Splash Screen. Chapter Menu Lesson 3-1Lesson 3-1Square Roots Lesson 3-2Lesson 3-2Estimating Square...

Splash Screen

Chapter Menu

Lesson 3-1 Square Roots

Lesson 3-2 Estimating Square Roots

Lesson 3-3 Problem Solving Investigation: Use a Venn Diagram

Lesson 3-4 The Real Number System

Lesson 3-5 The Pythagorean Theorem

Lesson 3-6 Using the Pythagorean Theorem

Lesson 3-7 Distance on the Coordinate Plane

Lesson 3-1 Menu

Five-Minute Check (over Chapter 2)

Main Idea and Vocabulary

Targeted TEKS

Example 1: Find Square Roots

Example 4: Use Square Roots to Solve an Equation

Example 5:Use Square Roots to Solve a Problem

Lesson 3-1 Ideas/Vocabulary

• Find square roots of perfect squares.

• Perfect square– Squares of integers

• square root– OPPOSITE of squaring a number

– Means “what number times itself”

• radical sign– The square root symbol

Lesson 3-1 TEKS

Square Roots

√X means “What number times itself = X”

Every POSITIVE number has TWO square roots!! EX: √64 = +8 and – 8

EX: √100 = +10 and –10

To find the square roots of fractions, find the square root of the numerator and denominator.

EXAMPLE: √(16/64)

= √16 / √64 = 4/8 = ½ and – ½

Remember: Whatever I do to one side of an equation I MUST DO THE SAME THING TO THE OTHER SIDE!

If they ask me to solve an algebra equation with a squared term, THEY WANT BOTH THE POSITIVE AND NEGATIVE SOLUTIONS!!

Lesson 3-1 Example 1

Find Square Roots

Answer:

indicates the positive square root of 81.

Interactive Lab: Square Roots

Lesson 3-1 Example 1 CYP

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Answer:

indicates the negative square root of

Find Square Roots

0% 0%0%0%

Find Square Roots

Answer: Since (1.2)2 = 1.44 and (–1.2)2 = 1.44, = ±1.2, or 1.2 and –1.2.

indicates both the positive and negative square roots of 1.44.

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A. ±1.2

B. ±1.25

C. ±1.5

D. ±1.75

x2 = 225 Write the equation.

ALGEBRA Solve x2 = 225.

Answer: The equation has two solutions, 15 and –15.

Use Square Roots to Solve an Equation

x = 15 and x = –15 Check 15 15 = 225 and

(–15) (–15) = 225

x = Definition of square root

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A. –9

C. –9 and 9

D. –8 and 8

ALGEBRA Solve x2 = 81.

Area is equal to the square of the length of a side.

MUSIC The art work on the square picture in a compact disc case is approximately 14,161 mm2 in area. Find the length of each side of the square.

Variable

Equation

Let s represent the length of a side.

14,161 = s2

Use Square Roots to Solve a Problem

Answer: The length of a side of a compact disc case is about 119 millimeters since distance cannot be negative.

14,161 = s2 Write the equation.

= s Definition of square root

ENTER=2nd

c 14161 Use a calculator.

119 = s

Use Square Roots to Solve a Problem

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A. 85 inches

B. 93 inches

C. 95 inches

D. 105 inches

ART A piece of art is a square picture that is approximately 11,025 square inches in area. Find the length of each side of the square picture.

End of Lesson 3-1

Lesson 3-2 Menu

Five-Minute Check (over Lesson 3-1)

Main Idea

Targeted TEKS

Example 1: Estimate Square Roots

Example 2: Estimate Square Roots

Example 3: Estimate Square Roots to Solve a Problem

• Estimate square roots.

Lesson 3-2 TEKS

Estimating Square Roots – PART 1

• To Estimate a NON-PERFECT square root:

1. Find the nearest perfect square LOWER

2. Find the nearest perfect square HIGHER

3. Graph them on a number line

4. “Guesstimate” the square root.

When estimating square roots, IT IS VERY USEFUL TO PLOT NUMBERS ON A NUMBER LINE.

Estimate Square Roots

The first perfect square greater than 54 is 64.

The first perfect square less than 54 is 49.

Estimate to the nearest whole number.

