse in right

triangles, 462, 470length of rectangle, 764length of sides of golden

rectangles, 675line segments, 473, 644, 645obtuse angles, 691patterns, 9perimeter, 469

equilateral triangles, 394geometric figures, 106golden rectangles, 675isosceles trapezoid, 680isosceles triangles, 680rectangles, 132, 133, 134, 135, 140,141, 152, 224, 302, 335, 336, 349,359, 363, 385, 417, 676, 701, 730squares, 378, 394, 440, 463, 760triangles, 467, 503, 591, 681, 760,770

pi, 208, 533, 534radius of circle, 443, 533, 536, 749ratio of width to length, 266

rectangular prism, 464right angles, 464, 691scalene triangle, 469straight angles, 691sum of angles of triangle, 676surface area, 594, 751

cubes, 157, 694prisms and cylinders, 573–577,597pyramids and cones, 578–582,597

three-dimensional figures,552–601

triangles, 38, 453–457, 468, 485, 528acute, 454, 456, 746angle measures, 453area, 521, 522, 523, 547congruent, 500–504, 545, 748equilateral, 455isosceles, 455obtuse, 454, 456, 746obtuse isosceles, 455, 470, 485right, 454, 456, 460, 461, 462,463, 464, 481, 485, 746right scalene, 470, 485scalene, 455similar, 471–475, 486vertice, 88

vertices, 88, 447, 453, 527,545–546, 556, 557, 559, 595, 599

volume, 750, 751complex solid, 564cones, 568–572, 596, 616cubes, 157prisms and cylinders, 563–567,596pyramids and cones, 568–572,596rectangular prisms, 695

Geometry ActivityBuilding Three-Dimensional

Figures, 554–555Similar solids, 583Volume, 562

Golden ratio, 253, 268

Golden rectangle, 268

Graphingalgebraic relationships, 87cubic functions, 692–696, 700equations, 691functions, 370, 757inequalities, 342, 343, 353, 354,

361, 362, 379, 419–422, 440, 740,744

linear equations, 376–377quadratic functions, 692–696, 700solutions of equations, 111, 113,

118, 428, 744

systems of equations, 414, 416,417, 422, 428

systems of inequalities, 346, 348

Graphing Calculator InvestigationBox-and-Whisker Plots, 622Families of Graphs, 402–403Families of Quadratic Functions,

697Finding Angles of a Right

Triangle, 482Function Tables, 374Graphing Inequalities, 423Histograms, 629Mean and Median, 243Probability Simulation, 315Scatter Plots, 45–46

Graph pairs, 88

Graph points, 55, 85, 86, 87, 92, 93

Graphsbar, 722–723circle, 723data display, 722–723identifying functions, 687line, 722–723relations as, 35, 36, 37, 50writing equations, 405

Greatest common factor (GCF),164–168, 179, 193, 199, 214, 252,731

Greatest possible error, 594

Grid In. See Assessment.

Gridded Response. See Preparingfor Standardized Tests

Grouping symbols, 48brackets, 12fraction bars, 12, 13inequalities, 356parentheses, 12, 15, 75solving equations, 334–338, 361

Guess and Check, 709

Half-Life Simulation, 180

Heptagon, 528

Hexagon, 528

Hexagonal prism, 572

Hexagonal pyramid, 571

Histograms, 623–628, 629, 633, 660,753comparison to frequency tables,

627interpretation, 624

H

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Homework Help, 9, 14, 20, 26, 31,36, 43, 59, 67, 73, 78, 83, 88, 101,106, 113, 118, 123, 129, 134, 151,156, 162, 167, 172, 178, 183, 189,203, 208, 213, 218, 222, 229, 235,241, 246, 251, 267, 273, 279, 284,291, 296, 301, 307, 313, 332, 337,343, 348, 353, 357, 371, 378, 384,390, 396, 400, 407, 411, 417, 421,439, 444, 450, 456, 463, 469, 474,480, 496, 503, 510, 516, 524, 530,542, 559, 566, 571, 576, 580, 587,593, 609, 615, 620, 626, 632, 638,644, 648, 653, 671, 676, 680, 685,690, 695

Horizontal lines, 383

Hypotenuse, 460, 463, 470, 475, 477,481, 485, 487, 746

Identity Property, 32, 63

Inclusive events, 672

Independent events, 650–651

Independent variable, 375

Indirect measurement, 471–475, 486

Inductive reasoning, 7, 25, 71

Inequalities, 326, 340–344, 361, 367,464graphing, 342, 343, 353, 354, 361,

362, 379, 419–422, 428, 440, 740,744

solving, 354, 373, 379, 385, 445,481, 561, 567, 649, 740, 741addition, 345–349, 361division, 350–354, 362multiplication, 350–354, 362multi-step, 355–359, 362subtraction, 345–349, 361

symbols, 57truth, 341writing, 740

Integers, 69, 451, 487, 745absolute value, 90addition, 62–63, 64–66, 74, 82, 84,

91, 97, 107, 199, 327comparing and ordering, 56, 57,

59, 60, 68division, 80–84, 92, 114, 199, 327modeling real-world situations,

61multiplication, 75–79, 82, 84,

91–92, 97, 152, 199, 327number line, 56, 57, 59, 68problem solving, 66

for real-world situations, 56–57subtraction, 70–72, 74, 82, 84, 91,

118, 199, 327, 385writing as fractions, 205

Intercepts, graphing linearequations using, 381–385, 425

Interest, 299, 738

Internet Connectionswww.pre-alg.com/careers, 42, 73,

129, 172, 223, 278, 339, 348, 358,399, 472, 480, 515, 579, 649, 670

www.pre-alg.com/chapter_test,51, 93, 141, 259, 321, 363, 429,487, 549, 599, 663, 701

