Algebra 1: All-In-One Answers Version B 30, 2013/High School... · ... Locn. B: mean 75.933, median 75, mode =66, range 26 ... it is still smaller than the range for plant B. 1A:

Chapter 1Practice 1-11. 7 + x 2. 3p 3. 10 - m 4. 7 - n 5. 2q 6. m + 37. 8 divided by a 8. 10 less than s 9. 13 more than x 10. 8 - n 11. 4 + n 12. 2n 13. 3 + n 14. c = 24.95s15. g = 30t 16. n = 48 - g 17. c = 32.95p 18–20. Choice of variables may vary.t = number of tickets, c = total cost;h = number of hours, d = distance;h = number of hours, p = total pay18. c = 3.50t 19. d = 55h 20. p = 5h

Guided Problem Solving 1-11. amount of money and the number of quarters 2. $0.25 3. $0.50 4. Multiply the value of a quarter, 0.25, times thenumber of quarters, 5; 0.25(5). 5. 0.25q 6. a = 0.25q7. Answers may vary. 8. B

Practice 1-21. 52 2. 2 3. 38 4. 4 5. 87 6. 2 7. 1 8. 9 9. 5 10. 2 11. 6 12. 26 13. 29 14. 31 15. 88 16. 85 17. 28 18. 1219. 26 20. 5 21. 55 22. 56 23. 60 24. 16 25. 22 26. 12

Guided Problem Solving 1-21. V = πr2h; SA = 2πr(r + h) 2. 12 fl. oz. 3. 1.3 in. 4. 4.5 in.5. 3.14 6. 23.88 in.3 7. 47.38 in.2 8. 2.0 in.3 9. 24 � 2 = 1210. 31.40 in.3

Practice 1-31. rational, real 2. rational, real 3. natural, whole, integers,rational, real 4. irrational, real 5. irrational, real 6. integers, rational, real 7. rational, real 8. natural, whole,integers, rational, real 9. true 10. false;-2 11. true12. false; 7 3 2 = 14 13. . 14. , 15. , 16. = 17. .

18. , 19. 20.

21. 22. 23.

24. 25. whole 26. rational 27. whole

28. irrational 29. 30. 327 31. 3.46 32.

Guided Problem Solving 1-31. Answers may vary.2.

3. R:-3; T: 3 4. -75.

6. C

Practice 1-41. p = 9t 2. c = 13n 3. m = 5n + 20 4. c = 2.50n + 7.50 5. number of hours; amount earned 6. number of people; cost 7. number of minutes; volume8. price; number of people

Guided Problem Solving 1-41. Add the lengths of all sides together.2.

3. 2 4. p = 3 + 2n 5. p = 3 + 2(3); p = 9 6. p = n + 2

Practice 1-51.

2.

3. positive correlation 4. negative correlation 5. no correlation 6. no correlation 7. positive correlation

Guided Problem Solving 1-51. toll charge and distance 2. tens 3. the distance a cartraveled on the Indiana toll road and the toll charged 4. The points have the same x-coordinate; they lie on thesame vertical line. 5. The points have the same y-coordinate;they lie on the same horizontal line. 6. Yes, there is a positivecorrelation. In general, as distance increases, the toll increases,but there is considerable scatter. 7. Answers will vary.8. maximum: about $3.25; minimum: about $0.60

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Algebra 1: All-In-One Answers Version B©

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45All-In-One Answers Version B Algebra 1L1

Practice 1-61. 2.5; 2; 1; mean 2. $120.50; $123; no mode; median 3. $31.16; $31.25; no mode; mean 4. 7.11; 8; 8 and 10; median 5. $2.81 6. 3 7a. Loaves of Bread Sold

1 7

2 1 8 9

3 3 4 5 6 7 7 8 9

4 0 0 1 2 2 3 4 5

5 0 1 4

6

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7b. 39.5; 39.5; 37, 40 and 42; 558. Dept. A. mean = 49.643, median = 50, mode = 58,range = 31; Dept. B: mean = 51.857, median = 52,mode = 52, range = 409. Locn. A: mean = 79.2, median = 81, mode = 83 and 90,range = 24; Locn. B: mean = 75.933, median = 75,mode = 66, range = 26

Guided Problem Solving 1-6

1. ; median: the middle value in the set when the numbers are arranged in order;mode: the data item that occurs the most times; range: thedifference between the greatest and least data values 2. Plant A: mean: 5.79; median: 5.75; mode: 5.4; range: 1.2 Plant B: mean: 5.56; median: 5.45; mode: none; range: 2.9 3. A: mean. There are no outliers. B: median. The mean isthrown off by a high outlier. 4. Plant A has better qualitycontrol. The strips of steel produced by their machines have asmaller range. 5. Yes. 6. Answers may vary. Sample: Eventhough the range is larger, it is still smaller than the range forplant B.

1A: Graphic Organizer1. Variables, Function Patterns, and Graphs 2. Answers mayvary. Sample: exponents, order of operations, functions, andscatter plots 3. Check students’ work.

1B: Reading Comprehension1. c; negative buses are not possible and partial buses are notpossible. 2. a, b, c 3. b, c; negative test grades are not possible4. a, b, c 5. b, c; distance is never negative 6. b; cost of anitem is never negative and cost of items are only to the nearestcent 7. a, b, c 8. b

1C: Reading/Writing Math Symbols1. 3 multiplied by 7 or 3 times 7 2. 5 multiplied by thevariable n or 5 times n 3. 3 divided by 4 4. 7 divided by 12 5. Use 2 as a factor x times or 2 to the x power 6. 6 multiplied by 7 or 6 times 7 7. 7 - 3 8. p � 2 or9. 4 � x or 10. y = 9

1D: Visual Vocabulary Practice1. Variable 2. Power 3. Range 4. Opposites 5. ScatterPlot 6. Absolute Value 7. Inequality 8. Whole Numbers9. Function Rule

1E: Vocabulary CheckAlgebraic Expression: A mathematical phrase that caninclude numbers, variables, and operation symbols.Equation: A mathematical sentence that uses an equal sign.Natural Numbers: The counting numbers.Integers: Whole numbers and their opposites.Absolute Value: The distance that a number is from zero ona number line.

1F: Vocabulary Review1. constant 2. base 3. like 4. open 5. power 6. origin 7. term 8. function

Chapter 2

Practice 2-11. 2 2. -15 3. -14 4. -17 5. -41 6. 5 7. 8.9. 33 10. 7 11. -7 12. -0.9 13. -0.7 14. -5 15. 5

16. -18 17. 18. 19. -188F

20. their own 11-yd line

Guided Problem Solving 2-11. The tables give the number of employees that work on eachSaturday and Sunday shift and how much they earn per hour.

2. Saturday: ; Sunday:

3. 4. 4 employees 5. Answers may vary.

Sample: Add the number of employees in each column,multiply that sum by 8 hours and then by the hourly wage forthat column and finally add the products for each columntogether. 6. $3230 7. Answers will vary. 8. 10 employees

Practice 2-21. 7 2. -16 3. -12 4. -8 5. 43 6. -49 7. 12 8. -189. 12 10. 3 11. 9 12. 9 13. -3 14. 17 15. -8 16. -19

17. 18. 19. 298F

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mean 5 sum of the data itemstotal number of data items

Algebra 1: All-In-One Answers Version B (continued)

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Algebra 1 All-In-One Answers Version B L146 Algebra 1 All-In-One Answers Version B L1

Guided Problem Solving 2-21. The tables describe the number of participants in city-widesports activities.

2.

3. 4. Answers may vary. Sample:

Invest in soccer; it is the only sport that has not lostparticipants in any age bracket. 5. Answers may vary.6. Basketball in both years. Answers may vary. Sample: To findthe total participation in e

Practice 2-31. -16 2. 54 3. 81 4. -32 5. -48 6. 6 7. -125 8. 4 9. 112 10. 49 11. 32 12. -4 13. 16 14. -120 15. -7 16. 64 17. 4 18. 72 19. -1019 20. -4

Guided Problem Solving 2-31. h: height in feet above the ground of the roller-coaster car;t: number of seconds since the start of the descent 2. h: feet;t: seconds 3. 139 ft 4. 91 ft 5. 0 ft 6. less than 4 seconds;Answer may vary. Sample: At 3 seconds the roller coaster is11 feet above the ground and at 4 seconds it is minus 101 feet.So the roller coaster is at 0 feet sometime between 3 and4 seconds. 7. Answers may vary. 8. 136 ft

Practice 2-41. 2x + 12 2. -40 + 5b 3. -4x + 28 4. -15c + 215. -3k + 12 6. 4x + 28 7. -2k + 22 8. -4 + 2b9. 6x - 18 10. 8r + 32 11. -5b + 25 12. 3f + 6 13. 1 + 8x 14. 2h + 4 15. 8 + 2y 16. 3w + 12 17. 6a + 4 18. 3t - 15 19. -b + 20 20. 2a + 7 21. 15x + 60 22. 2m + 2 23. 8a - 9 24. 3t - 36 25. 5(x + 6) 26. 2(y - 8) 27. 28. -8(4 - w)

Guided Problem Solving 2-41. a(b + c) = ab + ac 2. number of items and the unit cost 3. 4(1.02) 4. 3(0.99) 5. 3(0.52) 6. 4(1.02) + 3(0.99) +3(0.52) 7. $8.61 8. 4(1) + 3(1) + 3(0.50) = $8.50 9. 2(10.50) + 3(2.99) + 2(1.25) = $32.47

Practice 2-51. Comm. Prop. of Add. 2. Comm. Prop. of Add.3. Ident. Prop. of Mult. 4. Assoc. Prop. of Mult.5. Inverse Prop. of Mult. 6. Distributive Prop.7. Assoc. Prop. of Add. 8. Inverse Prop. of Add.9. Comm. Prop. of Add. 10. Assoc. Prop. of Mult.11. Ident. Prop. of Add. 12. Distributive Prop.

13. Mult. Prop. of Zero 14. Comm. Prop. of Mult.15a. Distributive Prop. 15b. Comm. Prop. of Add.15c. Assoc. Prop. of Add. 15d. Distributive Prop.15e. addition 16a. Distributive Prop. 16b. def. of subtr.16c. Comm. Prop. of Add. 16d. Distributive Prop.16e. addition 16f. def. of subtr. 17. 80 18. 7200 19. 2400

Guided Problem Solving 2-51. Use mental math to determine the total cost.2. Commutative Property of Addition, Associative Property ofAddition 3. You can add numbers in different order and thesum will be the same. 4. You can group numbers togetherdifferently and the sum will be the same. 5. 31.50 + 6.50 +14.97 6. (31.50 + 6.50) + 14.97 7. $52.97 8. 32 + 15 + 6 =$53 9. (24.50 + 12.50) + 13.99 = $50.99

Practice 2-6

1. 2. 3. 4. 5. 6. 7. 8.

9. 23,760 10. 60% or 11a. 11b. 11c.

Guided Problem Solving 2-61. 753,000 have birthdays; 10,700 people turn 16 2. What is theprobability that someone celebrating a birthday is turning 16?

3. 4. 10,700 5. 753,000

6. 7. about 1% 8. 112%; yes; overestimate; Answers

may vary. 9. about 99%

Practice 2-7

1a. 1b. 1c. 1d. 2. 3. 4. 5.

6a. 6b. 6c. 6d. 7. 8.

Guided Problem Solving 2-71. The percent of land in the state that is cropland.2. independent 3. 0.58 4. 0.07 5. 0.08 6. 0.003248 7. Answers may vary. 8. 0.0056

2A: Graphic Organizer1. Rational Numbers 2. Answers may vary. Sample: addingrational numbers, subtracting rational numbers, deductivereasoning and probability 3. Check students’ work.