Plot each square root on a number line. Then plot .

49 < 54 < 64 Write an inequality.

72 < 54 < 82 49 = 72 and 64 = 82

Find the square root of each number.

7 < < 8 Simplify.

Answer: So, is between 7 and 8. Since 54 is closer to 49 than 64, the best whole number estimate for is 7.

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The first perfect square greater than 41.3 is 49.

The first perfect square less than 41.3 is 36.

Plot each square root on a number line. Then plot

6 < < 7 Simplify.

Find the square root of each number.

36 < 41.3 < 49 Write an inequality.

62 < 41.3 < 72 36 = 62 and 49 = 72

Answer: So, is between 6 and 7. Since 41.3 is closer to 36 than 49, the best whole number estimate for is 6.

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FINANCE If you were to invest $100 in a bank

account for two years, your investment would earn

interest daily and be worth more when you withdrew

it. If you had $120 after two years, the interest rate,

written as a decimal, would be found using the

expression . Estimate this value.

Estimate Square Roots to Solve a Problem

100 < 120 < 121 100 and 121 are the closest perfect squares.

102 < 120 < 112 100 = 102 and 121 = 112

10 < < 11 Find the square root of each number.

First estimate the value of

Answer: The approximate interest rate is 0.10 or 10%.

Since 120 is closer to 121 than 100, the best whole number estimate for is 11. Use this to evaluate the expression.

FINANCE If you were to invest $100 in a bank account

for two years, your investment would earn interest daily

and be worth more when you withdrew it. If you had $150

after two years, the interest rate, written as a decimal,

would be found using the expression .

Estimate this value.

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A. 0.10

B. 0.15

C. 0.20

D. 0.25

FINANCE Estimate the value of .

End of Lesson 3-2

Lesson 3-3 Menu

Main Idea

Targeted TEKS

Example 1: Use a Venn Diagram

• Use a Venn diagram to solve problems.

Lesson 3-3 TEKS

A Venn Diagram usually consists of 2 or 3 circles that intersect each other.

Area that intersects represents number of people involved in BOTH circles!

To create Venn Diagrams do the following:

1) Figure out how many people go in the intersecting areas. – START IN THE MIDDLE!

2) Subtract to find out how many

ppl are in the non-intersecting areas.

REMEMBER: THE TOTAL

NUMBER OF PEOPLE IN EACH

CATEGORY IS THE TOTAL NUMBER

IN THE CIRCLE!!!

LANGUAGES Of the 40 foreign exchange students attending a middle school, 20 speak French, 23 speak Spanish, and 22 speak Italian. Nine students speak French and Spanish, but not Italian. Six students speak French and Italian, but not Spanish. Ten students speak Spanish and Italian, but not French. Only 4 students speak all three languages. Use a Venn diagram to find how many exchange students do not speak any of these languages.

Use a Venn Diagram

Explore You know how many students speak each of the different languages. You want to organize the information.

Use a Venn Diagram

Plan Make a Venn diagram to organize the information.

Solve Draw three overlapping circles to represent the three different languages. Since 4 students speak all 4 languages, place a 4 in the section that represents all three languages. Use the other information given in the problem to fill in the other sections as appropriate.

Use a Venn Diagram

Add the numbers in each region of the diagram:1 + 9 + 6 + 4 + 10 + 2 = 32

Since there are 40 exchange students altogether, 40 – 32 = 8 of them do not speak French, Spanish, or Italian.

Check Check each circle to see if the appropriate number of students is represented.

Use a Venn Diagram

Answer: Eight of the exchange students do not speak French, Spanish, or Italian.

SPORTS Of the 30 students in Mr. Hall’s gym class, 14 students play basketball, 9 students play soccer, and 11 students play volleyball. Three students play basketball and soccer, but not volleyball. One student plays soccer and volleyball, but not basketball. Six students play basketball and volleyball, but not soccer. Only 2 students play all three sports. Use a Venn diagram to organize this information and then answer the question on the next slide.

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A. 6 students

B. 8 students

C. 9 students

D. 10 students

How many students in Mr. Hall’s gym class do not play basketball, soccer, or volleyball?