www.pre-alg.com/data_update,43, 68, 114, 119, 157, 190, 229,267, 348, 396, 439, 543, 587, 649,690

www.pre-alg.com/extra_examples, 7, 13, 19, 25, 35,41, 57, 65, 71, 77, 81, 87, 99, 105,111, 117, 121, 127, 133, 149, 155,161, 165, 171, 177, 187, 201, 207,211, 217, 221, 227, 233, 239, 245,249, 265, 271, 277, 283, 289, 295,299, 305, 311, 331, 335, 341, 347,351, 355, 369, 377, 383, 389, 395,399, 405, 409, 415, 419–422, 437,443, 449, 455, 461, 467, 473, 479,493, 501, 507, 515, 521, 529, 535,541, 557, 565, 569, 575, 579, 585,591, 607, 613, 619, 625, 631, 637,643, 647, 651, 669, 675, 679, 683,689, 693

www.pre-alg.com/other_calculator_keystrokes, 45,243, 315, 402, 423, 482, 629, 697

www.pre-alg.com/self_check_quiz, 9, 15, 21, 27,31, 37, 43, 59, 67, 79, 83, 89, 101,107, 113, 119, 123, 129, 135, 151,157, 163, 167, 173, 179, 183, 189,203, 209, 213, 219, 223, 229, 235,241, 247, 251, 267, 273, 279, 285,291, 297, 301, 307, 313, 333, 337,343, 349, 353, 357, 371, 379, 385,391, 397, 401, 407, 411, 417, 421,439, 445, 451, 457, 463, 469, 475,481, 497, 503, 511, 517, 525, 531,537, 543, 559, 567, 571, 577, 581,587, 593, 609, 615, 621, 627, 633,639, 645, 649, 653, 671, 677, 681,685, 691, 695

www.pre-alg.com/standardized_test, 53, 95, 143,197, 261, 322, 365, 430, 489, 551,601, 665, 703

www.pre-alg.com/vocabulary_review, 47, 90, 138,191, 316, 360, 483, 595, 658, 698

www.pre-alg.com/webquest.com, 43, 79, 135, 136,145, 173, 242, 301, 314, 325, 333,412, 422, 433, 481, 542, 571, 594,603, 626, 690, 696

Interquartile range, 613, 614, 615,628, 659, 753

Intersecting lines, 493, 560

Inverse operations, 110, 121, 258,373, 440

Inverse Property of Multiplication, 215

Investigations. See Algebra Activity; Geometry Activity;Graphing CalculatorInvestigation; SpreadsheetInvestigation; WebQuest

Irrational numbers, 206, 441, 443,444, 451, 484, 487, 745

Irregular figures, area, 539–543, 548

Isosceles trianglesobtuse, 455, 470, 485

Key Concepts, 18, 23, 29, 58, 64, 65, 66, 70, 75, 76, 80, 81, 111, 115, 117,132, 175, 176, 181, 186, 210, 215,216, 221, 232, 233, 238, 270, 271,282, 288, 310, 345, 350, 352, 376,382, 388, 394, 436, 441, 449, 453,454, 455, 460, 466, 468, 472, 477,492, 493, 500, 507, 508, 514, 520,521, 522, 528, 533, 557, 563, 565,568, 569, 573, 575, 579, 585, 636,646, 650, 652, 688

Keystrokes. See GraphingCalculator Investigation; InternetConnections

Lateral area, 578

Lateral faces, 578

Least common denominator (LCD),227, 228, 229, 234, 236, 252, 735

Least common multiple (LCM),226–230, 228, 236, 257, 735

Leaves, 606

Like fractionsaddition, 220–224, 256subtraction, 220–224, 256

I

K

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R60 Index

Like terms, 103, 104, 105, 106, 122,674, 676, 677, 728

Linear equations, 408, 447, 667graphing, 376–377with intercepts, 381–385, 425two variables, 375–379, 425writing, 404–408, 427

Linear functions, 687–691, 700, 701,757

Line graphs, 722–723double, 722–723

Line of symmetry, 506, 507

Line plot, 239

Linesbest-fit, 409–413, 427, 429horizontal, 383intersecting, 493, 560parallel, 492–497, 495, 497, 544, 560perpendicular, 494, 495skew, 558, 560, 567vertical, 383

Line segments, 453, 644, 645

Line symmetry, 505

Lists, 708

Logical Reasoning. See CriticalThinking

Look Back, 18, 71, 76, 100, 111, 166,176, 210, 244, 264, 266, 293, 330,334, 335, 369, 442, 460, 466, 497,523, 535, 540, 570, 584, 607, 635,637, 652, 683, 684