2B: Reading Comprehension1. the blue whale 2. the weight of the whale skeleton and of the whale 3. About how much of the total weight of thewhale was not the skeleton? 4. 50,000 lbs 5. 160 tons 6. Multiply 160 tons by 2000 lb/ton. 7. 320,000 lb – 50,000 lb8. About 270,000 pounds of the total weight are not theskeleton. 9. b

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Algebra 1: All-In-One Answers Version B (continued)©

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2C: Reading/Writing Math Symbols1. D 2. F 3. G 4. C 5. A 6. B 7. E 8. N 9. J 10. L11. I 12. M 13. H 14. K

2D: Visual Vocabulary Practice1. odds 2. reciprocal 3. like terms 4. constant 5. matrix6. event 7. Multiplication Property of Zero 8. probability9. complement of an event

2E: Vocabulary CheckMultiplicative Inverse: Given a nonzero rational number , it is .

Coefficient: The numerical factor of a term.Like Terms: These have exactly the same variable factors in avariable expression.Constant: A term that has no variable.Matrix: A rectangular arrangement of numbers in rows andcolumns.

2F: Vocabulary Review1. E 2. C 3. D 4. A 5. G 6. B 7. F 8. K 9. L 10. I11. H 12. N 13. M 14. J

Chapter 3

Practice 3-11. 1 2. 2 3. 2 4. 1 5. 3 6. -10 7. 3.50 + 2.50r = 16; 5 roses 8. 24.95 + 5.95s = 50; 4 pair 9. -17 10. 4 11. -36 12. -6 13. 14 14. 16 15. 6 16. -3 17. 9 18. -5 19. 13 20. -2221. a. Subtr. Prop. of Eq.

b. Simplify.c. Mult. Prop. of Eq.d. Simplify.

22. a. Subtr. Prop. of Eq.b. Simplify.c. Mult. Prop. of Eq.d. Simplify.

Guided Problem Solving 3-11. Multiply the claim amount by 0.8 and subtract 500.2. insurance payment and claim amount 3. p: insurancepayment; c: claim amount 4. p = 0.8c - 500 5. p6. $6437.50 7. Answer will vary. 8. $1,900

Practice 3-21. -9.6 2. -3 3. -11 4. -9 5. 5 6. -11 7. 4 8. 3 9. -5 10. 2 11. -5 12. 3 13. 7 14. 23 15. 21 16. -8 17. -2 18. 44 19. 2n + 3(400 - n) =1050; 150 student tickets, 250 adult tickets 20. w + 2w + w + 2w = 30; 10 ft

Guided Problem Solving 3-21. $40 per month plus $.15 for each minute over 200 2. How many extra minutes she was billed for. 3. $40 4. $41.50 5. a = 40 + 0.15m 6. 120 min 7. Answers will vary.8. 4 channels

Practice 3-31. 7 2. 9 3. -15 4. 3 5. identity 6. 5 7. no solution 8. 4 9. 8 10. 2 11. identity 12. identity 13. identity 14. no solution 15. 3 16. 2 17. identity 18. -3 19. 40d = 60 + 20d; 3 days 20. 100 + c = 5c; 25 candles

Guided Problem Solving 3-31. The columns have values for the expressions x, 5(x - 3) and4 - 3(x + 1). 2. He is trying to determine when the expressions5(x - 3) and 4 - 3(x + 1) are equal. 3. A solution makes bothsides of the equation equal. 4. No. 5. 1 and 3 6. for valuesof x greater than 2 7. Answers will vary. 8. He should set upa spreadsheet with columns for x, 2(x + 5) - 2, and 4(x - 7).

Practice 3-41. $0.75/lb 2. 287 bagels/d 3. 680 cal/h 4. $0.56/oz 5. yes; 90 = 90 6. yes; 72 = 72 7. yes; 16 = 16 8. 3 9. 3.5 10. 2 11. 16 12. 2.1 13. 22.5 14. 15 15. 3 16. 4.5 17. 40 18. 18 19. 2 20. 7.2 21. 4.8 22. 3 23. 45 24. 11.25 25. 7 26. 52.5 min 27. beats

Guided Problem Solving 3-41. how the amount of time each person worked compare 2. amount of time each person worked 3. Answers will vary.Sample: amount Tim earned + amount Bonnie earned =total amount 4. 5. 6. 567. Bonnie: $56; Tim: $32 8. Answers will vary. 9. 5.8 tons

Practice 3-51. 7.2 2. 3. 3 4. 5. 6. 6 7. 20 8. 216 in.9. 27.5 ft

Guided Problem Solving 3-51. 1 in.:9 ft. 2. 2.5 in. by 3 in. 3. the actual dimensions of the room 4. 5. 6. 22.5 ft by 27 ft 7. Answers will vary. 8. 15 ft by 18 ft

Practice 3-61. 60(t - 1.5) = 40t; freight train: 4.5 h, passenger train: 3 h 2. 10(t + 1.5) = 25t; 2.5 h 3. 24 = 2(w + 4) + 2w;width: 4 in., length: 8 in. 4. 48 = 2(2w) + 2w; width: 8 in.,length: 16 in. 5. 60t + 50t = 330; 1:00 P.M. 6. 3t + 2t = 4;

h or 48 min 7. x + x + 1 + x + 2 = 126; 41, 42, 43

8. x + x + 2 + x + 4 + x + 6 = 216; 51, 53, 55, 57 9. 84 = 2(w + 8) + 2w; 17 in.10. x + 2x - 8 + 2x - 8 = 74; 18 in.

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Guided Problem Solving 3-61. the speed of each vehicle and information about the timetraveled 2. when the truck and train reach Smithfield3. look at the table and find when the train and truck haveboth traveled the same distance 4. 4:00 P.M. 5. time thetruck traveled 6. the distance traveled 7. Answers will vary.8. 165 mi. and 180 mi.

Practice 3-71. 25% decrease 2. 150% increase 3. 50% decrease 4. 200% increase 5. 40% increase 6. 75% increase 7. 14% increase 8. 31% increase 9. 150% increase 10. 20% decrease 11. 50% increase 12. 10% decrease 13. 11% increase 14. 300% increase 15. 45% increase 16. 0.5 cm; 16.7% 17. 0.05 cm; 10% 18. 0.5 in.; 3.1% 19. 0.005 g; 0.01% 20. 71.25 cm2; 89.25 cm2

21. 11.25 in.2; 19.25 in.2 22. 86.25 m2; 106.25 m2


1. the wholesale cost of a sweatshirt 2.

3. 100% 4. 100% 5. 50% 6. 50% 7. Answers will vary.8. 100%

Practice 3-81. Rational 2. Rational 3. Irrational 4. Rational 5. 4.47 6. 8.54 7. -6.16 8. 11.40 9. 12.22 10. -2.95 11. 14.62 12. -17.91 13. 7 14. -1.5 15. 16. 20

17. 2.5 18. 4 19. 14 20. 1.6 21. 6 and 7 22. 11 and 12

23. -9 and -8 24. 9 and 10 25a. 4.2 ft 25b. 6.4 ft 25c. 7.1 ft 25d. 11.3 ft

Guided Problem Solving 3-81. a formula that relates time and distance 2. t: time it takesfor an object to fall; d: distance an object falls 3. 5 s4. 10 s 5. No; the object takes twice as long to fall.6. Answers will vary. 7. 7.1 s

Practice 3-91. 37 2. 24 3. 60 4. 39 5. 17 6. 32 7. 30.0 8. 46.09. 41.2 10. 11.3 11. 19.0 12. 20.2 13. yes; 202 + 212 = 292 14. yes; 162 + 302 = 342

15. no; 242 + 6022 662 16. no; 142 + 182

2 232

17. no; 102 + 2422 282 18. yes; 452 + 282 = 532

19. yes; 20. yes; 242 + 702 = 742

21. 7 ft 22. 16 ft 23. 13.3 mi 24. 43.6 ft 25. 13.2 ft

Guided Problem Solving 3-91. Answers will vary. Check students’ sketches.2. Pythagorean Theorem 3. 6.9 ft 4. about 89.2 ft2

5. 981 watts 6. Answers will vary. 7. 1338 watts

3A: Graphic Organizer1. Solving Equations 2. Answers may vary. Sample: solvingequations, square roots, ratio and proportion, and thePythagorean Theorem 3. Check students’ work.

3B: Reading Comprehension1. 11.3 2. 12.6 3. a

3C: Reading/Writing Math Symbols1. cents per ounce 2. miles per hour 3. feet per minute 4. kilometers per hour 5. feet per mile 6. dollars per year 7. dollars per pound 8. feet per week 9. gallons per week10. miles per gallon 11. pounds per square inch 12. feet persecond squared 13. meters per second squared 14. dollarsper ounce 15. mi/gal 16. $/lb 17. km/h 18. ft/min

3D: Visual Vocabulary Practice/High-UseAcademic Words1. rate 2. conditional 3. consecutive integers 4. similarfigures 5. perfect squares 6. percent of increase 7. cross products 8. literal equation 9. hypothesis

3E: Vocabulary CheckIdentity: An equation that is true for every value of thevariable.Ratio: A comparison of two numbers by division.Unit analysis: The process of selecting conversion factors toproduce appropriate units.Proportion: An equation that states that two ratios are equal.Cross products: In a proportion, , the products ad andbc. These products are equal.

3F: Vocabulary Review PuzzleL

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Chapter 4

Practice 4-11a. yes 1b. no 1c. yes 2a. no 2b. yes 2c. yes3a. no 3b. yes 3c. yes 4a. no 4b. yes 4c. no5a. no 5b. yes 5c. no 6. x � -5 7. x � -58.

9.

10.

11. Let t = temperature (in degrees Fahrenheit); t # 38 12. Let w = weight (in lb); w # 2000 13. Let n = number of students; n $ 20 14. Let n = number of people; n # 250 15. C 16. D 17. B 18. A

Guided Problem Solving 4-11. Option A consists of flights from Chicago to Dallas toNew Orleans. 2. Option B consists of flights from Chicagoto Orlando to New Orleans. 3. comparing the mileage of option A and option B 4. 798 miles; 433 miles 5. 1231 miles 6. 985 miles; 528 miles 7. 1513 miles 8. Option A � option B 9. The total mileage for option A is less than the total mileage for option B.10. discount store � supply store

Practice 4-21. n � 9;

2. y � 2;

3. b � 6;

4. d � 2.7;

5. f � 10;

6. x � -4;

7. d � 5;

8. m � -1;

9. v � 7;

10. t � -13;

11. y � 9;

12. a � 4;

13. d � 1;

14. s � 0;

15. h � -4;

16. d � -5;

17. n + 94 + 82 + 87 - 2 $ 360, where n = number ofpoints; at least 99 points 18. n + 125 $ 140, where n =

number of at-bats; at least 15 at-bats 19. s + 19 - 5 $ 32,where s = average wind speed at 8 A.M.; 18 mi/h 20. t + 13.5 # 25, where t = time in minutes; 11.5 min

Guided Problem Solving 4-21. 34.0 2. 8.8; 7.9; 8.2 3. 24.9 4. p + 24.9 � 34.0 5. p � 9.1 6. She must score 9.1 or above in the floorexercise. 7. Answers may vary. 8. Answers may vary.9. t + 2.75 � 8; t � 5.25; Samuel has at most 5.25 hoursremaining.