End of Lesson 3-3

Lesson 3-4 Menu

Targeted TEKS

Key Concept: Irrational Numbers

Example 1:Classify Numbers

Concept Summary: Real Number Properties

Example 4:Graph Real Numbers

Example 5:Compare Real Numbers

Example 6:Compare Real Numbers

Example 7: Compare Real Numbers to Solve a Problem

• Rational Numbers– Numbers that can be written as a fraction

– Includes all WHOLE numbers and INTEGERS

– Whole numbers = 0, 1, 2, 3 …

– Integers = …, -3, -2, -1, 0, 1, 2, 3 …

• Irrational Number– Any number that CAN NOT be written as a fraction

– IT NEVER REPEATS AND NEVER ENDS!

• Real Numbers– All rational and irrational numbers

• Identify and classify numbers in the real number system.

Lesson 3-4 TEKS

CLASSIFYING NUMBERS There are two kinds of Irrational Numbers

A. Constants like PI

B. Square Roots of NON-PERFECT squares (and other roots of non-perfect numbers, but that’s for Algebra 2!)

EVERYTHING ELSE IS A RATIONAL NUMBER!!

Lesson 3-4 TEKS

NOTES – CONT.

ESTIMATING NON-PERFECT SQUARE ROOTS – Part 2 To Estimate a NON-PERFECT square root:

1. Find the nearest perfect square LOWER

2. Find the nearest perfect square HIGHER

3. Graph them on a number line

4. “Guesstimate” the square root. COMPARING REAL NUMBERS – I can only

compare things in math that ???? To compare a rational and irrational number,

SQUARE BOTH OF THEM!

Lesson 3-4 Key Concept 1

Name all sets of numbers to which 0.090909… belongs.

The decimal ends in a repeating pattern.

Classify Numbers

Answer: It is a rational number because it is

equivalent to

0% 0%0%0%

A. rational

B. irrational

C. whole, rational

D. integer, rational

Name all sets of numbers to which 0.1010101010… belongs.

Classify Numbers

Name all sets of numbers to which belongs.

Answer: Since , it is a whole number, an integer, and a rational number.

0% 0%0%0%

A. integer

B. integer, rational

C. integer, whole

D. integer, rational, whole

Classify Numbers

Answer: Since the decimal does not repeat or terminate, it is an irrational number.

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A. rational

B. irrational

C. integer

D. integer, irrational

Lesson 3-4 Concept Summary 1

Graph Real Numbers

Answer:

Estimate and to the nearest tenth. Then graph and on a number line.

or about 2.8

or about –1.4

Estimate and to the nearest tenth. Then graph and on a number line.

Answer:

Compare Real Numbers

Write each number as a decimal.

Replace with <, >, or = to makea true sentence.

Answer: Since 3.875 is greater than 3.872983346…,

0% 0%0%

Compare Real Numbers

Write as a decimal.

Answer: Since is less than 3.224903099…,

0% 0%0%

Replace with <, >, or = to make a true sentence.

BASEBALL The time in seconds that it takes an object to fall d feet is How many seconds would it take for a baseball that is hit 250 feet straight up in the air to fall from its highest point to the ground?

Replace d with

Answer: It will take about 4 seconds for the baseball to fall to the ground.

Compare Real Numbers to Solve a Problem

≈ 3.95 or about 4 Simplify.

≈ 0.25 15.81 Use a calculator. ≈ 15.81

0% 0%0%0%

A. about 4.9 seconds

B. about 5.3 seconds

C. about 5.6 seconds

D. about 6.2 seconds

BASEBALL The time in seconds that it takes an object to fall d feet is How many seconds would it take for a baseball that is hit 450 feet straight up in the air to fall from its highest point to the ground?

End of Lesson 3-4

Lesson 3-5 Menu

Targeted TEKS

Key Concept: Pythagorean Theorem

Example 1: Find the Length of a Side

Example 2: Find the Length of a Side

Key Concept: Converse of Pythagorean Theorem

Example 3: Identify a Right Triangle

• Legs– The shorter sides of a RIGHT triangle

– The sides that form the RIGHT angle

• Hypotenuse– The LONGEST side of a RIGHT triangle

• Pythagorean Theorem– Describes the relationship between the legs and

hypotenuse of RIGHT triangles!