Major arc, 538

Make a Conjecture. See Conjectures

Make a table or list, 708

Markup, 301

Matrices, 414, 669, 705

Maximum point, 695

Mean, 82, 92, 238–239, 248, 252, 258,605, 618, 735

Measurements, 213addition, 592capacities, 566–567, 718–721,

791–793comparing, 721, 790, 792converting, 118, 168, 213–214, 263,

272, 274, 718–721, 734, 789–796customary, 118, 720–721, 734,

790–796

geometric measures, 137,213–214, 272, 566–567, 718–721,794–796

metric, 718–719, 790–796multiplication, 592temperatures, 59–61, 333, 792–793times, 213, 219, 789weights, 213, 218, 718–721,

791–793

Measures of central tendency,238–242, 258, 605, 735

Measures of variation, 612–616, 659

Median, 238–239, 248, 252, 258, 605,611, 615, 618, 735

Mental Math, 25, 26, 29, 30, 31, 38,44, 49, 51, 66, 74, 79, 102, 104, 122,127, 150, 160, 201, 282, 525, 725,738

Metric system, convertingmeasurements, 718–719

Midpoint, 468, 486, 746

Midpoint Formula, 466–470,485–486

Minimum point, 695

Minor arc, 538

Mixed numbers, 200–201addition, 220, 233, 491, 716division, 216, 717multiplication, 211, 717subtraction, 221, 234, 716writing as decimals, 200, 201,

202, 214, 422writing as fractions, 205, 209writing decimals as, 207–208, 224,

733

Mode, 238–239, 248, 252, 258, 605,735

Modeling, 276–280, 317, 464adding integers, 62–63, 222algebraic expressions, 103, 106area

circles, 535parallelograms, 520–521rectangles, 132trapezoids, 522triangles, 521

area and geoboards, 518–519circumference of circles, 533congruent triangles, 500constructions, 498–499direct variation, 394, 395distance formula, 466Distributive Property, 99equations with variables on each

side, 328–329

integers on number line, 65irrational numbers, 465manipulatives, 62–63midpoint formula, 468monomials, 673multiplication, 682

polynomial by monomial, 683percent, 286–287polyhedrons, 557polynomials, 673, 677prime numbers, 162properties of equality, 123Pythagorean Theorem, 458–459,

460rational numbers, 207, 210, 215ratios of similar solids, 585real-world situations, 61right triangles, 476similar triangles, 472simulations, 656–657slope, 388solving equations, 108–109solving two-step equations, 120surface area

cones, 579cylinders, 575rectangular prisms, 573

three-dimensional figures,554–555, 560

triangles, 453trigonometric ratios, 477volume, 562

cones, 569cylinders, 565prisms, 563, 565pyramids, 568

Monomials, 148–152, 161, 163, 191,195, 667, 668, 669, 671, 681, 698,730, 731, 755degrees, 670division, 175–179, 176, 194factoring, 161, 162, 192, 195greatest common factor (GCF),

166, 167, 193identify, 150least common multiple (LCM),

227multiplication, 175–179, 194, 681powers, 179

More About. See also Applications;Cross-Curriculum Connectionsairports, 247amusement parks, 99, 644animals, 474architecture, 277, 503art, 560astronomy, 66attractions, 272aviation, 112

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baby-sitting, 106backpacking, 356baseball cards, 105basketball, 610, 685billiards, 456calling cards, 123candy, 10cheerleading, 217decorating, 337food, 284football, 15fruit drinks, 575games, 511, 651golf, 57gymnastics, 463hang gliding, 401Internet, 654movie industry, 31oceans, 189parks, 116planets, 229plants, 35pole vaulting, 412pools, 395population, 267presidents, 607rafting, 422ranching, 118recycling, 208scooters, 127scuba diving, 370skateboards, 299, 638skydiving, 693snow, 529snowboards, 417soccer, 19, 134sound, 408space, 586sports, 344state fairs, 347stock market, 306tides, 78track and field, 165travel, 219videos, 331water, 182weather, 444weddings, 149

Multiple Choice. See Assessment

Multiple representations, 18, 23, 29,58, 64, 65, 66, 70, 75, 76, 80, 81,98, 110, 111, 115, 117, 132, 175,176, 186, 207, 210, 215, 216, 221,225, 232, 233, 238, 270, 288, 298,310, 345, 350, 352, 377, 388, 394,436, 453, 460, 466, 468, 472, 477,500, 514, 522, 533, 535, 563, 565,568, 569, 573, 575, 579, 613, 636,650, 652

Multiplication, 11, 756algebraic fractions, 211decimals, 263, 491, 714, 715fractions, 567, 649integers, 75–79, 82, 84, 91–92, 97,

152, 199, 327measurements, 592mixed numbers, 211monomials, 176, 681negative fractions, 211negative numbers, 351–352notation, 13polynomials by monomials,

683–686, 699positive numbers, 350–351rational numbers, 256, 553, 577solving equations, 115–119, 139,

245solving inequalities, 350–354

Multiplication PropertiesAssociative, 24, 26, 49, 522Commutative, 23, 26, 49, 75, 522of Zero, 24, 49, 61, 725