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0 5 6 7 8 9 104321

0 5 6 7 8 9 104321

�13 �11 �9 �7 �5�15

0 5 6 7 8 9 104321

�5 �4 �3 �2 �1 0 54321

�2 �1 0 5 6 7 84321

�5�6�7�8 �4 �3 �2 �1 0 21

5 6 7 8 9 10 11 12432

0 0.9 1.8 3.62.7

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1098 11

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Practice 4-31. s � ;

2. b � 5;

3. r � -10;

4. n � 20;

5. n � 4;

6. n � -42;

7. c � -4;

8. d � -4;

9. t � 15;

10. k � -9;

11. w � 0;

12. v � 2.5;

13. m � 10;

14. p � 34;

15. v � -0.5;

16. x � 45;

17. d � -7;

18. x � -7;

19. c � 9;

20. a � -4;

21. 8h # 40, where h = number of hours; 5 hours 22. 7n $ 28, where n = number of vans; 4 vans 23. 0.5n # 31, where n = number of bricks; 62 bricks


1. 3 mi 2. 20 min 3. 4. ; 5. 9 mi/h

6. Answers may vary. 7. p � ; p � $12.50

Practice 4-41. z � 3 2. k � 2 3. h � -1 4. r � 3 5. u � 20 6. g � 2 7. h � 5 8. p � 5 9. m � 5 10. a � -111. x � 6 12. t � -9 13. 150 + 35n # 850, where n =

number of boxes; at most 20 boxes 14. 5(6) + 4n # 62,where n = number of tables seating four people; no morethan 8 tables 15. 3(200) + 5n $ 1000, where n = numberof adults; at least 80 adults 16. b � 7 17. n � -2 18. d � -0.5 19. j � -12 20. z � 1

Guided Problem Solving 4-41. $250 2. 200 sophomores 3. $1.25 4. $150 5. For x =the number of guests, 0.75(200) + 1.25x � 250, x � 80, so atleast 80 guests must attend. 6. 0.75(200) + 1.25(90) � 250;262.5 � 250 7. For p = the cost of popcorn, 18 + 2p � 30,p � 6, so the popcorn must cost no more than $6.

2500200

r $ 0.15r $ 320

mimin

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Practice 4-51. -10 � s � 0;

2. -1 � x � 2;

3. k � 4 or k � 2;

4. b � 20 or b � 18;

5. -3 � d � -2;

6. -6 � t � 2;

7. -6 � s � 4;

8. j � 2 or j � -2;

9. -2 � x � 2;

10. g � -3 or g � -3;

11. -5 � y � -1;

12. f � 5 or f � -2;

13. d � 7 or d � -1;

14. -2 � h � -1;

15. a � 1 or a � -2;

16. z � 1.05 or z � -1.95;

17. c � 3 or c � -1;

18. h � -1 or h � 2;

19. -750 # n - 10,000 # 750, where n = number of people; from 9250 to 10,750 people;

20. 25 , 5n , 30, where n = number of miles;between 5 and 6 mi;

Guided Problem Solving 4-51. 88° 2. 66° 3. and; Answers may vary. 4. 66 � C � 88 5. Answers may vary. 6. 15 � D � 45.

Practice 4-61. d � 2 or d � -2;

2. h � -6 or h � 6;

3. k � 4 or k � -4;

4. s � -6 or s � -2;

5. c � 3 or c � 1;

6. -4 � n � 1;

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0 1 2 3 4

�5 �4 �3 �2 �1�6�7

2�1�2�3 30 1�4�5 4 5

4�2�4�6 60 2�8 8

2�1�2�3 30 1

�2 �1 0 5 6 7 84321

9250 10000 10750

�2 �1 0 1 2 3

�2 �1 0 1 2 3 4

�1.95 1.05

�3 �2 �1 0 1 2

�3 �2 �1 0 1�4

�2 �1 0 5 6 7 84321

�2�3 �1 0 1 2 3 4 5 6

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�2�3�4�5 �1

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�2 �1�3 210 3 4 5

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7. -6 � x � 6;

8. -5 � t � 1;

9. j � 8 or j � -8;

10. -4 � v � 0;

11. -4.5 � y � -1;

12. n � 1 or n � 0;

13. 1 � h � 3;

14. -2 � x � 2;

15. 2 � s � 6;

16. w � 7 or w � -1;

17. 49.5 18. no solution 19. 412 20. 4,-18 21. ∆s - 25« � 3; between 22 and 28 seeds, inclusive22. ∆s - 72« � 2; between 70 and 74, inclusive23. ∆a - 75« � 6.50; between $68.50 and $81.50, inclusive24. ∆l - 25.5« � 0.025; between 25.475 and 25.525 cm, inclusive

Guided Problem Solving 4-61. 42% 2. 43% 3. v – 42 � 3 4. v � 45 5. 45% 6. v - 42 � -3 7. v � 39 8. 39% 9. Answers may vary.10. 272 gallons; 212 gallons

4A: Graphic Organizer1. Solving Inequalities 2. Answers may vary. Sample:inequalities and their graphs, solving inequalities, compoundinequalities, and absolute value equations and inequalities.3. Check students’ work.

4B: Reading Comprehension1. D 2. C 3. B 4. A 5. H 6. G 7. E 8. F 9. True 10. False 11. False 12. True 13. a

4C: Reading/Writing Math Symbols1. is less than 2. is greater than 3. is less than or equal to 4. is greater than or equal to 5. is equal to 6. 8 is greaterthan 4. 7. 12 is less than 25. 8. 3x is less than or equal to 15.9. 4x plus 2 is greater than or equal to 12. 10. 12x equals 36.11. 8 , 12 12. 17 . 2 13. 12x . 36 14. 15x - 8 , 3215. 10x + 4 $ 15 16. 3x - 12 # 21 17. 32x = 12 + 4x

4D: Visual Vocabulary Practice1. absolute value 2. graph of an inequality 3. compoundinequality 4. identity 5. equivalent inequalities 6. inequality 7. Addition Property of Inequality 8. graph ofa compound inequality 9. absolute value inequality

4E: Vocabulary CheckInequality: A mathematical sentence that compares the valueof two expressions using a less than or greater than symbol.Solution of an inequality: The value or values of a variablein an inequality that makes the inequality true.Variable: A symbol, usually a letter, that represents one ormore numbers.Identity: An equation that is true for every value.Evaluate an expression: Substitute a given number for eachvariable, and then simplify.

4F Vocabulary Review Puzzle1. reciprocal 2. exponent 3. whole numbers 4. variable 5. coefficient 6. quadrants 7. identity 8. compoundinequalities

Chapter 5

Practice 5-11. Speed vs. Time

Time

Spee

d

0

�2 �1 0 5 6 7 84321

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2.

3.

4. The distance from home is not changing.5. The distance from home decreases.6. The distance from home increases.7.

Answers may vary. Sample: In sections 0 to 1, 3 to 4, and 6 to 7,the speed is increasing. In sections 2 to 3, 5 to 6, and 8 to 9, thespeed is decreasing. In sections 1 to 2, 4 to 5, and 7 to 8, thespeed is constant. At 0, 3, 6, and 9, the car is not moving.

Guided Problem Solving 5-11. Horizontal axis: time; vertical axis: classmate’s distancefrom detector. 2. Match descriptions of the student’s walk toparts of the graph.3.

4. The student is standing still. 5. With distance decreasing,the graph should slant downward. 6. The first section.7. A straight line slanting up or down. 8. The first twosections. 9. The student walks toward the detector at

constant speed, then turns around and walks away at constantspeed, and finally stops and stands still for a while. This isconsistent with the preceding answers. 10. The student standsstill for a while, then walks away from the detector at constantspeed, and finally turns around and walks back toward thedetector at constant speed.

Practice 5-21. no 2. no 3. yes 4. no 5. yes 6. no 7. 2 8. 0 9. {-5, -1, 1, 3} 10. {0, 0, 6} 11. {-4, -1, -9}

12.

Guided Problem Solving 5-21. d = 180 - 25g means that to find d, the distance fromhome at any given moment, you take the starting distance of180 miles and subtract the distance already traveled, which isgiven by g, the number of gallons used so far, times 25, thenumber of miles each gallon is good for. 2. Use the equationd = 180 - 25g to make a table and predict how many gallonsthe homeward trip will take, then discuss the reasonabledomain for this situation.3.

4. 7 gallons 5. the domain of g is all real numbers between 0 and about 7 6. the range of d is all real numbers between 0 and 180 7. 175 miles; yes 8. With x = miles run and y = calories still remaining, y = 520 - 115x.

Practice 5-3

For Exercises 1–3, answers may vary. Sample:

1.

2a.

2b. No; n is a discrete variable.

12

43

5

21 3 4O n

T(n)n T(n)

2 4.00

3 4.50

4 5.00

6 6.00

23

21O x

f(x)x f(x)

-1 0

0 1

1 2

2 3

e 0, 12, 12 f

Dis

tan

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Time

increasingdistance

decreasingdistance constant

0

Trip to Mall

Time

Spee

d

10 2 3 4 5 6 7 8 9

Time

Spee

d

0

Time

Spee

d

0


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g 2 4 6 8

d 130 80 30 -20

3. 4.

For Exercises 5–6, answers may vary. Sample:

5. 6.

Guided Problem Solving 5-31. One, two, three and four, respectively2. A function relating the perimeter of the block of tiles to thenumber of tiles.3.

4. Use a = b = 2: P(t) = 2t + 2 5.

6. The function correctly predicts a perimeter of 12 units.7. y =-3x + 7

Practice 5-41. ƒ(x) = x + 3 2. ƒ(x) = 3x 3. ƒ(x) = x - 5 4. C(p) = 0.9p 5. f(h) = 3h 6a. C(n) = 10 - 1.50n6b. $4.00 6c. no 7a. P(n) = 25.00a - 500 7b. $750.00 7c. 20 jackets

Guided Problem Solving 5-41. Dependent: gallons of water; independent: number of loads2. Write a function, and use the function to find the number ofgallons given the number of loads, and vice versa. 3. 34 4. 34 gallons of water 5. With n = number of loads and w =

gallons of water, w(n) = 34n. 6. 238 gallons 7. 442 = 34nimplies that n = 13 loads. 8. Yes, 34 � 0 = 0. 9. m = 45g

Practice 5-51. yes; 3 2. yes;-3 3. no 4. yes; 6 5. yes; 2 6. no 7. 4 8. -3 9. 3 10. 5 11. 3 12. -8 13. yes; y = 2x14. yes; y = 4x 15. no 16a. g = 4c 16b. 96

Guided Problem Solving 5-51. Answers may vary. Possible answer: “y is directlyproportional to x.” 2. Find the relationship between bloodand weight, describe the relationship with an equation, and usethe equation to estimate the volume of blood in my body,

based on my weight. 3. y = kx 4. 5.6. Answers will vary. Possible answer: For a 140-lb student, the

answer should be quarts. 7. Yes,

8. about one sixteenth

Practice 5-61. xy = 6 2. xy = 20 3. xy = 21 4. xy = 18 5. xy = 44 6. xy = 15 7. 10 8. 8 9. 16 10. 2 11. 37 12. 2 13. Inverse 14. Direct 15. Inverse variation; xy = 50 16. Inverse variation; xy = 48 17. Direct variation; y = 11x18. Direct variation; y = 2x 19. Inverse variation; xy = 2020. Inverse variation; xy = 12

Guided Problem Solving 5-61. The variable quantities involved in the situation, and anequation relating them to each other.2. pay = hours worked � hourly rate3.

4. Pay is fixed at $80. 5. Hours worked (t) and hourly rateof pay (r). 6. 80 = rt. 7. In each column, rate of pay timeshours worked equals 80. 8. 200 = pn

Practice 5-71. 6 2. -3 3. 5 4. 3 5. 6. 7. 10, 20 8. 0,-209. 15, 30 10. -31,-46 11. 25, 50 12. 2.7, 7.7 13. 9, 1114. 12, 16 15. -19,-24 16. -26.6,-35.7 17. yes;common diff. = -0.2 18. no 19. no 20. no

Guided Problem Solving 5-71. Use the given rows to predict the next row, and find thesum of the numbers in each row, including a predicted sum forthe next row. 2. Except for the 1s, every number is the sum ofthe two numbers above it to the right and left in the precedingrow. 3. The next row is 1 5 10 10 5 1. 4. 1, 2, 4, 8, and 16 5. Each sum is 2 times the sum before it. 6. 327. 1 + 5 + 10 + 10 + 5 + 1 = 32 8. Except for the 1s,every number is the sum of the three numbers above it in thepreceding two rows. The sixth row is 1 9 25 25 9 1.

212

12

13

y 51

16 x;

132 (320 lb) 5 10 qt .43

8

y 51

32 xk 51

32

16

12

8

4

01 2 3 4

x f(x)

-2 2

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x f(x)

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Number of tiles (t) 1 2 3 4

Perimeter (P) 4 6 8 10

Rate of Pay $5/hr $8/hr $10/hr $20/hr

Hours worked 16 10 8 4

5A: Graphic Organizer1. Graphs and Functions 2. Answers may vary. Sample:relating graphs to events, relations and functions, writing afunction rule, and number patterns 3. Check students’ work.