– ONLY APPLIES TO RIGHT TRIANGLES!!

• Converse– “The opposite of”

• Use the Pythagorean Theorem.

Lesson 3-5 TEKS

In a Right triangle:

A2 + B2 = C2

Can be used to find the third side of any right triangle if I know the other two sides.

Write an equation to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth, if necessary.

Find the Length of a Side

c2 = a2 + b2 Pythagorean Theorem

Answer: The equation has two solutions, 20 and –20. However, the length of a side must be positive. So, the hypotenuse is 20 inches long.

c2 = 122 + 162 Replace a with 12 and b with 16.

c2 = 144 + 256 Evaluate 122 and 162.

c2 = 400 Add 144 and 256.

c = 20 or –20 Simplify.

c = Definition of square root

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A. 17 in.

B. 19 in.

C. 20 in.

D. 21 in.

Write an equation to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth, if necessary.

The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. What is a, the length of the other leg?

332 = a2 + 282 Replace c with 33 and b with 28.

1,089 = a2 + 784 Evaluate 332 and 282.

1,089 – 784 = a2 + 784 – 784 Subtract 784 from each side.

305 = a2 Simplify.= a Definition of square root

17.5 ≈ a Use a calculator.

Answer: The length of the other leg is about 17.5 centimeters.

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A. about 16.2 cm

B. about 18.5 cm

C. about 19.7 cm

D. about 21.4 cm

The hypotenuse of a right triangle is 26 centimeters long and one of its legs is 17 centimeters. What is a, the length of the other leg?

Lesson 3-5 Key Concept 2

The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle.

Identify a Right Triangle

252 = 72 + 242 Replace a with 7, b with 24, and c with 25.

?625 = 49 + 576 Evaluate 252, 72, and 242.

625 = 625 Simplify.

Answer: The triangle is a right triangle.

Lesson 3-5 CYP 3

0% 0%0%

A. It is a right triangle.

B. It is not a right triangle.

C. Not enough information to determine.

The measures of three sides of a triangle are 13 inches, 5 inches, and 12 inches. Determine whether the triangle is a right triangle.

End of Lesson 3-5

Lesson 3-6 Menu

Main Idea

Targeted TEKS

Example 1:Use the Pythagorean Theorem to Solve a Problem

Example 2:Test Example

• Solve problems using the Pythagorean Theorem.

Lesson 3-6 TEKS

To Solve problems with the Pythagorean Theorem:

1. Draw and Label a picture

2. Write down the Pythagorean Theorem

3. “Plug in what you know, and solve for what you don’t!”

1. Be CAREFUL to plug the hypotenuse in for C!!!!

RAMPS A ramp to a newly constructed building must be built according to the guidelines stated in the Americans with Disabilities Act. If the ramp is 24.1 feet long and the top of the ramp is 2 feet off the ground, how far is the bottom of the ramp from the base of the building?

Notice the problem involves a right triangle.

Use the Pythagorean Theorem.

Use the Pythagorean Theoremto Solve a Problem

Answer: The end of the ramp is about 24 feet from the base of the building.

24.12 = a2 + 22 Replace c with 24.1 and b with 2.

580.81 = a2 + 4 Evaluate 24.12 and 22.

580.81 – 4 = a2 + 4 – 4 Subtract 4 from each side.

576.81 = a2 Simplify.

24.0 ≈ a Simplify.

= a Definition of square root

Use the Pythagorean Theoremto Solve a Problem

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A. about 30.4 feet

B. about 31.5 feet

C. about 33.8 feet

D. about 35.1 feet

RAMPS If a truck ramp is 32 feet long and the top of the ramp is 10 feet off the ground, how far is the end of the ramp from the truck?

The cross-section of a camping tent is shown below. Find the width of the base of the tent.A. 6 ft

B. 8 ft

C. 10 ft

D. 12 ft

Use the Pythagorean Theorem

Read the Test Item

From the diagram, you know that the tent forms two

congruent right triangles. Let a represent half the base of

the tent. Then w = 2a.

Solve the Test Item

c2 = a2 + b2 Write the relationship.

102 = a2 + 82 c = 10 and b = 8

100 = a2 + 64 Evaluate 102 and 82.