Multiplicative identity, 24, 38, 49,725

Multiplicative inverse, 215–216,218, 504, 734

Multi-step inequalities, solving,355–359, 362

Mutually exclusive events, 652, 672

Natural numbers, 205, 444, 451, 487, 745

Negative coefficients, 122, 161

Negative exponents, 181–185, 187,194

Negative fractions, multiplication,211

Negative integers, 64

Negative numbers, 56division, 351–352multiplication, 351–352

Negative slope, 388

Nonlinear functions, 687–691, 700,701, 757

Nonscientific calculators, 12

Number line, 56, 57, 113, 740absolute value, 58addition, 64, 65, 68comparison and ordering of

integers, 56, 57integers, 56, 57, 59

multiplication, 75, 77subtraction, 70

Numbers, 12–13, 48base 2, 158base 10, 158binary, 158comparison, 283composite, 159, 161, 162, 192, 229,

285, 731decimal, 158even, 148factoring, 149irrational, 206, 441, 443, 444, 451,

484, 487, 745mixed, 200–201natural, 205, 444, 451, 487, 745negative, 56, 351–352odd, 148positive, 56, 350–351prime, 159, 161, 162, 192, 440,

731properties, 24rational, 198–261, 205–209,

210–214, 215–219, 244–248, 255, 256, 258, 440, 441, 443, 444, 451, 487, 553, 577, 745

real, 441, 745triangular, 457whole, 27, 84, 205, 216, 444, 451

Number theory, 156, 162, 740

Numerical expressions, 12, 14evaluating, 13, 17, 21, 22, 58, 60,

72, 74finding value, 14translating, 11, 13, 14, 15, 38, 51writing for verbal phase, 724

Octagonal prism, 566

Octagons, 528

Odd numbers, 148

Odds, 646–649, 662, 755notation, 647

Online Research. See also InternetConnections; Researchcareer choices, 42, 73, 129, 172,

223, 278, 348, 358, 399, 472, 480,515, 579, 649, 670

data update, 43, 68, 114, 119, 157,190, 229, 267, 348, 396, 439, 543,587, 625, 690

Open circles, 346

Open Ended, 9, 14, 19, 26, 30, 36, 42,59, 67, 72, 77, 83, 87, 100, 105, 113,117, 128, 133, 155, 158, 161, 162,

N

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R62 Index

166, 171, 177, 183, 188, 202, 212,217, 222, 228, 234, 241, 246, 266,272, 278, 283, 291, 295, 300, 306,312, 332, 336, 342, 347, 353, 357,371, 377, 384, 389, 395, 400, 407,410, 416, 421, 429, 438, 443, 449,455, 462, 468, 473, 479, 487, 495,502, 509, 515, 523, 529, 535, 540,559, 565, 570, 575, 580, 586, 592,599, 608, 614, 619, 625, 631, 637,643, 648, 653, 670, 676, 680, 684,689, 694

Open Response. See Preparing forStandardized Tests

Open sentences, 28, 31, 32solving, 28

Operationsintegers, 82inverse, 110

Opposites, 66, 476

Ordered pairs, 33–35, 36, 37, 39, 44,50, 51, 55, 61, 79, 84, 85, 86, 87,88, 124, 136, 367, 377, 378, 391,422, 425, 429, 725, 728, 742functions, 369–370

Ordered pair solutions, tables, 375,378, 686

Ordering decimals, 616

Ordering integers, 59, 68, 87, 88, 726

Order of operations, 12–13, 14, 16,24, 48, 51, 147, 154, 192, 401, 464,525

Origin, 33, 34

Outcomes, 310

Outliers, 621

Parabola, 697

Parallel lines, 495, 560angles and, 492–497, 497, 544

Parallelogram, 514, 515, 546altitude, 520area, 520–521, 547base, 520

Parentheses ( ), 15, 75as grouping symbol, 12, 15solving equations, 334–335

Pascal’s triangle, 640

Patterns, 9, 16, 47, 48, 55, 74, 84, 102,167

Pentagon, 528

Percent equations, 298–302, 319,373

Percent-fraction equivalents, 293

Percent of change, 304–308, 320

Percent of decrease, 306, 320, 739

Percent of increase, 305, 306, 320,739

Percent proportion, 288–292, 297,318, 321, 738

Percents, 281–308, 318, 359, 525, 737,738applying, 289, 290, 299–308of change, 304–308comparing, 283compound interest, 303decimals as, 282–283equations, 298–302estimating with, 294–295finding mentally, 293finding percent, 288, 289, 299finding the base, 290, 299finding the part, 290, 298fractions as, 282greater than 100%, 283less than 1%, 283modeling, 281, 286, 287and predictions, 312and probability, 310proportion, 288–292simple interest, 299, 300writing as decimals, 282, 298writing as fractions, 281–282, 283,

288, 475

Perfect squares, 436, 438

Perimeter, 137polygon, 530rectangle, 132, 134, 140rectangles, 132, 133, 134, 135, 140,

141, 152, 224, 302, 335, 336, 349,359, 363, 385, 417, 676, 701, 730

Permutations, 641–645, 661, 754

Perpendicular lines, 494, 495

Perspective, 554–555

Pi, 208, 533, 534

Plane, 556

Points, 447writing equations given two, 406

Polygons, 527–531, 547, 553classification, 527–528, 530, 549, 749frequency, 628interior angles, 528

measures of angles, 528–529, 530regular, 529

Polyhedron, 556

Polynomials, 669–672, 698, 755addition, 674–677, 699classification, 669, 681, 698, 701degrees, 670, 671, 677, 681, 698,