5B: Reading Comprehension1. about 450 cm3 2. about 26 servings 3. a

5C: Reading/Writing Math Symbols1. D 2. E 3. H 4. A 5. C 6. G 7. B 8. F 9. C 10. D 11. F 12. B 13. A 14. H 15. E 16. G

5D: Visual Vocabulary Practice1. continuous data 2. conjecture 3. relation 4. inversevariation 5. common difference 6. discrete data 7. arithmetic sequence 8. function notation 9. direct variation

5E: Vocabulary CheckRelation: A set of ordered pairs.Vertical-line test: If any vertical line passes through morethan one point of the graph then for some value of x there ismore than one value of y.Function notation: Using f(x) to indicate the outputs of afunction.Continuous data: Data where numbers between any twodata values have meaning.Direct variation: A function of the form y = kx, where k � 0.

5F: Vocabulary Review Puzzle


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Chapter 6Practice 6-1

1. 2. -2 3. 4. 5. 6. 1 7. 8. 9.10. 7; point score increases by 7 for each touchdown.

11. ; sound travels 1 mi for each 5 s.

12. -16; the speed decreases 16 ft/s every second.

Guided Problem Solving 6-11. no closer than 5 ft 2. 12 ft; 18 ft 3. the maximum possible slope 4. The slope is the height divided by thedistance of the base from the vertical surface. 5. Put the baseas close to the vertical surface as is allowed, namely at 5 ft.

6. 12 ft; 18 ft 7. or ; or 8. The one that reaches

higher ends up with the greater slope. This makes sense, sinceit has the greater height (18 ft versus 12 ft) being divided bythe same horizontal distance at the base (5 ft). 9. 4 ft

Practice 6-21. 1; 4 2. 2;-2

3. ;-4 4. ; 3

5. -1;-4 6. -5;-6

7. y = 2x + 4 8. y = -3x - 5 9.

10. y = -x + 3 11. 12. y = 4x

13. y = x + 6 14. y = 9 15.

Guided Problem Solving 6-21. 12 in. 2. 8 in. 3. Draw a graph showing candle height as itchanges over time, then write an equation for the samerelationship, and finally predict the time for the candle to burndown to nothing.

4.

5. 12 in. 6. - in./min 7. 8. 90 min

9. 90 is three times 30. The answer checks. 10. ;

120 hours (5 days)

Practice 6-31. y = 2.5x

no

2. y = 2x - 110yes

3. yes

4. y = 25x + 800. The slope of 25 means a charge of $25 perguest, and the y-intercept of 800 means an additional flatcharge of $800 regardless of how many guests are staying.

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50 100 150

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h 512t 1 30

h 5 22

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Guided Problem Solving 6-31. discount price as a function of original price, at ClothingConnection and at Teen World 2. State which store has lowerdiscount prices, write an equation giving discount price as afunction of original price at each store, and find the discountprice at each store when the original price is $16. 3. 0 in both

cases 4. at Clothing Connection and at Teen World

5. at Clothing Connection and at Teen World

6. $12.80 at Clothing Connection and $9.60 at Teen World 7. Yes; the Clothing Connection graph passes through thepoint (16, 12.8) and the Teen World graph passes through the

point (16, 9.6). 8. ; $12 exactly

Practice 6-41. 2.

3. 4.

5. 6.

7. -2x + y = -7 8. -3x + y = -79. 5x + y = -8 10. -6x + y = -2411. -7x + 2y = -22 12. -5x + 2y = 25 13. x + 5y = 2 14. 4x + y = -2015a. 5x + 3y = 45015b.

15c. Answers may vary. Sample: (75 adult, 25 student),(60 adult, 50 student)

16a. 5x + 7y = 7016b.

Guided Problem Solving 6-41. $30 2. $4.29/lb for roast beef; $3.99/lb for turkey. 3. Writean equation relating the amount purchased of each kind ofmeat to the total amount available to spend. 4. x = poundsof roast beef, y = pounds of turkey 5. 4.29x dollars on roastbeef, 3.99y dollars on turkey 6. 4.29x + 3.99y7. 4.29x + 3.99y = 30 8. 6.99 lb or just under 7 pounds. At 2 oz = lb per sandwich, this is enough for 56 sandwiches—realistic for a party of several dozen people.9. 0.75x - 0.10y = 81

Practice 6-5Note: One possible form of the answer is given.1. y - 7 = x - 5 2. y - 4 = -2(x + 3)

3. y - 5 = 6(x + 3) 4.

5. y + 1 = - (x - 5) 6.

7. 8.

9. y = 7 10. x = 3 11. y - 10 = -2(x - 3)

12. 13. yes; y - 3 = 4(x - 2)

14. no 15. yes; y - 5 = -2(x + 2)

16. 17.

18.

Guided Problem Solving 6-51. 2.6 million metric tons per year 2. 79 million metric tons3. Write a linear equation to model the relationship betweencarbon monoxide emissions and time. 4. (91, 79) 5. The rateof decrease describes the downward slope of the line.Point-slope form is easiest. 6. y - 79 =-2.6(x - 91) 7. y =-2.6x + 315.6 8. -2.6(91) + 315.6 = 79 9. y =-1800x + 27,000

Practice 6-6

1. 3 2. 3. -7 4. 5. 0 6. undefined

7. 8. 9. y = -6x - 10

10. 11. 12. y = -2x - 1y 5 243xy 5

23x 1 2

y 515x 1 6y 5 2

13x 1 6

14

23

y 2 2 525(x 2 2)

y 2 4 5 232(x 2 2)y 2 2 5

43(x 2 2)

y 2 3 549(x 2 2)

y 2 4 5 214(x 1 3)y 1 1 5

12(x 1 2)

y 2 6 512(x 2 1)

23

y 1 5 512( x 2 2)

18

x

y

O2�2 4 6

�28 10 12

2468

x

y

O15 30 45

�3060 75

306090

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13. y = 2x - 4 14. y = 3x - 6 15. y = x - 6

16. 17. y = 5x + 20 18.19. neither 20. parallel 21. perpendicular

Guided Problem Solving 6-61. The white grid can be used to calculate slope as verticalchange divided by horizontal change. 2. The slope of New

Hampshire Avenue is about . 3. Each street has a slope of

about - . They are parallel. 4. No. The negative reciprocal of

- is 2, not . New Hampshire Avenue is not perpendicular to

Pennsylvania Avenue. 5. The line with slope 2 should run at aslight angle to New Hampshire Avenue and at right angles toPennsylvania Avenue and Massachusetts Avenue.6. The street would have to have a slope of - .

Practice 6-71. Answers may vary. Sample: y = 25x + 202. not linear3. Answers may vary. Sample: y = + 554. y = -2.6x + 9.6;-0.8535; yes5. y = -3x + 12;-0.6049; no6. y = 0.4223x + 3.9990; 0.7649; no7. Answers may vary. Sample: y = 3x + 15

8. Answers may vary. Sample: y = 3x + 15

Guided Problem Solving 6-71. 3 cm to 12 cm; 9.3 cm to 39.5 cm 2. circumference variesdirectly with diameter.3.

4. Answers will vary. Possible answer:

5. Answers will vary. Possible answer: y - 25 = 3.25(x - 8)6. Answers will vary. Possible answer: y = 3.25x - 1.7. Answers may vary. Sample: The slope is the approximateratio of the circumference to the diameter.8. The circumference of a circle is π, or about 3.14, times thediameter. This implies an equation of the form y = 3.14x.The equation actually obtained is slightly different, possiblydue to measurement errors. 9. Answers will vary.

Practice 6-81. 2.

3. 4.

5. 6.

7. y = ∆x - 1« + 3 8. y = ∆x + 4« - 39. y = ∆x - 2« - 1 10. y = -∆x - 7« + 411. y = -∆x + 1« - 4 12. y = -∆x - 4« + 313. y = ∆3x« 14. y = -∆x - 1« 15. y = -∆x« + 3

Guided Problem Solving 6-81.

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2. It means to write the equation whose graph is shiftedhorizontally or vertically from the graph of the other equation.3. One adds or subtracts from the right side of the equation—add to shift up, subtract to shift down. 4. One replaces x withx plus or minus some amount—plus to shift left, minus to shift right. 5. ;

6. ; 7. Answers will vary.8. , which simplifies to .Since is shifted up 5 units, it makessense that is shifted down 5 units.

6A: Graphic Organizer1. Linear Equations and Their Graphs 2. Answers may vary.Sample: rate of change and slope, slope-intercept form,standard form, scatter plots and equations of lines 3. Check students’ work.

6B: Reading Comprehension1. D 2. C 3. A 4. B 5. b

6C: Reading/Writing Math Symbols1. x-intercept 2. absolute value of x 3. is greater than orequal to 4. slope-intercept form of an equation 5. is lessthan 6. standard form of an equation 7. is equal to 8. slope 9. y-intercept 10. the opposite of x11. y-intercept 12. multiply

6D: Visual Vocabulary Practice/High-UseAcademic Words1. rule 2. equivalent 3. table 4. pattern 5. graph 6. order 7. common 8. property 9. analyze

6E: Vocabulary CheckRate of change: Change in the dependent variable, dividedby change in the independent variable.Slope: The rate of change of a line on a graph.Linear equation: An equation whose graph is a line.Parent function: The simplest equation of a function.Slope-intercept form: y = mx + b

6F: Vocabulary Review1. Parallel lines 2. y-intercept 3. slope-intercept 4. slope 5. range 6. Independent 7. median 8. variable9. reciprocal 10. Commutative Property of Addition 11. decrease 12. absolute value

Chapter 7

Practice 7-11. (1, 2) 2. no solution 3. (11.25, 6.25) 4. (-1,-1) 5. (-1,-1) 6. (3, 0) 7. no solution 8. no solution 9. (8, 7) 10. infinitely many

Guided Problem Solving 7-11. y = 3x 2.y = –2x + 100 3. The location of the ball,which is the point where the two paths cross 4. Slope = 3;y-intercept = 0 5. Slope = –2; y-intercept = 100 6.