100 – 64 = a2 + 64 – 64 Subtract 64 from each side.

36 = a2 Simplify.

Use the Pythagorean Theorem.

= a Definition of square root

6 = a Simplify.

Answer: The width of the base of the tent is 2a or (2)6 = 12 feet. Therefore, choice D is correct.

The cross-section of a camping tent is shown below. Find the width of the base of the tent.A. 6 ft

B. 8 ft

C. 10 ft

D. 12 ft

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A. 15 ft

B. 18 ft

C. 20 ft

D. 22 ft

This picture shows the cross-section of a roof. How long is each rafter, r?

End of Lesson 3-6

Lesson 3-7 Menu

Main Ideas and Vocabulary

Targeted TEKS

Example 1:Name an Ordered Pair

Example 2:Name an Ordered Pair

Example 3:Graphing Ordered Pairs

Example 4:Graphing Ordered Pairs

Example 5:Find Distance on the Coordinate Plane

Example 6: Use a Coordinate Plane to Solve a Problem

• coordinate plane – TURN TO PAGE 173 AND DRAW A COORDINATE PLANE

• Graph rational numbers on the coordinate plane.

• origin

• y-axis

• x-axis

• quadrants

• ordered pair

• x-coordinate

• abscissa

• y-coordinate

• ordinate

• Find the distance between two points on the coordinate plane.

Lesson 3-7 TEKS

To graph a point on a coordinate Move LEFT or RIGHT on the X axis FIRST

Move UP or DOWN on the Y axis SECOND

Remember “RUN BEFORE YOU JUMP!”

To Find the Distance between two points do the following:

1. DRAW a right triangle connecting the dots using the gridlines on the graph

2. FIND the lengths of the legs (count or subtract)

3. USE the Pythagorean Theorem to find the distance.

• Start at the origin.

Name the ordered pair for point A.

Name an Ordered Pair

• Move right to find the x-coordinate of point A, which is 2.

• Move up to find the y-coordinate, which is

Answer: So, the ordered pair for point A is

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Name the ordered pair for point A.

• Start at the origin.

Name the ordered pair for point B.

Name an Ordered Pair

• Move down to find the y-coordinate, which is –2.

• Move left to find the x-coordinate of point B,

which is

Answer: So, the ordered pair for point B is

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Name the ordered pair for point B.

• Start at the origin and move 3 units to the left. Then move up 2.75 units.

• Draw a dot and label it J(–3, 2.75).

Graph and label point J(–3, 2.75).

Graphing Ordered Pairs

Answer:

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Graph and label point J(–2.5, 3.5).A.

Graphing Ordered Pairs

Answer:

Graph and label point K

• Start at the origin and move 4 units to the right.

Then move down units.

• Draw a dot and label it

0% 0%0%0%

Graph and label point KA.

Let c = the distance between the two points, a = 5, and b = 5.

Graph the ordered pairs (0, –6) and (5, –1). Then find the distance between the points.

Find Distance in the Coordinate Plane

Answer: The points are about 7.1 units apart.

c ≈ 7.1 Simplify.

= Definition of square root

c2 = 50 52 + 52 = 50

0% 0%0%0%

A. about 3.1 units

B. about 3.6 units

C. about 3.9 units

D. about 4.2 units

Graph the ordered pairs (0, –3) and (2, –6). Then find the distance between the points.

TRAVEL Melissa lives in Chicago, Illinois. A unit on the grid of her map shown below is 0.08 mile. Find the distance between McCormickville at (–2, –1) and Lake Shore Park at (2, 2).

Let c = the distance between McCormickville and Lake Shore Park. Then a = 3 and b = 4.

Use a Coordinate Plane to Solve a Problem

Answer: Since each unit equals 0.08 mile, the distance is 0.08 5 or 0.4 mile.

c = 5 Simplify.

c2 = 25 32 + 42 = 25

= Definition of square root

The distance between McCormickville and Lake Shore Park is 5 units on the map.