701multiplication, 683–686, 699monomials, 683–686, 699subtraction, 678–681, 699

Positive exponents, 182, 183, 185,187, 194

Positive integer, 64

Positive numbers, 56division, 350–351multiplication, 350–351

Positive slope, 388, 391

Powers, 153–157, 174, 192, 194

Practice Chapter Test. SeeAssessment

Practice Quiz. See Assessment

Precision, 589, 590–594, 598

Precision unit, 590, 591, 592, 593

Predictions, 310–314, 320, 395best-fit lines, 409, 410, 412, 413equations, 410scatter plots, 42sequences, 251

Preparing for Standardized Tests,771–778Constructed Response, 780–783,

784–788Extended Response, 771, 784–788Free Response, 780–783Grid In, 776–779Gridded Response, 771, 776–779Multiple Choice, 771, 772–775Open Response, 780–783Selected Response, 772–775Short Response, 771, 780–783Student-Produced Questions,

780–783Student-Produced Response,

776–779Test-Taking Tips, 771, 773, 776,

777, 780, 781

Prerequisite Skills. See alsoAssessmentAdding and Subtracting

Decimals, 713Comparing and Ordering

Decimals, 710

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Converting Measurementswithin the Customary System,720–721

Converting Measurementswithin the Metric System,718–719

Displaying Data in Graphs,722–723

Estimating Products andQuotients of Decimals, 714

Estimating Products andQuotients of Fractions andMixed Numbers, 717

Estimating Sums and Differencesof Decimals, 712

Estimating Sums and Differencesof Fractions and MixedNumbers, 716

Getting Ready for the NextLesson, 10, 16, 21, 27, 32, 38, 61,68, 74, 79, 84, 102, 107, 114, 119,124, 130, 152, 157, 163, 168, 173,179, 185, 204, 209, 213, 219, 224,230, 236, 242, 248, 268, 274, 280,285, 292, 297, 302, 308, 333, 338,344, 349, 354, 373, 379, 385, 391,397, 401, 408, 413, 418, 440, 445,451, 457, 464, 470, 475, 497, 504,511, 517, 525, 531, 538, 561, 567,572, 577, 582, 588, 611, 616, 621,628, 633, 639, 645, 649, 672, 677,681, 686, 691

Getting Started, 5, 55, 97, 147,199, 263, 327, 367, 435, 491, 553,605, 667

Multiplying and DividingDecimals, 715

Problem-Solving StrategyGuess and Check, 709Make a Table or List, 708Solve a Simpler Problem, 706Work Backward, 707, 709, 712,713, 714, 715, 716, 717, 719

Rounding Decimals, 711

Prime, 285relatively, 168twin, 162

Prime factorization, 159–162, 192,224, 236, 731

Prime factors, 227, 230

Prime numbers, 159, 161, 162, 192,440, 731

Prisms, 557, 595height, 564hexagonal, 572octagonal, 566rectangular, 557, 560, 563, 565,

566, 575, 576, 582, 597

surface area, 573–577, 597triangular, 557, 562, 564, 566, 572,

587volume, 563–567, 596

Probability, 310–314, 320, 333, 338,604–605, 672, 677, 739, 754, 755compound events, 650–655, 662dependent events, 652event, 636–637experimental, 311mutually exclusive events, 652notation, 650outcomes, 310simple, 605simple events, 310theoretical, 311two independent events, 650–651

Probability simulation, 315

Problem solvingadding polynomials, 675angles, 449area, 523circumference, 534combinations, 643comparing fractions in, 202direct variation, 395distance formula, 467distributive property, 99dividing powers, 177divisibility rules, 149equations, 116, 125, 405four-step plan, 5, 6–8, 9, 10,

47–48, 51fractions, 234functions, 693graphing equations, 399graphing inequalities, 420guess and check, 709inequalities, 347integers, 66, 76integers in, 76making a table or list, 708mixed, 758–770polynomials, 675, 684proportions, 271scientific notation, 187solving simpler problem, 706square roots, 438subtracting integers, 71subtracting polynomials, 679trigonometric ratios, 479volume, 570work backward, 122, 707, 709,

712, 713, 714, 715, 716, 717, 719

Product of Powers rule, 184

Products, 27, 69, 74, 78, 79, 84,91–92, 93, 147, 175, 176, 177, 178,185, 224, 252, 255, 280, 285, 327,

567, 577, 605, 715, 725, 727, 732,756. See also Multiplicationestimating, 714, 717signs, 79

Profit, 301

Projects. See WebQuest

Properties of Equality, 23–25, 29,30, 31, 49Substitution, 18Symmetric, 29, 30, 31Transitive, 29, 30, 31

Proportions, 262, 270–274, 280, 285,317, 413, 440, 470, 473, 474, 553,582, 599, 677, 747identifying, 271property, 271solving, 271, 272, 737

Protractor, 448, 449, 450, 457, 464,484, 497, 512, 745

Pyramids, 557, 595hexagonal, 571rectangular, 557, 570, 572, 577square, 557, 571, 581, 582, 585surface area, 578–582, 597triangular, 557volume, 568–572, 596

Pythagorean Theorem, 460–464,469, 485converse, 462

Pythagorean triple, 459

Quadrants, 86, 87, 92

Quadratic functions, 688families, 697graphing, 692–696, 700

Quadrilaterals, 513–517, 528, 546angles of, 514classification, 514–515, 516, 531naming, 513