7. (20, 60) 8. Yes, opposing players could be racing towardthe ball from different directions, each trying to get there first.With two players on the same team, more likely one would gofor the ball and the other would try to get into position toreceive a pass. 9. (10, 30)

Practice 7-21. (1, 1) 2. (2, 10) 3. (5, 6) 4. (4,-3) 5. infinitely manysolutions 6. (-2,-4) 7. no solution 8. (1, 9)

9. 10. infinitely many solutions

11. no solution 12. infinitely many solutions 13. (1,-3) 14. no solution 15. infinitely many solutions

16. 17. 18. no solution

19. 88 popcorns

Guided Problem Solving 7-21. $17,655 to purchase, plus $1230/yr to operate 2. $15,900 topurchase, plus $1425/yr to operate 3. The time at which thecosts of the two cars are equal 4. c = 17,655 + 1230t5. c = 15,900 + 1425t 6. Answers may vary. Possible answer:You want to find a single time (same t for both cars) when thecost is the same for both cars (same c for both cars). This is thesame as finding a single ordered pair (t, c) for which bothequations are true. 7. It makes more sense to replace c withan expression containing t, since the equations already give cin terms of t. Also, t is the variable we are interested in, so itmakes sense to do a substitution that leads directly to asolution for t, without having to worry about c. 8. Thereplacement leads to 17,655 + 1230t = 15,900 + 1425t, andthe solution is t = 9. 9. It will take exactly 9 years for thetotal costs for the two cars to be the same. 10. Car A costsmore up front but is cheaper to operate. So at first there is acost savings from buying car B, but over time that savingsshrinks and eventually disappears. 11. Same as car A after 7 years; same as car B after 12.2 years

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Practice 7-31. (4, 8) 2. (2,-2) 3. (4,-8) 4. (-18,-30) 5. (0,-1)6. (-3, 2) 7. (5, 5) 8. (7, 4) 9. (0, 2) 10. (4.8, .6) 11. (8, 7) 12. (16, 24) 13. (13, 19) 14. (18,-8) 15. (1, 1) 16. (1.5, 3) 17. (54,-88) 18. (1, 9) 19. shirts: $7.50; pants: $18.50

Guided Problem Solving 7-31. The total cost of each shipment, and the mix of parts ineach shipment 2. The cost of each type of part and, based onthat, the cost of a third shipment 3. 3b + 10s = 484. 7b + 4s = 54 5. Multiplying one or both equations by aconstant 6. 29b = 174 7. b = 6; s = 3; a steel part costs $3and a brass part costs $6. 8. $99 9. The answer makes sense.At a hardware store, brass items (screws, hinges, and so on)are typically a lot more expensive than the same items madefrom steel. 10. $2750 at 3% and $7250 at 5%

Practice 7-41. 30 2-pt; 8 5-pt 2. 15 houses 3. $20; $15 4. 180 min/wk; 150 min/wk 5. 90 T-shirts 6. $2.50; $1.50

Guided Problem Solving 7-41. Buy equipment: $400 plus $35/day; don’t buy equipment:$60/day 2. The minimum number of days you have to ski forit to make sense to buy the equipment, and then also whetherit makes sense to buy the equipment if you expect to ski 5 days a year. 3. c = 400 + 35d 4. c = 60d5. The substitution method, because c is already known interms of d, and since d is the variable of interest, eliminating cwill give the solution directly. 6. d = 16 (and then c = 960).You must ski at least 16 days to justify buying the equipment.(At 16 days you will have spent $960 either way, and after thatbuying the equipment is the cheaper plan.) 7. Answers mayvary. Possible answer: At 5 days of skiing per season, you haveto ski for three seasons and 1 day of a fourth season toaccumulate 16 days. Buying the equipment makes sense only ifyou think your interest in skiing will last that long, and if youthink the equipment will hold up that long. 8. Yes, it seemsreasonable that it takes a couple weeks’ worth of skiing or soto recoup the cost of the equipment. 9. The break-even pointis 11 days of skiing—2 seasons and plus 1 more day. A closecall, but it’s probably best not to buy the used equipment.

Practice 7-51. 2.

3. 4.

5. 6.

7. 8.

9a. 5x + 3y � 150 9b.

9c. Answers may vary. The solutions are all of the coordinatesof the points that are both positive integers within theshaded region. Samples: 20 T-shirts and 20 sweatshirts;25 T-shirts and 10 sweatshirts

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Guided Problem Solving 7-51. $8 2. $12 3. $180 4. 21 5. 12x + 8y � 1806.

7. Yes, which means you have enough money to buy 8 CDsand 9 tapes. (In fact, you have enough to buy 9 CDs and 9tapes.) 8. 22 tapes, plus 21 free CDs makes a total of 43recordings. 9. 36; yes, because the CDs are more expensive,so you can afford fewer of them. 10. Buy 5 CDs and 13 tapes.

Practice 7-61.

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11c. Answers may vary. The solutions are all of thecoordinates of the points that are both positive integers withinthe shaded region or on the boundary lines. Sample: 4 basketsand 5 free throws

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Guided Problem Solving 7-61. Pants cost $10.99, shirts cost $4.99, and you can spend up to$45. 2. You want to buy at least one pair of pants, and in theend you need to buy at least three pairs of pants.3. Write a system of inequalities, and then identify thesolutions that include at least three pairs of pants.4. 10.99x + 4.99y � 45; x � 15.

6. (3, 0), (3, 1), (3, 2), (4, 0) 7. 4 pairs; this is the solution (4, 0).8. (0, 6), (0, 7), (0, 8), (0, 9), (1, 6)

7A: Graphic Organizer1. Systems of Equations and Inequalities 2. Answers mayvary. Sample: solving systems by graphing, solving systemsusing substitution, linear inequalities, systems of linearinequalities 3. Check students’ work.

7B: Reading Comprehension1. y = 1, y = 5, x = 1, x = 5 2. -2, 3. a

7C: Reading/Writing Math Symbols1. C 2. A 3. C 4. B

7D: Visual Vocabulary Practice1. substitution method 2. solutions of a system of linearinequalities 3. linear inequality 4. solution of a system ofequations 5. elimination method 6. infinitely many solutions7. system of linear inequalities 8. no solution 9. solutions ofan inequality

7E: Vocabulary CheckSystem of linear equations: Two or more linear equationstogetherSolution of a system: Any ordered pair in a system thatmakes all the equations true.No solution: A system of equations whose graphs do notintersect.Substitution method: Solving a system by replacing onevariable with an equivalent expression containing the othervariable.Elimination method: Using the Addition and SubtractionProperties of Equality to solve a system.

7F: Vocabulary Review1. B 2. G 3. C 4. E 5. D 6. F 7. A 8. G 9. C 10. E 11. A 12. D 13. B 14. F

Chapter 8

Practice 8-11. 1 2. 3. 4. 12 5. 1 6. 15 7. 8. 1 9.

10. 11. 12. 13. 14. 15. 16.

17. 18. 19. x3 20. 3a8 21. 5d7 22. 10-4

23. 10-6 24. 10-7 25. 0.001 26. 0.00001 27. 0.9


1. Four questions, five choices each. 2.

3. 4.

5. 0 or 1

6. Yes, 0.4096 + 0.4096 + 0.1536 + 0.0256 + 0.0016 = 1.

7. 0 correct:

1 correct:

2 correct:

3 correct:

4 correct:

Practice 8-21. 30,000 2. 0.06 3. 470,000 4. 0.0000234 5. 81,550,0006. 453.07 7. 42,400,000 8. 750,200,000 9. 0.0018 10. 2.4 � 107 11. 5.25 � 1011 12. 6.3 � 10-7

13. 3.85 � 105 14. 4.26 � 10-1 15. 7 � 104

16. 1.6 � 106 17. 3.0 � 10-1 18. 6.3 � 1010

19. 7.2 � 107 20. 3.6 � 10-4 21. 1.22 � 10-7

22. 3.6 � 10-4 23. 1.29 � 10-3 24. 9.6 � 10-2

Guided Problem Solving 8-21. 4.66 � 108 2. Convert instructions per second intoinstructions per minute and per hour, using scientific notation.3. 60 seconds per minute 4. 279.6 � 108 instructions perminute 5. 2.796 � 1010 instructions per minute 6. Conversion factor = 60 minutes per hour; 2.796 � 1010

instructions per minute = 167.76 � 1010 instructions perhour = 1.6776 � 1012 instructions per hour 7. Conversionfactor = 3600 seconds per hour; 4.66 � 108 instructions persecond = 16776 � 108 instructions per hour = 1.6776 � 1012

instructions per hour 8. About 9.5 � 1015 meters per year, or9.5 � 1012 kilometers per year

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Practice 8-3

1. 25a4 2. -24x12 3. 4. r4 5. 313 6. 7. y2

8. b9q2 9. 10. r10a5 11. 12. 25 13. f 5 14.

14. 16. 2.5 � 103 17. 6 � 1012 18. 1.9 � 10-8

19. 1.64 � 1018 20. 1.44 � 10-11 21. 3 � 1011

22. 3.12 � 10-1 23. 3.6 � 1015 24. 4.88 � 1024

Guided Problem Solving 8-31. About 10–10 meter 2. 1000 3. Find the wavelength ofultraviolet rays, and compare the wavelengths of ultravioletrays and visible light. 4. About 10–7 meter 5. Thewavelengths 7.5 � 10–7 meters and 4 � 10–7 meters are bothlonger than a wavelength of 10–7 meter = 1 � 10–7, becausethe exponent on the 10 is the same each time, namely –7, and7.5 and 4 are both greater than 1. 6. Since ultraviolet rayshave a shorter wavelength than visible light and can burn theskin, you would expect X-rays, with an even shorterwavelength, to be even more dangerous. And in fact peoplewho work with X-ray machines take special precautions tolimit everyone’s exposure (lead vests and so on). 7. Longerthan all the others

Practice 8-4

1. 16a10 2. 3. 625 4. x10 5. 8192 6. d18 7. c16

8. z12 9. a8b4 10. 11. 12. y15 13. s18 14. x12y3

15. d13 16. 4 � 10-5 17. 2.7 � 10-17 18. 6.4 � 1023

19. 4.9 � 1015 20. 3.2 � 1013 21. 2.16 � 1017

22. 6.25 � 1022 23. 2.7 � 10-8 24. 8 � 10-9

Guided Problem Solving 8-41. Find expressions for the surface area and volume of eachcube, and compare the two cubes. 2. 6 3. s2 4. 6s2; 6(2x)2

or 24x2; 6(4x)2 or 96x2 5. The large cube’s surface area is4 times the small cube’s surface area. 6. s3 7. (2x)3 or 8x3;(4x)3 or 64x3 8. The large cube’s volume is 8 times the smallcube’s volume. 9. A factor of 4; a factor of 8; yes, it does.10. 216x2; 216x3; surface area is 9 times as great, volume is27 times as great.

Practice 8-5

1. c6 2. 3. 4. 27 5. 343 6. a2b2 7. 8. z10

9. 10. 11. 1 12. 13. 14. 15.

16. 17. 18. 19. � 4.95 � 10-5

20. � 3.19 � 102 21. 2 � 104 22. 2.5 � 10-3

23. � 1.72 � 109 24. 2 � 10-11 25. 4 � 108

26. 3 � 10-5 27. 7 � 108

Guided Problem Solving 8-51. 97.4 million 2. 544 billion local and 97 billion longdistance 3. The average number of local and long distancecalls per household 4. 1 million = 106; 1 billion = 109

5. 97.4 million = 97.4 � 106 = 9.74 � 107 households;544 billion = 544 � 109 = 5.44 � 1011 local calls;97 billion = 97 � 109 = 9.7 � 1010 long-distance calls 6. About 5585 local calls per household 7. About 996 long

distance calls per household 8. � 5.61 9. 4.061 � 103

square miles; 6.1 � 106 motor vehicles; about 1502 vehiclesper square mile

Practice 8-61. 243, 729, 2187 2. 3.

4. 5. 6. 3.75, 1.875, 0.9375

7. geometric 8. arithmetic 9. arithmetic 10. geometric

11. A(n) = 3 ? 3n-1 12. A(n) =

13. A(n) = 16 ? 14. A(n) = 30 ?

15. A(n) = 1 ? 4n-1 16. A(n) = 6 ? 2n-1

17. A(n) = 125 ? 18. A(n) = 50

19. -1, -125, -78, 125 20. 4, 32, 512 21. 4, 64

22. A(n) = 4 ? 3n-1; 972

23. A(n) = -2 ? ;

Guided Problem Solving 8-61. 36 cm 2. 90% or 0.9 3. The arc length of the sixth swing,using a formula for the length of the nth swing 4. 36 cm,32.4 cm, 29.16 cm, 26.244 cm 5.6. 1 for the first swing, 6 for the sixth swing. 7. 21.3 cm 8. For the first, second, third, etc. swings, the values of n are 1, 2, 3, etc. For n =1, becomes

, which is correct. Each swing afterthat is 0.9 times the swing before, which is also correct.9. About 0.266 seconds

Practice 8-71. 2.