Use a Coordinate Plane to Solve a Problem

0% 0%0%0%

A. about 0.1 mile

B. about 0.2 mile

C. about 0.3 mile

D. about 0.4 mile

TRAVEL Sato lives in Chicago. A unit on the grid of his map shown below is 0.08 mile. Find the distance between Shantytown at (2, –1) and the intersection of N. Wabash Ave. and E. Superior St. at (–3, 1).

End of Lesson 3-7

Resources Menu

Five-Minute Checks

Image Bank

Math Tools

Square Roots

The Pythagorean Theorem

Lesson 3-1 (over Chapter 2)

Lesson 3-2 (over Lesson 3-1)

Five-Minute Menu

Image Bank 1

To use the images that are on the following three slides in your own presentation:

1. Exit this presentation.

2. Open a chapter presentation using a full installation of Microsoft® PowerPoint® in editing mode and scroll to the Image Bank slides.

3. Select an image, copy it, and paste it into your presentation.

Image Bank 2

Image Bank 3

Image Bank 4

(over Chapter 2)

5 Min 1-1

0% 0%0%0%

A. 1.2...

B. 0.911

C. 0.8181...

D. 0.11

Write the fraction as a decimal.

(over Chapter 2)

5 Min 1-2

0% 0%0%0%

A. 7.6

B. 6.625

C. 5.375

D. 3.75

Write the mixed number as a decimal.

(over Chapter 2)

5 Min 1-3

0% 0%0%0%

Multiply. Write in simplest form.

(over Chapter 2)

5 Min 1-4

0% 0%0%0%

A. –27

B. –18

C. –16

D. –4.5

Divide. Write in simplest form. –9 ÷

5 Min 1-5

0% 0%0%0%

Mercury is the closest planet to the Sun. Mercury is 3.6 × 107 miles away from the Sun. Write the distance from Mercury to the Sun in standard form.

A. 360,000 miles

B. 3,600,000 miles

C. 36,000,000 miles

D. 360,000,000 miles

(over Chapter 2)

5 Min 1-6

0% 0%0%0%

A. 3/12 cup

B. 2/7 cup

C. 3/7 cup

D. 11/12 cup

Samuel used 1/4 cup of regular sugar and 2/3 cup of brown sugar to make molasses cookies. How much sugar did Samuel use to make the molasses cookies?

(over Chapter 2)

5 Min 2-1

0% 0%0%0%

(over Lesson 3-1)

5 Min 2-2

0% 0%0%0%

A. –14

B. –12

(over Lesson 3-1)

Find –

5 Min 2-3

0% 0%0%0%

Solve the equation q2 = 16.

(over Lesson 3-1)

C. ± 4

D. ± 8

5 Min 2-4

0% 0%0%0%

(over Lesson 3-1)

Solve the equation .

5 Min 2-5

0% 0%0%0%

Find the positive square root of 36.

(over Lesson 3-1)

5 Min 2-6

0% 0%0%0%

The chairs in the multi-purpose room of a school need to be arranged in a square. If there are 225 chairs, how many should be in each row?

(over Lesson 3-1)

5 Min 3-1

0% 0%0%0%

(over Lesson 3-2)

5 Min 3-2

0% 0%0%0%

(over Lesson 3-2)

5 Min 3-3

0% 0%0%0%

Estimate the solution of x2 = 102 to the nearest integer.

A. ± 4

B. ± 5

C. ± 10

D. ± 11

(over Lesson 3-2)

5 Min 3-4

0% 0%0%0%

Estimate the solution of p2 = 62 to the nearest integer.

A. ± 3

B. ± 4

C. ± 7

D. ± 8

(over Lesson 3-2)

5 Min 3-5

0% 0%0%0%

Choose the two numbers that have square roots between 9 and 10.

A. 82, 87

B. 80, 87

C. 79, 101

D. 82, 101

(over Lesson 3-2)

5 Min 3-6

0% 0%0%0%

Which of the following is in order from least to greatest?

(over Lesson 3-2)

5 Min 4-1

0% 0%0%0%

PETS The table shows the pets of students in the 8th grade. How many students have a dog?A. 7

(over Lesson 3-3)

5 Min 4-2

0% 0%0%0%

CONCESSIONS One evening at a movie concession stand, 80 customers bought popcorn, 55 customers bought a soft drink, and 35 bought a box of candy. Of those who bought exactly two items, 35 bought popcorn and a soft drink, 10 bought a soft drink and candy, and 5 bought popcorn and candy. Three customers bought all three. How many customers bought only popcorn?

(over Lesson 3-3)

5 Min 4-3

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Mrs. Jenkins conducted a survey of her student’s favorite type of book. Of the 28 students in her class, 14 said fiction was their favorite, and 7 said nonfiction was their favorite. Of her students, 3 said that both types of books were their favorite. How many students said that neither fiction nor nonfiction was their favorite?

(over Lesson 3-3)

5 Min 5-1

0% 0%0%0%

Name all sets of numbers to which the real number 286 belongs.

A. rational, integer, whole number, real

B. integer, irrational, rational, real

C. integer, irrational, real

D. irrational, real

(over Lesson 3-4)

5 Min 5-2

0% 0%0%0%

A. rational, real

B. integer, real

C. whole number, real

D. irrational, real

(over Lesson 3-4)

Name all sets of numbers to which the real number belongs.

5 Min 5-3

0% 0%0%0%

B. 5.8

D. 2.9

(over Lesson 3-4)

Estimate to the nearest tenth.

5 Min 5-4

0% 0%0%0%

A. 16.6

C. 17.9

(over Lesson 3-4)

Estimate to the nearest tenth.

5 Min 5-5

0% 0%0%1. A

A. always

B. sometimes

C. never

(over Lesson 3-4)

Are irrational numbers sometimes, always, or never rational numbers?

5 Min 5-6

0% 0%0%0%

A. real

B. rational

C. fractions

D. negative integers

(over Lesson 3-4)

To which set does not belong?

5 Min 6-1

Write an equation you could use to find the length of the missing side of the right triangle in the figure. Then find the missing length. Round to the nearest tenth if necessary.A. x2 + 42 = 32; 5 cm

B. x2 + 32 = 42; 3.6 cm

C. 32 + 42 = x2; 5 cm

D. 32 + 42 = x2; 25 cm

(over Lesson 3-5)

5 Min 6-2

0% 0%0%0%

Write an equation you could use to find the length of the missing side of the right triangle in the figure. Then find the missing length. Round to the nearest tenth if necessary.A. 152 + x2 = 252; 20

B. 252 + x2 = 152; 24.7

C. 152 + 252 = x2; 25.3

D. 152 + 252 = x2; 29.2

(over Lesson 3-5)

5 Min 6-3

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Write an equation you could use to find the length of the missing side of the right triangle in the figure. Then find the missing length. Round to the nearest tenth if necessary.A. 122 + 132 = x2; 17.7

B. 122 + 132 = x2; 13.5

C. x2 + 122 = 132; 12.5

D. x2 + 122 = 132; 5

(over Lesson 3-5)

5 Min 6-4

(over Lesson 3-5)

Is a triangle with side lengths of 18, 25, and 33 a right triangle?

A. yes

5 Min 6-5

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A man drives 33 miles east and 12 miles south. Approximately how many miles is the man from his starting point?

(over Lesson 3-5)

5 Min 7-1

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In the figure, a plane is traveling from point A to point B. How far will the plane have flown when it reaches its destination? Write an equation that can be used to answer the question and solve. Round to the nearest tenth if necessary.

A. 3002 – 2002 = p2; 223.6 km

B. 300 – 200 = p; 100 km

C. 300 + 200 = p; 500 km

D. 3002 + 2002 = p2; 360.3 km

(over Lesson 3-6)

5 Min 7-2

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Refer to the figure. A girl is pinning ribbon to a 3’ × 4’ bulletin board. How long will the ribbon have to be to stretch from corner to corner diagonally? Write an equation that can be used to answer the question and solve. Round to the nearest tenth if necessary.

A. 42 + 32 = r2; 5 ft

B. 4 + 3 = r; 7 ft

C. 42 – 32 = r2; 3.6 ft

D. r2 – 32 = 42; 2.6 ft

(over Lesson 3-6)

5 Min 7-3

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A. 42 in.

B. 58 in.

C. 72 in.

D. 84 in.

In the figure, triangle ABC is a right triangle. What is the perimeter of the triangle?

(over Lesson 3-6)

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