Quantitative relationships, 96

Quartiles, 613

Quotient of Powers rule, 184

Quotients, 13, 38, 69, 79, 83, 84, 89,92, 93, 177, 178, 185, 218, 224, 230,242, 252, 256, 274, 280, 327, 714,715, 717, 727, 732, 734. See alsoDivision

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R64 Index

Radical sign, 436, 437

Radiuscircles, 443, 533, 536, 749cones, 571

Range, 35, 36, 37, 44, 50, 51, 136, 367,612–616, 618, 628, 659, 725, 753

Rate of change, 392, 393–397, 426,743

Rates, 264–268, 316converting, 266, 280

Rational numbers, 198–261, 440,441, 443, 444, 451, 487, 745division, 215–219, 256identifying and classifying, 206multiplication, 210–214, 255, 553,

577solving equations, 244–248, 258writing as fractions, 205–206

Ratios, 264–268, 273, 316, 321, 359,386, 445, 454, 481, 553, 645, 736common, 250, 251, 258comparison, 269writing as fractions, 264–265

Reading and Writing, 5, 55, 97, 147,199, 263, 327, 367, 435, 491, 553,605, 667

Reading Math, 17, 23, 24, 56, 57, 64,75, 80, 88, 98, 103, 148, 149, 150,159, 177, 200, 205, 206, 281, 300,311, 341, 370, 381, 383, 437, 448,453, 471, 472, 477, 493, 500, 508,624, 641, 642, 643, 647, 650, 678,688

Reading MathematicsDealing with Bias, 634Factors and Multiples, 225Language of Functions, 380Learning Geometry Vocabulary,

446Learning Mathematics Prefixes,

526Learning Mathematics Vocabulary,

69Making Comparisons, 269Meanings of At Most and At

Least, 339Powers, 174Precision and Accuracy, 589Prefixes and Polynomials, 668Translating Expressions into

Words, 11Translating Verbal Problems into

Equations, 125

Real numbers, 441, 745

Real number system, 441–445, 484

Reasonableness, 7, 586

Reasoning. See also Critical Thinkingdeductive, 25inductive, 7, 25, 71

Reciprocals, 215, 247

Rectangles, 514, 546area, 132, 133, 134, 135, 140, 141,

152, 214, 224, 349, 671, 730, 767perimeter, 132, 133, 134, 135, 140,

141, 152, 224, 302, 335, 336, 349,359, 363, 385, 417, 676, 701, 730

Rectangular prisms, 557, 560, 563,565, 566, 575, 576, 582, 597

Rectangular pyramid, 557, 570, 572,577

Reflections, 506, 508, 509, 510, 512,686, 748

Regular polygon, 529

Regular tessellations, 527

Relations, 35, 50, 367as tables and graphs, 35, 36, 37, 50

Relationships, types of, 41, 42, 43,51 50, 68

Relative frequencies, 627

Relatively prime, 168

Repeating decimals, 201, 202, 203,206, 214, 224, 254, 338, 733

Replacement set, 102

Research, 43, 46, 83, 113, 151, 225,253, 268, 291, 308, 380, 446, 526,530, 543, 560, 583, 589, 610, 668,672. See also Online Research

ReviewLesson-by-Lesson, 47–53, 90–92,

138, 191–194, 254–258, 316,360–362, 424–428, 483–486,544–548, 595, 658–662, 698

Mixed, 16, 21, 27, 32, 44, 61, 68,74, 79, 84, 89, 102, 107, 114, 119,124, 130, 136, 152, 157, 163, 168,173, 179, 185, 190, 204, 209, 213,219, 224, 230, 236, 242, 248, 252,268, 274, 280, 285, 292, 297, 302,308, 314, 333, 338, 344, 349, 354,359, 373, 379, 385, 391, 397, 401,408, 413, 418, 422, 440, 445, 451,457, 464, 470, 475, 481, 497, 504,511, 517, 525, 538, 543, 561, 567,572, 577, 582, 588, 594, 611, 616,621, 628, 633, 639, 649, 655, 672,677, 681, 686, 691, 696

Rhombus, 514, 546

Rotational symmetry, 505

Rotations, 506, 507, 508, 509, 510,512, 532, 686coordinate plane, 509

Rounding, 9, 10, 201, 242, 283, 284,291, 314, 443, 445, 457, 462, 463,468, 469, 475, 478, 480, 481, 482,484, 486, 487, 491, 531, 534, 535,536, 543, 548, 549, 565, 566, 568,569, 570, 571, 572, 577, 580, 581,582, 588, 592, 593, 596, 597, 598,599, 605, 611, 672, 711, 735, 736,737, 738, 745, 746, 747, 749, 750,751, 752

Rows, 705

Sample space, 311

Scale, 276, 631, 737

Scale drawings, 276–280, 317

Scale factor, 277, 285, 583, 587

Scale model, 276

Scalene trianglesright, 470, 485

Scatter plots, 39, 40–42, 43, 45–46,50, 61, 68, 107, 408, 410, 411, 412,422, 427, 429, 726constructing, 40interpreting, 41predictions, 42trends, 44