3. 0.25, 1, 4 4. , 10, 90 5. 1, 25, 625 109

Time Number ofAnimals

Initial 23 mo 46 mo 89 mo 1612 mo 3215 mo 64

Time Value ofInvestment

Initial $6005 yr $90010 yr $135015 yr $202520 yr $3037.5025 yr $4556.25

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9. 5.5; 915.0625 10. 12; 3072 11. 36; 1296

12. ; 625 13. -3 14. 3

Practice 8-81a. y = 1500 ? 1.0475x; $4785.66

1b. y = 1500 ? ; $4906.80

2a. $31,492.80 2b. $79,304.23 3a. y = 250,000 ? 1.035x; $296,921.58 3b. $433,496.51 4a. 4,067,644 4b. 3,676,828 5a. y = 25,000 ? 0.88x; $22,000 5b. $13,193.30

Guided Problem Solving 8-81. 1% 2. 6,284,000 people 3. An equation to modelVirginia’s population growth and, based on that formula,the population in 2010 4. 6,284,000 5. 1.01 6. y = 6,284,000 (1.01)x; number of years since 1990 7. 20 8. 7,667,674 people 9. From 6,284,000 to 7,667,674 is a 22% increase, which is reasonable for a 20-year period.10. y = 604,000 ? (1.01)x; 701,225 people

8A: Graphic Organizer1. Exponents and Exponential Functions 2. Answers mayvary. Sample: zero and negative exponents, scientific notation, properties of exponents, exponential functions 3. Check students’ work.

8B: Reading Comprehension1. 80 ft 2. 10 m 3. 645 cm or 6.45 m 4. b

8C: Reading/Writing Math Symbols1. 2 times x cubed, y to the fourth power 2. 4 to the negativethird power 3. x squared 4. x times y 5. the quantity xsquared, cubed 6. x divided by y 7. 5 times x times y to thefourth power 8. x to the fifth power plus x to the seventhpower 9. the square root of the quantity x squared y

10. 8 times x squared minus 3 times y 11. x squared dividedby x to the eighth power 12. 4 times x to the eleventh power

8D: Visual Vocabulary Practice1. common ratio 2. order of operations 3. base 4. scientific notation 5. geometric sequence 6. integers 7. exponent 8. algebraic expression 9. power

8E: Vocabulary CheckEquivalent equations: Equations that have the samesolution.Exponent: A number that shows repeated multiplication.Base: A number that is multiplied repeatedly.Power: The base and the exponent of an expression of theform ax.Scientific notation: A number expressed in the form a � 10n, where n is an integer and 1 � a � 10.

8F: Vocabulary Review1. scientific notation 2. term 3. geometric 4. Substitution 5. no solution 6. increase 7. compound 8. interest 9. perpendicular 10. outcome 11. growth 12. real numbers

Chapter 9Practice 9-11. 4y3 - 4y2 - y + 3; cubic polynomial with four terms 2. x4 + x2 - 6; fourth degree trinomial 3. x + 2; linearbinomial 4. n2 - 5n; quadratic binomial 5. 7x2 + 6; quadratic binomial 6. a3 + 3a2 - 4a + 3;cubic polynomial 7. -x3 + 4x2 + 2; cubic trinomial 8. 4x3 - 2x2; cubic binomial 9. y2 - 3y - 7; quadratic trinomial 10. 2x2 - 9x - 3 11. 3x3 - 7x2 + 4 12. 6x2 + x - 9 13. 3n2 - n - 4 14.-2x3 - x2 - 2x15. 2d3 - 4d2 - 6d + 5 16. 16x2 + 14x + 15 17. -15x2 - 6x + 3 18. 2x2 - x + 2 19. -2x2 - 8x + 1 20. x3 - x2 + 7x - 6 21. 6s2 + 7s + 4 22. 4x2 + 20 23. x3 - 8x2 - x + 12

Guided Problem Solving 9-11. Answer may vary; Sample: add the lengths of all sides.2. The sides marked alike are congruent. 3. The lengths ofthe two missing sides. 4. See student work. 5. 9c - 10 + 5c+ 2 + 9c - 10 + 5c + 2 or 28c - 16 6. See student work.7. 7x - 2 + 5x + 1 + 7x - 2 + 5x + 1 = 24x - 2

Practice 9-21. 4a - 12 2. -5x + 10 3. -3x4 - 9x3

4. 2x4 - 3x3 + 2x2 5. 4d4 - 12d3 - 28d2

6. 5m4 + 30m3 7. 4 8. 15x 9. x 10. 7x2 11. 4x 12. 913. 4d 14. 3 15. 8 16. 2(4x + 5) 17. 4n(3n2 - 2) 18. 2(7d - 1) 19. x2(x - 5) 20. 4x(2x2 - 3x + 1)21. 7x3(3x + 1) 22. 2w(w2 + 3w - 2) 23. 6c2(2c - 5)24. 2(x2 + 4x - 7) 25. c(18c3 - 9c + 7) 26. 3y2(2y2 + 3y - 9) 27. 3c(2c - 1)

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Guided Problem Solving 9-21. circular 2. A = πr2 3. It represents the castle that the moatsurrounds. 4. A = 16πx2 5. A = 4x2 6. A = 16πx2 - 4x2

7. A = 4x2(4π - 1) 8. The entire circle should have thelargest area. If x = 5 the area of the entire circle is about 1256,the area of the castle is 100, and the area of the moat is 1156.9. 16x2π - 6x2 or 2x2(8π - 3)

Practice 9-31. 2x2 + x - 15 2. x3 + 2x2 - 1 3. 6w2 + 5w - 4 4. x3 + 2x2 - 21x + 18 5. 20x2 - 2x - 6 6. 12y2 + 43y + 35 7. x3 + 2x2 - 4x - 8 8. 6r2 + r - 19. 3k2 + 8k - 16 10. 8x2 + 10x + 3 11. 9x2 - 16 12. 18x2 - 9x - 5 13. n2 - 3n - 28 14. 6x2 + x - 1 15. d2 - 2d - 99 16. 4x3 + 24x2 + 27x - 28 17. 3x3 + 23x2 + 63x + 55 18. 35x2 + 64x + 21 19. 8x2 - 34x + 35 20. 3x2 - 22x - 45

Guided Problem Solving 9-31. Check students’ work. 2. x by 2x 3. x + 4 by 2x + 4 4. 2x2 + 12x + 16 5. 12x + 16 6. 10 ft by 5 ft 7. 14 � 9 - 10 � 5 = 126 - 50 = 76 � 76 8. 14 ft by 7 ft

Practice 9-41. w2 - 4w + 4 2. y2 + 8y + 16 3. 16w2 + 16w + 44. w2 - 18w + 81 5. 9x2 + 42x + 49 6. 9x2 - 42x + 497. 4x2 - 36x + 81 8. x2 - 24x + 144 9. 36x2 + 12x + 110. 16x2 - 56x + 49 11. x2 - 64 12. x2 - 121 13. x2 - 144 14. y2 - w2 15. 4x2 - 1 16. 25x2 - 417. 36x2 - 1 18. 4x2 - 16 19. 324 20. 4096 21. 899 22. 798 23. 4x2 + 4x + 1 24. 9x2 - 4

Guided Problem Solving 9-41. Answers will vary. Sample: the Punnett square models thepossible combinations of color genes that parents who carryboth genes can pass on to their offspring.

2.3. The offspring has inherited one of each gene and R and a W.

4. 5.

6. 7. 0

8. Since 0 � 0 � 1, the probability is a reasonable value for a

probability. 9.

Practice 9-51. (x + 4)(x + 4) 2. (y + 4)(y + 2) 3. (x - 4)(x - 5) 4. (a + 2)(a + 1) 5. (x + 7)(x - 2) 6. (x + 9)(x + 5) 7. (x - 6)(x - 2) 8. (n - 5)(n - 2) 9. (x - 9)(x + 3) 10. (x + 5)(x + 2) 11. (x - 8)(x + 3) 12. (x - 6)(x + 3) 13. (x + 4)(x + 5) 14. (x - 4)(x - 4)

15. (n - 3)(n + 2) 16. (x + 4)(x + 3) 17. (b + 6)(b - 2) 18. (x + 5)(x - 4)19. (a - 5)(a + 7) 20. (x + 5)(x - 2) 21. (x + 9)(x - 7) 22. (x - 15)(x + 4) 23. (x - 5)(x - 3) 24. (c + 5)(c - 2) 25. (y - 8)(y - 8) 26. (r - 17)(r + 3) 27. (a + 6)(a + 1) 28. (x - 7)(x - 4)

Guided Problem Solving 9-51. The sum or difference of monomial terms in descendingorder. 2. Add the area of each rectangle and collect liketerms. 3. 4x2 + 12x + 5 4. (2x + 1)(2x + 5) 5. Both expressions represent the same area.6. 9x2 + 9x + 2; (3x + 1)(3x + 2)

Practice 9-61. (x + 1)(2x + 1) 2. (n + 2)(2n - 3) 3. (x + 1)(3x - 4) 4. (x + 1)(5x - 7) 5. (n + 1)(7n + 2) 6. (x + 2)(3x + 2) 7. (y - 6)(3y + 2) 8. (x + 1)(5x - 3) 9. (x - 1)(7x - 3) 10. (x + 1)(3x + 5) 11. (x - 1)(5x - 2) 12. (x - 4)(5x - 2) 13. (x - 7)(5x + 2) 14. (x - 2)(3x + 4) 15. (y - 3)(4y + 1) 16. (y - 1)(5y + 2)17. (y + 2)(7y + 5) 18. (x + 5)(3x + 2) 19. (2x - 1)(x + 3) 20. (3x + 1)(x + 3) 21. (2x - 7)(x + 3) 22. (x - 3)(3x + 2) 23. (2x + 3)(x - 4) 24. (4x + 3)(x + 1)

Guided Problem Solving 9-61. multiplication 2. Polynomials with two terms.3. (2x + 2)(x + 2); (x + 1)(2x + 4) 4. 2x2 + 6x + 4; 2x2 + 6x + 4; yes 5. Answers may vary. Sample: Neither factoring is complete.Each one has a common factor, 2. 6. 2(x + 1)(x + 2);2(x + 1)(x + 2) 7. 6x2 + 4x - 2; 6x2 + 4x - 2

Practice 9-71. (x - 3)(x + 3) 2. (a + 1)2 3. (2x + 3)2

4. (n - 2)(n + 2) 5. (3x - 2)(3x + 2) 6. (3x - 5)2 7. 3(n - 1)(n + 1) 8. (3d - 7)(3d + 7) 9. 3(a - 4)(a + 4) 10. (b + 2)2 11. (5x - 8)(5x + 8) 12. 3(2w - 3)(2w + 3) 13. (x + 3)2 14. (a - 5)(a + 5)15. (x - 8)2 16. (d - 7)(d + 7) 17. 5n(n + 2)(n - 2) 18. (3n + 2)2 19. (2a - 9)(2a + 9) 20. (3d - 8)(3d + 8) 21. (y + 4)2 22. (x - 5)2 23. (y - 9)(y + 9) 24. (a - 10)(a + 10) 25. 2d(d - 5)(d + 5) 26. (x - 9)2 27. (b - 8)(b + 8) 28. (2r - 5)(2r + 5) 29. (b - 7)2

Guided Problem Solving 9-71. Answers may vary. 2. A = lw 3. A = πr2 4. n(3.14n)5. 3.14m2 6. 3.14n2 - 3.14m2 7. 3.14(n - m)(n + m) 8. 285.74 in.2 9. Check students’ work. 10. 593.46 in.2

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Practice 9-81. (x - 2)(a + 2) 2. (m + k)(x - 3) 3. (a - b)(y + 1)4. (y + 4)(y - 5w) 5. (y - 2)(x + 4) 6. (a + b)(x + y)7. (a + b)(x - y) 8. (x - 2y)(3x + 2) 9. (2x + b)(a + 3c) 10. (2 + x2)(3 + y) 11. (2x - 1)(x - 1) 12. (3x + 2)(2x + 1)13. (2x + 3)(2x + 1) 14. (4x - 1)(x - 2) 15. (2x + 1)(x - 2) 16. (6x + 1)(x + 3) 17. (3y - 2)(4y + 1) 18. (5y + 3)(y + 2) 19. (8y + 1)(2y + 1) 20. (4x + 1)(4x + 3) 21. (5x + 1)(2x - 1) 22. (7x - 3)(2x + 3) 23. (x + 4)(2x2 + 1) 24. (x2 + 3)(5x - 1) 25. (x + 3)(x2 + 4) 26. (x + 3)(3x2 + 2) 27. (3x - 4)(3x2 + 1) 28. (x - 5)(4x2 + 3)

Guided Problem Solving 9-81. V = lwh 2. common factor 3. 2w 4. 42w2 + 41w + 55. (6w + 5)(7w + 1) 6. 2w, 6w + 5, 7w + 17. 2w(6w + 5)(7w + 1) = 84w3 + 82w2 + 10w8. 3m, 3m + 1, 2m + 3

9A: Graphic Organizer1. Polynomials and Factoring 2. Answers may vary. Sample:adding and subtracting polynomials, multiplying special cases,factoring special cases, factoring by grouping 3. Checkstudents’ work.

9B: Reading Comprehension1. 8 days 2. 50 mCi 3. 25 mCi 4. 10 mCi 5. 20 minutes 6. 1.5625 mCi 7. b

9C: Reading/Writing Math Symbols1. B 2. E 3. A 4. D 5. F 6. C

9D: Visual Vocabulary Practice/High-UseAcademic Words1. notation 2. interpret 3. consecutive 4. formula 5. apply 6. simplify 7. test 8. solve 9. methods

9E: Vocabulary CheckDegree of a monomial: The sum of the exponents of itsvariables.Polynomial: A monomial or the sum or difference of two ormore monomials.Standard form of a polynomial: The form of a polynomialin which the degree of the terms decreases from left to right.Degree of a polynomial: The degree of the term with thegreatest exponent for a polynomial in one variable.Greatest common factor: The greatest factor that dividesevenly into each term of the expression.


Chapter 10Practice 10-11. (1, -1); minimum 2. (2, 4); maximum 3. (-3,-4); minimum 4. y = x2, y = 3x2, y = 5x2 5. y = x2, y =-x2, y =-8x2

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Guided Problem Solving 10-11. circle 2. square 3. Answers may vary. 4. 0 � r � 6 5. 0 � A � 36π � 113.16.

7. parabola 8. 0 � r � 5; 0 � A � 25π � 78.5

Practice 10-21. x = 5; (5, -23) 2. x = -6; (-6, -45) 3. x = 1; (1, 2) 4. x = -3; (-3, -18) 5. x = 0; (0, 3) 6. x = 2; (2, 16) 7. 8.

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Guided Problem Solving 10-21. Check students’ work. 2. Shape is modeled by y =-0.1x2 + 12. 3. 0 � y � -0.1x2 + 12 4.

5. Check students’ work. 6. Yes, when x = 6, y = 8.4 socamper will fit. 7. Answers will vary. 8. No, when x = 6,y = 8.4 so the load will be too tall.

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Practice 10-31. 44 2. 412 3. 43 4. No solution 5. 43.5 6. 47

7. No solution 8. 410 9. 44 10. 48.9 11. 4 12. 46.7

13. 417.3 14. 42.8 15. No solution 16. 48 17. 418. 411 19. 41.4 20. 43.3 21. 44.2 22. 46.4

23. No solution 24. No solution 25. 4 26. 0 27. 425 28. 43 29. 410.49 30. 40.87

Guided Problem Solving 10-31. The area of the picture is supposed to be 75% of the totalarea enclosed by the frame. 2. the sides of the picture are x;the sides of the frame are 12 in. 3. x2 4. 144 in.2 5. 108 in.2

6. x2 = 108; x � 10.39 7. It is not exactly 75% because theanswer was rounded. 8. about 9.30 in. square

Practice 10-41.-5, 3 2. 2,-9 3. 12,-12 4.-1.5, 4 5.-7,

6.-3.5, 3.5 7. ,-0.5 8. ,-0.25 9.-1.2,-1.25 10.-3,-211. 9,-2 12. -2, 2 13. -10, 2 14. -13,-1 15. 5,-2 16. -8, 1 17. 5,-5 18. -7,-3 19. 4,-8 20. 3, 9

21. -3, 3 22. 3.5,-3 23. 2, 24. 4.5,-1 25. 4,-1.5

26. 1, 27. 3, 0.4 28. 3.5,- 29. 2.5,-1.5 30. 1,-0.75

Guided Problem Solving 10-41. The initial velocity is 29 ft/s. The initial height is 6 ft. Theformula h =-16t2 + 29t + 6 gives the ball’s height h in feetat time t in seconds. 2. h: ball’s height in feet; t: time inseconds 3. factor and use the zero-product property 4. 2 s 5. y =-16t2 + 29t + 6 6. about 19 ft 7. maximum heightat t = 0.9;-16(0.9)2 + 29(0.9) + 6 = 19.14 8. 3 s

Practice 10-51. 49 2. 9 3. 1 4. 25 5. 5,-1 6. -1, 2 7. -1.36, 7.368. -2 9. 6,-3 10. -0.47, 8.47 11. 6, 0 12. -1.12, 7.1213. 0, 7 14. 2,-6 15. -10,-1 16. -5, 3 17. 9,-1

18. -2,-3 19. -10, 12 20. 15, 7 21. 3, 22. -5, 1

23. 2, 24. -8, 2

Guided Problem Solving 10-51. Rectangular garden is against a house. 50 ft of fencingmaterial is available. The area of the garden should be 150 ft2.

2. 3 sides 3. l = 50 - 2w 4. w(50 - 2w) = 150; 21.5, 3.5 5. 7 ft � 21.5 ft or 43 ft � 3.5 ft 6. Not precisely; answerswere rounded. 7. 8.35 ft � 16.65 ft

Practice 10-61.-7.32,-0.68 2.-6, 6 3.-8, 12 4.-14.72, 2.725. 4.5,-4.5 6. -10,-3 7. 0.33, 3.5 8. -9, 0.75 9. -1, 1 10. -12.31, 7.31 11. -2, 2 12. No real solutions

13. 4,-0.6 14. -3, 18 15. -0.67, 0.67 16. -1.75,-34.25 17. No real solutions 18. -3, 13 19. -2.61, 0.86 20. -1.82,-1.30 21. 2.83,-2.83 22. No real solutions 23. -2, 2 24. -0.75, 0.75 25. No real solutions 26. 16.34,-7.34 27. 4.5, 0.25 28. No real solutions29. 3.17,-1 30. -3, 3

Guided Problem Solving 10-61. A = bh 2. base: x + 2; height: x; Area: 20 ft2

3. A = x(x + 2) 4. x2 + x - 20 = 0 5. x = 5.40 ft

6. 7.40 ft and 5.40 ft 7. 19.98 ft2; 20 ft2; the answers wererounded. 8. 5.65 ft and 2.65 ft

Practice 10-71. 0 2. 2 3. 1 4. 2 5. 0 6. 0 7. 1 8. 2 9. 2 10. 0 11. 2 12. 1 13. 0 14. 2 15. 2 16. 1 17. 0 18. 1 19. 220. 0 21. 2 22. 2 23. 2 24. 0

Guided Problem Solving 10-71. The equation relates the price to total sales. 2. S: totalsales; p: price 3. S =-0.75p2 + 54p 4. No. 5. $366. If a product is too expensive, fewer people will buy it.7. Check students’ work. 8a. h=-16t2 + 256t 8b. yes8c. 8 seconds

Practice 10-81. Quadratic; y = 3x2 2. Linear; y = -2x3. Linear; y = x + 1 4. Quadratic; y = -2x2

5. Quadratic; y = x2 6. Linear; y = -2x - 4

7. Quadratic; y = x2 8. Exponential; y = -2 ? 4x

9. Quadratic; y = -5x2 10. Linear; y = - x +

11a. Linear 11b. y = 32x + 100 11c. $964 11d. 168 computers

Guided Problem Solving 10-81. world population in millions from 1980 to 2000 2. linear,quadratic, and exponential 3. 5 4. 398, 429, 407, 389;79.6, 85.8, 81.4, 77.8 5. about 81.2 6. p = 81.2t + 4457 7. 6893 million or about 6.9 million 8. 5 years: 4863;15 years: 5675 9. Answers may vary. Sample: p = 4484(1.016t)

10A: Graphic Organizer1. Quadratic Equations and Functions 2. Answers may vary.Sample: quadratic functions, solving quadratic equations,completing the square, using the discriminant 3. Checkstudents’ work.

10B: Reading Comprehension1. speed of animals 2. speed (mph) 3. 0 to 80 4. bar graph5. cheetah 6. snail 7. a

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10D: Visual Vocabulary Practice1. quadratic formula 2. linear function 3. factor 4. exponential function 5. parabola 6. completingthe square 7. Zero-Product Property 8. perfect squaretrinomial 9. discriminant

10E: Vocabulary CheckQuadratic function: A function that can be written in theform y = ax2 + bx + c.Axis of Symmetry: The fold or line that divides a curve intotwo matching halves.Vertex: The highest or lowest point of a parabola.Standard form of a quadratic function: A quadraticequation written in the form ax2 + bx + c = 0.Zeros of a quadratic function: The solutions of thequadratic equation.

10F: Vocabulary Review1. quadratic 2. standard 3. degree 4. solution 5. constant 6. axis of symmetry 7. discriminant 8. slope 9. distributive 10. function 11. system 12. minimum 13. vertex

Chapter 11Practice 11-11. 4 2. 4 3. 7 4. 5. 6. 4

7. 3 8. 9. 2x2 10. 10 11. 3

12. 2 13. 14. 5 15. 16. 4s

17. 6 18. 4 19. 2 20. 2 21. 12

22. 23. 5 24. 4 25. 2 26. 2

27. 5x 28. 29. 30. 2 31. 32. 5

33. 10 34. 5 35. 2x2 36. 37.

38. 39. 40. 12 41. 18 42. 245 43. 4

44. 125 45. 2 46. x 47. 20 48. 8

Guided Problem Solving 11-11. A = s2 2. all the perfect-square factors are removed fromthe radicand

3.

4. See picture above. 5. x2 = 24; x = 6.7. 4.90 in. 8. decimal was rounded 9. or about 10.95 cm

Practice 11-21. 8 2. 18 3. 8 4. 5 5. 19

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14. 16 15. 5 16. 7

17. 32 - 24 18. 22 19. 21 20. 18

21. 3 22. 4 23. 3 24. 4

25. 7 26. -4 27. 32 28. -9

29. -3 30. 8 31. 3 32. 19 33. 5

34. 24 35. 4 - 14 36.

37. or 38. 39. 80

40. 4

Guided Problem Solving 11-21. Sides of the square opening are 2 ft. 2. Pythagorean

Theorem 3. 22 + 22 = d2; d = 4. 2.83 ft

5. s2 + s2 = d2; d = 6. 7. Check students’ work.

8. about 11.31 ft

Practice 11-31. 64 2. 4 3. 2 4. 16 5. 4 6. 4, 7 7. 144 8. 4, 8 9. 5, 810. no solution 11. 22 12. 5 13. -2 14. 1 15. 4 16. 117. 8 18. 4 19. 11 20. 4 21. 6 22. 27 23. 224. no solution 25. 40 26. 10 27. 24 28. 5 29. 330. no solution

Guided Problem Solving 11-31. Answers may vary. 2. v: car’s velocity; h: height of hill;r: radius of loop 3. r 4. 5. r = 68 ft 6. 20.5 mi/h 7. As radius increases, velocity decreases.8. As height decreases, velocity decreases. 9. Velocitydepends upon the difference of the height and twice theradius. 10. Check students’ work. 11. 205 ft

30 5 8Í150 2 2r

sÍ2Í2s2Í8

Q"6 1 3R15 2 6"6

23Q"5 2 5R20

23"5 1 1520

2"3 2 "2"2

"19"35"3"6"29

"2 2 9"10"13"7

"6"13"2"10 2 4"15

"26"3"3"2

"6 1 9"2"21"5 1 40"2

"3 2 21"15"2"2

"2 2 6"6"7"6 2 8

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9

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Practice 11-41. x � 7 2. x � 12 3. x � -14 4. x � -8 5. x � 0 6. x � 07.

8. 9.

10. 11.

12.