Scientific calculators, 12, 16

Scientific notation, 186–190, 194,195, 204, 268, 733

Segment measure, 472

Selected Response. See Preparingfor Standardized Tests

Sequencesarithmetic, 249–252, 258, 259, 268,

344, 736Fibonacci, 253geometric, 249–252, 258, 259, 344,

736

Sets, 733replacement, 102

Shadow reckoning, 473

Short Response. See Preparing forStandardized Tests

S

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Index

Index R65

Side lengths of rectangles, 152

Sides of the angle, 447

Sierpinski’s triangle, 471

Significant digits, 590–594, 598,599, 752

Similar figures, 471–475, 486

Similar solids, 599

Simple interest, 300

Simplest form, 104

Simulationprobability, 315

Simulations, 656–657half-life, 180

Sine, 477–481, 486, 747

Skew lines, 558, 560, 567

Slant height, 578

Slides, 506

Slope, 387–391, 395, 397, 398, 400,401, 404, 408, 412, 413, 418, 426,427, 429, 470, 639, 742, 743negative, 388positive, 388, 391undefined, 389zero, 388

Slope-intercept form, 398–401, 401,406, 407, 413, 418, 427, 696, 742,743

Solids, 556, 750, 751, 752similar, 584–588, 598

Solution, 28

Solving Equations. See Equations

Spreadsheet InvestigationCircle Graphs and Spreadsheets,

452Compound Interest, 303Expressions and Spreadsheets, 22Perimeter and Area, 137

Spreadsheets, 22

Square pyramid, 557, 571, 581, 582,585

Square roots, 436–440, 451, 483, 628,745solving equations, 443

Squares, 436–440, 483, 514, 546area, 439, 523

Square units, 575

Standard form, 154, 188, 189, 194,195, 209, 733

Standardized Test Practice. SeeAssessment

Statistics, 418, 604–665, See also Data bias, 634misleading, 630–633, 661

Stem-and-leaf plots, 606–611, 658,681, 752back-to-back, 607–608, 609, 611interpretation, 607

Stems, 606

Straight line, 102

Student-Produced Questions. SeePreparing for Standardized Tests

Student-Produced Response. SeePreparing for Standardized Tests

Study organizer. See Foldables™Study Organizer

Study Tips, 6, 7, 12, 13, 18, 25, 28,34, 41, 58, 60, 65, 70, 71, 76, 82, 86algebra tiles, 674alternate strategy, 406alternative methods, 128, 170,

220, 250, 265, 335, 522altitudes, 521angles, 447Base, 289box-and-whisker plots, 618break in scale, 624calculating with Pi, 534calculator, 187checking equations, 111, 405checking reasonableness of

results, 494checking solutions, 121, 346check your work, 443choosing a method, 164choosing points, 388choosing x values, 376circles and rectangles, 574classifying polynomials, 669common misconceptions, 58, 132,

154, 175, 355, 420, 449, 467, 507,557, 591, 617

commutative, 160cones, 569congruence statements, 501cross products, 271degrees, 670dependent variable, 375diagonals, 558different forms, 398dimensions, 556dividing by a whole number, 216division expressions, 117equiangular, 454equivalent expressions, 104estimation, 288, 409

exponents, 155expression, 126finding percents, 295first power, 153fractions, 283frequency distribution, 623graphing, 692graphing shortcuts, 382growth of functions, 688height of pyramid, 568hypotenuse, 460independent variable, 375inequalities, 341, 345irregular figures, 539labels and scales, 631Look Back, 18, 71, 76, 100, 111,

166, 176, 210, 244, 264, 266, 293,330, 334, 335, 369, 442, 466, 472,523, 535, 540, 570, 584, 635, 637,652, 683, 684

matrices, 414, 669mean, median, mode, 238measures of volume, 563mental computation, 122mental math, 127, 160, 201, 282multiplying more than two

factors, 636naming quadrilaterals, 513negative fractions, 211negative number, 352negative signs, 233, 675negative slopes, 399n-gon, 528notation, 507parallel lines, 492percents, 294pi, 533, 565plotting points, 377positive and negative exponents,

187positive number, 350powers of ten, 186precision, 590, 592precision units, 591prime factors, 226probability, 310properties, 270Reading Math, 215, 455reciprocals, 245relatively prime, 230remainders, 161repeating decimals, 206rolling number cubes, 646rounding, 478scale factors, 277, 585slopes, 394slopes/intercepts, 415solutions, 421statistics, 613, 630substitution, 467trends, 372

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Index

R66 Index

triangular pyramids, 581use a table, 405use a venn diagram, 169writing prime factors, 165zeros, 679

Substitution, 107, 379, 413, 440solving equations, 744solving systems of equations,

416, 417, 418, 428

Substitution Property of Equality, 18

Subtraction, 11, 328, 727, 734, 735,756decimals, 5, 712, 713fractions, 221, 716integers, 70–72, 74, 82, 84, 91, 118,

199, 327, 385like fractions, 220–224, 256mixed numbers, 221, 234, 716polynomials, 678–681, 699simplifying expressions, 100solving equations, 110–111, 113,

139, 244solving inequalities, 345–349unlike fractions, 232–236, 257

Subtraction expressions, 100, 102,104

Subtraction Property of Equality,110, 111, 360

Sums, 61, 64, 67, 74, 79, 91, 93, 107,230, 235, 242, 256, 257, 327, 605,712, 716, 725, 726, 734, 735, 756.See also Addition

Surface area, 594, 751cubes, 157, 694prisms and cylinders, 573–577,

597pyramids and cones, 578–582, 597

Symbols. See also Grouping symbolsbar notation, 201break in scale, 624congruent, 493equality, 28equals sign, 126inequality, 28, 57, 59, 90, 93� (is about equal to), 437negative signs, 675radical sign, 436variable, 17

Symmetric Property of Equality, 29,30, 31

Symmetry, 505bilateral, 505line, 505rotational, 505turn, 505

Systems of equationsgraphing, 422solving, 414–418, 428, 440, 582

Systems of inequalities, 422graphing, 346, 348

Tables, 708functions, 369–370identifying functions, 688ordered pair solutions, 375, 378,

686relations, 35, 36, 37, 50writing equations, 406

Tangent, 747

Tangent ratios, 477–481, 479, 486

Term, 103

Terminating decimals, 200, 203, 206

Tessellations, 527, 529, 530, 531, 532

Test preparation. See Assessment

Test-Taking Tips. See Assessment

Theoretical probability, 311

Three-dimensional figures,552–601building, 554–555identifying, 556–561precision and significant digits,

589, 590–594, 598similar solids, 583, 584–588, 598surface area

prisms and cylinders, 573–577,597pyramids and cones, 578–583,597

volumeprisms and cylinders, 563–567,596pyramids and cones, 568–572,596

Transformations, 512, 686coordinate plane, 506–511,

545–546

Transitive Property of Equality, 29,30, 31

Translations, 506, 507, 509, 510, 512,686, 748

Transversal, 492–493, 495, 496, 544,549, 747

Trapezoids, 514, 515, 546

area, 521, 522–523, 547

Tree diagram, 635, 637, 638, 645

Triangles, 38, 453–457, 485, 528acute, 454, 456, 746angle measures, 453area, 521, 522, 523, 547congruent, 500–504, 545, 748equilateral, 455isosceles, 455obtuse, 454, 456, 746obtuse isosceles, 455, 470, 485right, 454, 456, 460, 461, 462, 463,

464, 481, 485, 746right scalene, 470, 485scalene, 455similar, 471–475, 486vertex, 88

Triangular numbers, 457

Triangular prisms, 557, 562, 564,566, 572, 587

Triangular pyramid, 557

Trigonometric ratios, 477–481, 486

Trigonometry terms, 477

Trinomials, 669, 671, 681, 698, 755

Turn symmetry, 505

Twin primes, 162

Two-dimensional figures, 490–551,561

Two-step equations, 120solve, 327solving, 120–122, 140, 327, 354,

451writing, 126–130, 140

Unit fraction, 236

Unit rates, 265–268, 359, 445, 736

Unlike fractionsaddition, 232–236, 257subtraction, 232–236, 257

Unlike terms, 674, 677

Variables, 17, 18, 19, 28, 30, 31, 48, 49, 725defining, 18dependent, 375independent, 375

T

U

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Index

Index R67

linear equations in two, 375–379,425

showing relationships, 17, 21solving equations, 328–329,

330–333, 360, 397

Venn diagram, 164, 441

Verbal expressionstranslating expressions into, 11,

38, 124, 125translating into expressions, 13,

14, 15, 18, 19, 20, 30, 32, 51, 74,105

writing numerical phrases, 724

Verbal problems, two-step, 127

Vertical lines, 383

Vertical line test, 370

Vertices, 88, 447, 453, 527, 545–546,556, 557, 559, 595, 599

Volume, 750, 751 complex solid, 564cones, 568–572, 596, 616prisms and cylinders, 563–567,

596pyramids and cones, 568–572,

596

WebQuest, 43, 79, 135, 136, 145, 173, 242, 301, 314, 325, 333, 412, 422,433, 481, 543, 571, 594, 603, 626,691, 696

Whole numbers, 27, 84, 205, 216,444, 451

Work backward, 122, 240, 362, 707,709, 712, 713, 714, 715, 716, 717,719

Writing in Math, 10, 16, 27, 32, 37,44, 61, 68, 74, 79, 84, 89, 101, 106,114, 119, 123, 130, 136, 152, 157,162, 168, 173, 179, 184, 190, 204,213, 219, 223, 236, 242, 247, 251,268, 274, 280, 285, 292, 297, 302,307, 314, 333, 338, 344, 349, 354,359, 373, 379, 385, 391, 397, 401,408, 412, 418, 422, 440, 445, 451,457, 464, 469, 475, 481, 497, 504,511, 517, 525, 531, 537, 543, 561,567, 571, 577, 582, 588, 594, 611,616, 621, 627, 633, 639, 645, 649,654, 672, 677, 681, 686, 691, 695

x-axis, 33, 36, 40, 86, 92, 508

x-coordinate, 33, 34, 35, 38, 50, 85,86, 508

x-intercept, 381–385, 391, 397, 425,429, 742

y-axis, 33, 36, 40, 86, 92, 508, 509

y-coordinate, 33, 34, 35, 36, 38, 50,85, 86, 508

y-intercept, 381–385, 391, 397,398–399, 400, 401, 404, 406, 408,410, 412, 413, 418, 425, 427, 429,470, 639, 742, 743

Zero, 56Multiplicative Property, 24, 49,

61, 725

Zero pair, 62

Zero slope, 388

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