13. shift down 9 14. shift down 8 15. shift left 20 16. shift left 18 17. shift right 32 18. shift right 4 and shift down 7

Guided Problem Solving 11-41. Single-use cameras sales 2. How the number of camerasales is related to the number of months.3. 4. about 213 cameras

5. 6. month 4 7. Check students’work. 8. about 309 cameras

Practice 11-51. 2. 3. 4. 5. 6. 7. 1.6643

8. 0.9659 9. 0.1392 10. 0.9744 11. 0.5299 12. 2.3559

13. 10.1 14. 12.7 15. 25.4 16. 22.5 17. 3.8 18. 40.2 19. 20 ft

Guided Problem Solving 11-51. two angle measures and the adjacent side measure2. sine, cosine, and tangent 3.4. p � 514.3 5. The opposite and adjacent sides are used.6. 7.51 cm and 28.01 cm

Practice 11-61. 11.1 ft 2. 30.8 ft 3. 6625 ft 4. 2428 ft 5. 57.4 ft6. 33.69º 7. 57 ft

Guided Problem Solving 11-61. See students’ diagrams. 2. See students’ diagrams.3. sine 4. sin 65° = 5. about 55 m

6. 1 m must be added on since your hand is 1 m above theground. 7. 18.20 ft

11A: Graphic Organizer1. Radical Expressions and Equations 2. Answers may vary.Sample: simplifying radicals, solving radical equations,graphing square root functions, and trigonometric ratios 3. Check students’ work.

11B: Reading Comprehension1a. Circle 1b. Triangle 1c. Right Triangle 1d. The squareof the slant height equals the sum of the square of the heightof the cone and the square of the radius. 2a. This diagonal isthe hypotenuse of a right triangle and the lengths of the legsare known. 2b. Yes, This diagonal is the hypotenuse of a righttriangle. The length of one leg is known and the other one canbe calculated as described in part a. 3. b

11C: Reading/Writing Math Symbols1. B 2. F 3. E 4. G 5. D 6. C 7. A 8. G 9. C 10. A11. F 12. B 13. E 14. D

11D: Visual Vocabulary Practice1. like radicals 2. sine 3. trigonometric ratios 4. cosine 5. square root function 6. radical equation 7. DivisionProperty of Square Roots 8. angle of elevation 9. tangent

11E: Vocabulary CheckRadical expression: An expression that contains a radical.Rationalize: Rewrite as a rational number. It may benecessary to obtain the simplest radical form.Unlike radicals: Expressions that do not have the sameradicand.Conjugates: The sum and difference of the same two terms.Extraneous solution: A solution that does not satisfy theoriginal equations.

x60; x < 54.38

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Chapter 12Practice 12-11. Parabola 2. Rational function 3. Radical function 4. Line 5. Absolute value 6. Exponential growth 7. 0 8. -7 9. -3 10. 8 11. x = 0 12. x = 1

13. x = -4 14. x = 0

Guided Problem Solving 12-11. I: intensity of the light in lumens; x: distance from the light bulb in feet 2. The light bulb is 445 watts. 3.

4. 17.8 lumens 5. 6. lumens 7. decrease

8. about 6.7 ft

Practice 12-21. 2. 3. 4. 5. 6. x - 2

7. 2t - 1 8. 9. 10. 11. 12. 13.

14. 15. x2 16. -1 17. 18.

19. 20. 21. 22.

23. 24. 25. 26.

Guided Problem Solving 12-21. 2.3. 4. 5.6. 7. 8. 9.

10. 11. 12. Answers may vary. 13.

Practice 12-3

1. 2. 3. 4. 5. 6. 7. 8.

9. 10. 11. 12. 13. 14. 3a - 6

15. 16. 17. 2 18. 19. 12p2 20. 3 21. 4h

22. (n - 1)(n - 2) 23. x - 2 24. 25. 26. 1

27. 28. 29. 30. 2x 2 14x 1 9

x2 2 x 1 63x 1 9

x 2 5x 1 3

x 1 3x 1 1

x3

5x 1 2

y2

34b

245b

4r3

5n2

36n5

5r8

10x4

27

3x2

2059

4x2

94

m221

1526364

92

29

2 1 hh

49; 49

2h 1 2rrh

pr2h2pr2 1 2prh2b 1 4hbhb2h

2b2 1 4bhV 5 pr2hSA 5 2pr2 1 2prhV 5 lwhSA 5 2lw 1 2lh 1 2wh

2x 2 2x 2 5

x 1 8x 1 7

x 1 5x 2 42

x 1 3x 1 4

2x 1 2x 1 1

3x

2x 2 3x 1 1

2(x 1 2)x 2 1

x 1 2x2

x 1 3x 1 1

x 1 3x2

x 1 1x 2 12

x5

x3

4x2

3y23x2y

a2

x 2 22

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Guided Problem Solving 12-31. length: ; width: ; height:

2. 3.

4. factor and simplify 5. 6. Both expressions

have a value of zero when x = 2. 7.

Practice 12-41. 2x - 5 2. 4x2 - 3 3. x - 2 4. 5x - 3 5. -x3 + 2x2 - 3x + 4 6. 3x - 6 7. x - 7 8. 2x - 79. 2x - 4 10. x + 6 11. x + 8 12. 4x + 1

13. 14.

15. 16. x2 + 2x + 3

17. 18.

19. 2x + 5 + 20. x + 4

Guided Problem Solving 12-41. rational function 2. For a rational function in the form

, the function has a vertical asymptote at

x = b and a horizontal asymptote at y = c.

3.

4.

5. x =-3 6. y = 2 7. Answers may vary.

8.

Practice 12-51. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13.

14. 15. 16. 17. 18.

19. 20. 21.

22. 23. 24. 25.

26. 27. x

Guided Problem Solving 12-51. The team is rowing with the current. 2.3. 4. 5. Yes. The rates have

been adjusted for the current. 6. Both expressions have

a value of 0.9. 7.

Practice 12-61. 9 2. -6 3. -1, 1 4. No solution 5. -1, 4 6. 4 7. 0, 12 8. -6,-1 9. -2 10. -6, 3 11. -2, 0.5 12. No solution 13. no solution 14. No solution 15. 3 16. No solution 17. -5, 5 18. 2 19. 4,-1 20. -1 21. -8

Guided Problem Solving 12-61. Add R1 and R2 2. Solve the equation

for RT. 3. 15 � 4. 3.75 �

5. �

�

�

�

True

6. 4 �

Practice 12-71. 42 2. 665,280 3. 990 4. 720 5. 362,880 6. 3,991,6807a. 7,893,600 7b. 120 7c. 8. 362,880 9. 12 10. 7500 11. 12,144

Guided Problem Solving 12-71. If there are m ways to make a first selection and n ways tomake a second selection, there are m ? n ways to make the twoselections. 2. Answer may vary. Sample: 12A1234 3. The numbers that are fixed by county. 4. 260,000 licenseplates 5. 23,920,000 license plates 6. The answer in step 5should be larger. There are more license plates in 92 countiesthan there are in one county. 7. 100,000 license plates

Practice 12-81. 126 2. 495 3. 84 4. 5005 5. 45 6. 1716 7. 20 8. 792 9a. 12,650 9b. 495 9c. 0.039 10. 42,504

11a. 364 11b. 56 11c.

Guided Problem Solving 12-81. It is a permutation because the order of the numbers isimportant. 2. That there are 40 numbers that can be used.3. 59,280 sequences 4. 1482 sequences 5. 6. Answer may vary. Sample: It is unlikely someone will guess the rightsequence with more than 59,000 possibilities. 7. Checkstudents’ work. 8. 100,000 possibilities

140

213

165780

13.75

13.75

415 ?

1414

13.75

415

13.75

115 1

315

13.75

115 1

15

13.75

1RT

51

R11

1R2

2r 1 2

1.1r; 2d 1 20.91d

2d 1

20.8d; 9

2d2r 1

21.25r ; 18

5r

D 5 rt; t 5Dr

15a2 2 2

7r 2 9r2 2 4

14a

136(x 1 3)

18 2 56t2

21t3

10x 1 10(x 1 3)(x 2 2)

10a 1 4

8a 2 36a3

3t4

2x 1 3x2 2 1

7x 1 13x2 2 1

52z22

4k 1 3

4a32

4x

3m 2 15(m 1 1)(m 2 1)

9 1 8d6d2

2d

5d3

37t

5x14

7m6

8x15

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y 5 3 11

x 1 1

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x 2 22 2 21 2 0 2 1 2 2y 1 3

253

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x 1 3

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x 2 b 1 c

82x 2 1

x 1 3 216

x 1 22x 2 1 11

x 1 6

3x 1 4 25

x 2 2

x 2 5 224

x 2 3x 1 3 14

x 1 2

1(2x 1 3)3

x 2 24(x 1 7)

a x 2 2x2 1 2x 2 35

b a3x 1 24 b a x 2 5

3x 1 2bV 5 lwh

x 2 53x 1 2

3x 1 24

x 2 2x2 1 2x 2 35


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12A: Graphic Organizer1. Rational Expressions and Functions 2. Answers may vary.Sample: simplifying rational expressions, dividing polynomials,counting methods and permutations, and combinations 3. Check students’ work.

12B: Reading ComprehensionBatches Cups Cups Total

of of of ProfitCookies Flour Sugar ($)

Oatmeal x 2x 2x 3xWhite Chocolate y 3y y 2yMacadamia NutTotals 18 10 P

1. You are asked to find the number of batches of each typeof cookie Jessica should make to maximize profit.2. P = 3x + 2y 3a. 2x + 3y # 18 3b. 2x + y # 10 3c. x $ 0 3d. y $ 04.

5. Vertex: (0, 0), P = $0; Vertex: (5, 0), P = $15;Vertex: (0, 6), P = $12; Vertex: (3, 4), P = $17 6. Tomaximize profits Jessica would need to make 3 batches ofoatmeal and 4 batches of white chocolate macadamia nutcookies. 7. b

12C: Reading/Writing Math Symbols1. leg squared plus leg squared equals hypotenuse squared;Pythagorean Theorem—used to find a side of a right triangle2. Interest equals principal times rate times time; calculateinterest 3. a times x squared plus b times x plus c equals zero;standard form of a quadratic equation 4. b squared minus 4times a times c; discriminant—used to find the number of rootsof a quadratic formula 5. tangent of an angle equals theopposite side divided by the adjacent side; tangent formula—

used to determine a leg or angle in a right triangle 6. cosineof an angle equals the adjacent side divided by the hypotenuse;cosine formula—used to determine a side or angle in a righttriangle 7. sine of an angle equals the opposite side divided bythe hypotenuse; sine formula—used to determine a side orangle in a right triangle 8. the sum of the x-coordinates of twopoints divided by 2, and sum of the y-coordinates of two pointsdivided by 2; Midpoint Formula—find the midpoint of asegment 9. x equals opposite of b plus or minus the squareroot of b squared minus 4 times a times c, all divided by 2times a; Quadratic Formula—used to solve quadratic equations10. the distance equals the square root of the difference of thex-coordinates, squared, plus the difference of the y-coordinates,squared; Distance Formula—used to find the length of asegment or the distance between two points

12D: Visual Vocabulary Practice1. linear function 2. asymptote 3. rational function 4. absolute value function 5. rational expression 6. quadratic function 7. square root function 8. rationalproportion 9. exponential function

12E: Vocabulary CheckRational function: A function that can be written in the

form .

Asymptote: A line which the graph of a function gets closerto as x or y gets larger in absolute value.

Rational expression: An expression which can be written in

the form .

Multiplication Counting Principle: If there are m ways tomake a first selection and n ways to make a second selection,there are m ? n ways to make the two selections.Permutation: An arrangement of some or all of a set ofobjects in a specific order.

12F: Vocabulary Review Puzzle1. asymptote 2. combination 3. inverse variation 4. permutation 5. rational function 6. parabola 7. discriminant 8. vertex 9. tangent 10. rationalize

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Algebra 1: All-In-One Answers Version B 30, 2013/High School... · ... Locn. B: mean 75.933, median 75, mode =66, range 26 ... it is still smaller than the range for plant B. 1A: