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Selected Answers R19

Chapter 1 The Tools of Algebra

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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domain � {4, 5, 1};range � {5, 2, 6}

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

35.

domain � {0, 2};range � {1, 3, 5, 0}

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

point on the graph.• longitude and latitude lines.

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

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

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

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

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

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

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

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

Chapter 2 Integers

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

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

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

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

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

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

• Sample answer:

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

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

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

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

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

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

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

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

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

23–34.

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

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

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

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

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41. 5-point star

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

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

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

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

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

40–43. 41. III 43. None

Chapter 3 Equations

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

Pages 100–102 Lesson 3-11. Sample answer: 2(3 � 4) � 2 � 3 � 2 � 4 3. 5 � 7 � 5 � 8,75 5. 2 � 6 � 4 � 6, 36 7. 3n � 6 9. �6x � 30 11. $56.2513. 5 � 7 � 5 � 3, 50 15. 4 � 3 � 3 � 3, 21 17. 8 � 2 � 8 � 2, 3219. 6 � 8 � 6(�5), 18 21. �3 � 9 � (�3)(�2), �2123. 10(�5) � 3(�5), �35 25. 12($15 � $10 � $8), 12($15) � 12($10) � 12($8); $396 27. 5y � 30 29. 7y � 5631. 10y � 20 33. 10 � 5x 35. 9m � 18 37. 15s � 4539. 12x � 36 41. 2w � 20 43. �5a � 50 45. �5w � 4047. �5a � 30 49. 3a � 3b 51. $488.75 53. No; 3 � (4 � 5) � 23, (3 � 4)(3 � 5) � 56 55. C57. 8(20 � 3) � 184 59. 16(10 � 1) � 17661. 9(100 � 3) � 927 63. 12(1000 � 4) � 12,048 65. 667. 4 69. 21, 25, 29 71. 80, 160, 320 73. �8 � (�4)75. 3 � (�9) 77. �7 � (�10)

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

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

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

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39.

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

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

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

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

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

37. ��x4� � 8; �32

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

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

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

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

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

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

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

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

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

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

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

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

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

a � �vf �

t

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

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

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

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

Chapter 4 Factors and Fractions

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

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

4 cm

4 cm4 ft

3 ft

5 in.

4 in.

30 31 32 33 34 35 36 37

�3 �2 �1 0 1 2 3 4

�3 �2�6 �5 �4�9 �8 �7

�3�4 �2 �1 0 1 2 3

8 9 10 11 125 6 7


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

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

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

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

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

21. 2x2y2 23. 9(p � 1)2 25. (8 � 102) � (0 � 101) � (3 � 100)27. (2 � 104) � (3 � 103) � (7 � 102) � (8 � 101) � (1 � 100)29. 1000 31. �32 33. 81 35. �54 37. 13 39. 9 41. 24343. 81 � 92 or 34, 64 � 82 or 43 or 26 45. (�8)3;(�8)(�8)(�8); �512 47. Always; the product of twonegative numbers is always positive. 49. 21, 22, 23, 24, 25

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

17

�

5. simplified 7. �1167� 9. �

2a

� 11. simplified 13. B 15. �56

�

17. �29

� 19. �292� 21. simplified 23. �

13

� 25. �152� 27. �

1290�

29. �932� 31. �

y1

2� or y2 33. �

2201� 35. �

81t� 37. �

74z2� 39. simplified

41. �g3h� 43. �

2245� 45a. yes; �34

3400

� � �34

� 45b. No; �239449

� cannot

be simplified. 45c. yes; �256248

� � �12

� 47. �3510� 49. �

170�

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

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

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

�14

� foot.

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


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

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

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

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

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

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

or 105.

53. B 55. simplified 57. �32

xy� 59. 2 61. a 63. Positive; as

the high temperature increases, the amount of electricity

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

210� 69. �

614�

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

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

t16� 7. 3�4

9. 7�2 11. �312� 13. 10�3 15. �

513� 17. �

(�13)3� 19. �

1104�

21. �a110� 23. �

q14� 25. x2 27. �

514� ; 0.0016 29. 5�5 31. 13�2

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

41. ��1128� 43. �

7129� 45. 128 times 47. x�5 49. x�3

51. a3b�2 or �ba3

2�

53. Yes; (x3)�2 � �(x

13)2�

� �x3

1� x3� or �

x16�

(x�2)3 � (x�2)(x�2)(x�2)

� x�6 or �x16�

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

Page 185 Practice Quiz 2

1. 5 3. 2a 5. �25

� 7. �2n7 9. �b16�

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

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

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

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

35. 2.3 � 105 37. 5000 39. Arctic, Indian, Atlantic, Pacific41. 6.1 � 10�5, 0.0061, 6.1 � 10�2, 6100, 6.1 � 104

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

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

419�

57. 15a4 59. c � $2.50

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

37. 2(t � 10) 39. 2(15 � 2n) 41. �35

� 43. �1107� 45. simplified

47. �58cb

2� 49. c4 51. r2 53. �

712� 55. �

b14� 57. �

(�14)3�

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

Chapter 5 Rational Numbers

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

35

� 13. �1285� 15. 6

17. �13 19. 15 21. 9

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

79

� , 0.8, �78

�

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

answer: 0.7 and 0.7�; �16

� � 0.16� and �89

� � 0.8�; 0.7 and 0.7� are

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

than those who chose English in the survey because �17

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

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

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

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

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

12)7� 59. �

y13�

61. 29 63. �32 65. 56 67. �113� 69. �

23

� 71. �47

� 73. �18

�

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

73

�

5. �45

� 7. ��79

� 9. I, Q 11. �1,00309,000� 13. ��

171� 15. �

610�

17. �1900� 19. 1�

1275� 21. 8�

2150� 23. ��

13

� 25. 5�23

� 27. 2�2959�

29. �530� 31. �

25090

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

41. not rational 43. 200�11090

� 45. Sometimes; �12

� and 2 are

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

150� in.

49. Yes; 2�38

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

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

whole numbers integers, and rational numbers.

• The number �12

� belongs only to the set of rationalnumbers.

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


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

Pages 212–214 Lesson 5-3

1. Sample answer: �12

�, �13

� 3. �230� 5. �

59

� 7. �1232� 9. �

67

� 11. �8t�

13. �14

29� 15. ��

410� 17. �

485� 19. �

13

� 21. ��14

� 23. �38

� 25. 1�16

�

27. 3�13

� 29. 14�23

� 31. 10 33. �4�49

� 35. 6 37. 27 39. 27

41. �181c� 43. �

x3z2� 45. �

295� 47. �

6101� 49. 12.7 51. 10.257

53a. Sample answer: �84

� � �35

� 53b. Sample answer: �34

� � �56

�

55. A 57. �58

� 59. �13

32� 61. ��

15

� 63. �79

� 65. 0.16� 67. �4.875

69. 8n 71. 2t 73. 9

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

reciprocal. 3. �54

� 5. �285� 7. �

45

� 9. 1�175� 11. �1�

2396� 13. �

32a�

15. 6 boards 17. ��51

� or �5 19. �214� 21. ��

299� 23. �

89

�

25. ��12

52� 27. �

11

56� 29. �1 31. 1�

12

� 33. �10 35. 1�13

� 37. 2

39. �6�14

� 41. �43

� 43. �65r� 45. �

1t56� 47. 6 ribbons 49. �

28516

�

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

four sections, represents 2 � �14

�. Since there are 8 sections,

2 � �14

� � 8.

• Division of fractions and multiplication of fractions are

inverse operations. So, 2 � �14

� equals 2 � 4 or 8.

55. C 57. �254� 59. ��

12

01� 61. Q 63. not rational 65. 7

67. 1�17

� 69. 6�14

� 71. 3�23

� 73. 1�23

�

Pages 222–224 Lesson 5-51.

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

first term. 5. �47

� 7. ��34

� 9. 8�12

� 11. �181r� 13. ��

31x� 15. �

35

�

17. �23

� 19. ��12

� 21. �1�12

� 23. ��29

� 25. 11�45

� 27. 9�13

� 29. �34

�

31. 4�67

� 33. 8�18

� 35. 2�35

� 37. �15

� 39. �58x� 41. �

m3� 43. 2�

37

�c

45. 5�38

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

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

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

18

� of an

inch, �14

� of an inch, and �12

� of an inch.

• Fractional measures are used in sewing and construction.

51. A 53. �1�78

� 55. �130� 57. 1�

13

� 59. 42 cm; 90 cm2

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


1. 0.16 3. 3.125 5. �235� 7. �

227� 9. �

152�

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

61. B 63. �12

� 65. 1�17

� 67. 3 69. �a5d� 71. 7 � 2n � 11; 2

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

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

denominators of unlike fractions. 5. �29

� 7. ��56

� 9. �4�14

�

11. �190� 13. �

258� 15. 1�

116� 17. �

18

� 19. ��18

� 21. 1�115� 23. �7�

59

�

25. �11�79

� 27. �14�58

� 29. 3�3161� 31. 5�

35

� lb 33. 8�34

� in.

35. Sample answer: Fill the �12

�-cup. From the �12

�-cup, fill the

�13

�-cup. �16

� cup will be left in the �12

�-cup because �12

� � �13

� � �16

�.

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

�14

� � �56

� � �132� � �

1102� � �

1132� or 1�

112�.

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

39. B 41. Sample answer: �12

� � �110� 43. 36 45. 6n3 47. 9�

12

�

49. 2�45

� 51. 1�45

� 53. 27 55. �9

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

be less. 21. C 23. 9�56

� 25. �3�78

� 27. 29. 18 31. �5

33. 7.9 35. 3

27

47

67


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

7. 1�13

30� 9. �2�

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

19. 5.9 21. ��33

16� 23. 6�

79

� 25. ��125� 27. �2�

130� 29. 4

31. 5 33. �32 35. 1�14

� 37. 5�34

� 39. 2�78

� 41. 13�12

� in. by

21�12

� in. 43. $16.66 45. 2�14

� ft 47. Equations with fractions

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

C, then �54

�n vibrations per second produce the note E

above middle C.

• The equation �53

�n � 440 represents the number of

vibrations per second to produce middle C. To solve,

multiply each side by the reciprocal of �53

�, �35

�.

49. D 51. 13; 12; 11 and 12 53. 70.8; 66; 60 55. �1274� 57. �

1376�

59. 7�1151� 61. �

38

� 63. �6 65. �6 67. 5 69. ��13

�


1. 72 3. 10 5. �11

36� 7. 1�

23

� 9. 32.4; 30.5; 29

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

5. neither 7. A; ��13

�; �53

�, �43

�, 1 9. $11,027.36 11. A; 11; 38,

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

17. G; ��15

�; ��1125�, �6

125�, ��

31125� 19. A; �

16

�; �23

�, �56

�, 1 21. A; �0.5,

2.5, 2, 1.5 23. neither 25. G; ��13

�; �29

�, ��227�, �

821�

27. G; �12

�; �312�, �

614�, �1

128� 29a. Arithmetic; the common

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

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

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

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

43. 102�78

� in. 45. b3 47. 6 49. 15

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

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

� 19. �18

�

21. 4�2151� 23. �

59

� 25. 1�79

� 27. 3�141� 29. ��

277� 31. 6�

25

� 33. 1�13

�

35. �3 37. 9�49

� 39. x 41. �6 43. �3�34

� 45. �4�15

� 47. �241x�

49. �59

� 51. 1�13

� 53. 2�35

� 55. �34x� 57. 120 59. 21c2 61. �

63. � 65. 1�23

� 67. 2�56

� 69. 1�1151� 71. 3�

16

� 73. 6.0; 6.5; 3.6

and 7.2 75. 3.25 77. �2�12

� 79. G; 3; 81, 243, 72981. neither

Chapter 6 Ratio, Proportion, andPercent

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

23. 3.04 25. �13

� 27. simplified 29. simplified 31. �34

�


1. Sample answer:

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

� 7. �13

�

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

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

� 19. �37

� 21. �32,

9000�

23. �17

160� 25. �

11178

� 27. �31

� 29. 0.10 cents/pencil

31. 4.5 m/sec 33. 7.8 ft/h 35. 39 pages/week 37. The 6-pack of soda costs $0.37 per can. The 12-pack of sodacosts $0.35 per can. So, the 12-pack is less expensive.39. 26.4 41. 19.2 43. 72 45. 105 47. about 579 mi/h49. $9 51. C 53b. The ratios should be close in value.53c. Sample answer: Pyramid of Khufu in Giza, Egypt; The Taj Mahal in India; The Lincoln Memorial inWashington, D.C. 55. arithmetic; 0.3; 13.3, 13.6, 13.9

57. ��112� 59. 13�

13

� 61. 5.2 � 107 63. 3.8 � 10�2 65. 30

67. 40 69. 13

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

33. �132� � �

7m2�; 18 35. �

6.525� � �

8.d75�; 7 37. about 360.8 ft

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

� c

43. �ac

� � �db

�, �ba

� � �dc

�, or �ac

� � �db

� 45. C 47. 57.3 mph

49. 4 51. �74y� 53. 102 55. 6.5


1. 3. 40 mi 5. 1 in. � 5 ft

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

15. 49�12

� ft 17. �23

�

19. 1 cm � 0.25 cm

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

15 ft

10 ft

0.5 in. � 10 ft

1 unit 3 units


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scale factor greater than 1 means the drawing or model is

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

� 25b. �14

�

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

112�

33. 18t5 35. �4m

33

� 37. �210� 39. �

25

� 41. �3590� 43. �

4510�

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

than �1100�. 3. �

130�, 0.3 5. 1�

14

�, 1.25 7. 1�270�, 1.35 9. 45%

11. 0.8% 13. 133.3% 15. daily newspaper 17. �2225�, 0.88

19. �78

�, 0.875 21. 3�12

�, 3.5 23. �16010

�, 0.61 25. 2�12030

�, 2.23

27. �10

5,0300

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

37. 175% 39. 1.7% 41. �1

30

700� 43. 0.45 45. 19%

47. 61%, �23

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

possibilities that satisfy the conditions, �14

� and �25

�.

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

• 25% � �14

� � 0.25; 30% � �130� � 0.3; 40% � �

25

� � 0.4;

65% � �12

30� � 0.65 55. A 57. �

112� 59. �

2111� 61. 1�

133�

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


1. �numbe5r0correct��

1%00� 3. 40% 5. 104 7. 60% 9. 45%

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

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

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

copper, nickel). The outer layer is �34

� or 75% copper and �14

�

or 25% nickel.

29. �2510� 31. 1�

15

� 33. �79

� 35. 3�12

� 37. 8 39. 6 41. 25

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


1. 18% is about 20% or �15

�. 216 is about 220. �15

� of 220 is 44.

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

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

method: �13

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

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

25. Sample answer: �14

� � 8 or 2 billion 27. Sample answer:

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

fraction method: �25

� � 90 or 36 31. Sample answer: 2; 1%

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

�% of 806 is about �14

� of

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

and Jupiter 39. Sample answer: �13

� � 90,000 or 30,000 miles

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

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

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

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

�24

x.99� � �1

600�

Method 2: Percent Equationn � 0.06(24.99)

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

65%

40%

30%25%


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

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

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

•

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

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

37. rational 39. 20% 41. 83�13

�%


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

� � 70 or 28

3. $14.50 5. 158%

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

5. �12

�; 50% 7. �25

�; 40% 9. 1; 100% 11. 75 13. �14

�; 25%

15. �12

�; 50% 17. 0; 0% 19. �78

�; 87.5% 21. �29

�; 22.2%

23. �1181�; 61.1% 25. �

13

�; 33�13

�% 27. 1; 100% 29. �16

� 31. �116�

33. �14

� 35. 0.05; 5% 37. 444

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

• E: �11020

� or 12%; A, I: �1900� or 9%; O: �1

800� or 8%; N, R, T: �1

600�

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

300� or 3%; B, C, F, H, M,

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

100� or 1%

41. 146.9% 43. 23.9 45. 2x5 47. �18

7n2�

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

7. �34

� 9. �14

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

270�; 0.35

21. �225�; 0.08 23. 1�

15

�; 1.2 25. �58

�; 0.625 27. 24% 29. 45.2%

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

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

� � 32 or 16

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

� � 50 or 10

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

3, �13

�% of 304 is about �13

� of 3 or 1. 53. 48% 55. 94.5

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

� 65. �23

� 67. 0

Chapter 7 Equations and Inequalities

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

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

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

�

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

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

�n � �92

�

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

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

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

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

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

9.

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

9873 4 5 61 2

6540 1 2 3�2 �1

1 2

4 3

Greater than 100%

Less than 100%Original Rectangle


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23.

25.

27.

29.

31.

33.

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

49b.

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

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

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

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

31. n � 5

33. p � 2

35. x � �5

37. m � 27

39. b � 134

41. s � 423

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

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

5. x � �2

7. a � 50

9. m � �8.4

11. y � �72

13. C

15. y � 9

17. b � �3

19. t � 5

21. h � 98

23. z � 3

25. w � 2

27. r � 4

29. k � �18

31. t � �16

33. n � 4

35. y � 5.7

37. b � 72

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

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

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

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

2ca 53. 4

55. �9 57. 32

70 8674 78 82

5 5.85.2 5.4 5.6

1 9832 64 5 7

�20 �12�18 �16 �14

�12�14�18 �16�20

9873 4 5 61 2

�2 �1�3 1 20 43�4

9873 4 5 61 2

10610294 9890

9873 4 5 61 2

�2 �1�3 1 20 43�4

8 976 12 1311105

�80 �76 �72 �68 �64

�7.4�7.8�8.6 �8.2�9

907030 5010

�2 �1�3 1 20 43�4

3 4 5

0 1 1 212

12

23 25 27 29 31

0�7�6 �5�4�3�2 �1 1

9873 4 5 61 2

9873 4 5 61 2

9 1087 13 14 151211

�1�2 1 20 4 53�3

�1�2 1 20 4 53�3

0�8�7�6 �5�4 �3�2 �1

�3�2�4�5 1 20�1�6

6540 1 2 3�2 �1

9 1087 13 1412116

6 754 10 11 1298

6 7540 1 2 3�1


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1.

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

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

5. n � 2

7. c � 1

9. x � 8

11. d � �9�12

�

13. x � 8

15. c � �4

17. x � 3

19. k � �5

21. n � �5

23. b � 2

25. y � 30

27. c � �4

29. n � 7

31. n � 4.5

33. t � �1

35. c � �4

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

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

31. t � 3�12

�

33. k � 5.1

35. y � �7

37. a � �2�25

�

39. n � 4 41. t � �12 43. b � �4�14

�

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

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

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

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

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

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

y

xO

y

xO

(4, 3)

(1, 2)

(�3, 3)

(�2, �1)

40�2�4 2 6

�4�8�10�12 �6

�1 8 9543210 6 7

4 5210 3

22 24181614 20

�10 �2�8 �6 �4

�4 4�2 0�3 �1 1 32

1 9832 64 5 7

�10 �2�8 �6 �4

10 9030 50 70

�4 4�2 0�3 �1 1 32

�7 1�5 �3�6 �4 �2 0�1

�7 1�5 �3�6 �4 �2 0�1

�4 4�2 0�3 �1 1 32

�4 4�2 0�3 �1 1 32

1 93 52 4 6 87

�10 �6�9 �8 �7

1 93 52 4 6 87

�4 4�2 0�3 �1 1 32

1 93 52 4 6 87

�4 4�2 0�3 �1 1 32


6 8

7 10

8 12

x y

0 4

�3 3

x y

�8 5

7 �1

6 1

1 �2

x y

1 2

4 3

�2 �1

�3 3

x y

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

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

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

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

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

(0, 5), (1, 6)

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

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

(2, 10), (4, 14)

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

35. 37.

39. 41.

43.

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

61. �67

� 63. 3 65. 4

5 6 74321

P

s

1412108642

10 2 3 4 5 6 7

(1, 4)

(2, 8)

(3, 12)

y

xOy � �3

y

xO

3x � y � 7

y

xO

x � y � 6

y

xO

y � 3x � 4

y

xO

y � �x � 6

y

xO

y � x � 5

y

xO

y � 2x � 1


�3 �3 � 5 2

�1 �1 � 5 4

0 0 � 5 5

1 1 � 5 6

x x � 5 y

�4 2(�4) � 6 �2

0 2(0) � 6 6

2 2(2) � 6 10

4 2(4) � 6 14

x 2x � 6 y

R19-R50 C1-13 SA-825200 3/5/03 11:51 AM Page R33

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

9.

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

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

25. 27.

29. 31.

33.

35.

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

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

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

slope � �rriusne

� � �ru

0n� or 0. 3. Mike; Chloe should have

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

� 7. 2

9. 0 11. B 13. 4 15. ��34

� 17. 0 19. 1 21. ��32

�

23. undefined 25. ��34

� 27. It decreased; negative slope.

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

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

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

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

39. y � �2x 41. y � �13

�x

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

y

xO

y � 2x(1, 2)

(�1, �2)

y

x

y � 18 � 3x

Number of Books

Mo

ney

($)

2

0 1 2 3 4 5 6 7 8 9

468

1012141618

y

xO

3x � 6y � 18

(6, 0)

(0, 3)

y

x(0, �2)

O

y � �2

y

xO

y � �2x � 4

(2, 0)

(0, 4)

y

xO

x � y � 4

(4, 0)

(0, 4)

y

xO

y � x � 2

(0, 2)(�2, 0)

y

xO

y � 6x � 3

(0, 3)

(�0.5, 0)

y

xO

x � 2y � 6 (0, �3)

(6, 0)


R19-R50 C1-13 SA-825200 3/5/03 11:51 AM Page R34

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

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

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

23. B 25. 227.

29. 14 31. y � 1 � 3x


1. No; 1 is paired with 2 and �3.3.

5. �9; 9 7. 5; �4 9. �2

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

y � ��12

�x � 4. 5. �1; 0

7. 9.

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

19. 21.

23. 25.

27. 29.

31.

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

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

y

xOy � �3

y

xO

2x � 3y � 12

y

xO

5x � y � �3

y

xO

x � y � 0

y

xO

y � x � 234

y

xO

y � �x � 6

y

xO

y

xOx � 2y � 4

y

xO

y � x � 114

y

xO

y � x � 4

y

xO

(0, 1) (1, 0)

y � �x � 1

y

x

Time (h)

Dis

tan

ce (

mi)

10 2 3 4 5 6

100

200

300


1966–1982 �2.25 0.1875

1982–1990 �3 4.625

1990–1992 0 8

1992–1994 1.5 14.5

1994–1996 12.5 3.5

Interval Condors in Condors inthe Wild Captivity

Rate of Change(number per year)

R19-R50 C1-13 SA-825200 3/5/03 11:52 AM Page R35

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

43. 4 45. 6x � 2x � 28; 7 47. ��35

� 49. 29 51. 11

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

3. y � �12

�x � 1 5. y � �2x � 3 7. y � �12

�x � 1

9. y � �34

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

�x � 8

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

�x 23. y � x � 1

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

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

5. y � 20x � 3207. Sample answer:

9. Sample answer:

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

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

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

27.

29. n � 7 31. d � ��32

� 33. 2 35. 4.5 37. 3 39. �141. �2

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

5. no solution

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

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

xO

2x � 3y � 0

y � x 23

y

xO

(3, 3)

x � y � 6

y � x

y

xO

x � y � 2

x � y � 4

y

xO

y � �x � 3

Bar

om

etri

c Pr

essu

re(i

n. m

ercu

ry)

5

0

15

25

35

10

20

30

Altitude(1000s ft)

10 30 50 7020 40 60 x

y

Att

end

ance

(m

illio

ns)

1200

1150

0

125013001350

14001450

1500

Year’93 ’94 ’95’96 ’97 ’98 ’99

y

x

y

x

510

15

2025

3035

40

’95 ’96 ’97 ’98 ’99 ’00 ’01 ’020

Year

Nu

mb

er o

f H

ou

seh

old

s(m

illio

ns)


R19-R50 C1-13 SA-825200 3/5/03 11:53 AM Page R36

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17. (�2, 4)

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

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

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


1. �1; 8 3. ��12

�; 3 5. y � 1

7. Sample answer:

9. (0, 5)

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

5. 7.

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

11. 13.

15. 17.

19. 21.y

xO

y � � x � 1 13

y

xO

y � 2x � 4

y

xO

y � 0

y

xOy � x � 4

y

xOy � �3

y

xO

y � x

Ch

ildre

n

10

15

5

0

20

25

30

35

40

45

Adults15105 25 3520 30

25x � 15y � 630

y

x

y

xO

y � �3x � 2

y

xO

y � x � 1

y

x

Ag

e

25

27

29

24

26

23

0

28

30

Year’84 ’00 ’04 ’08’92’88 ’96

0

25

50

75

Time (s)

BA

y

x

Dis

tan

ce (

m)

1 2 3 4 5 6 7

Dis

tan

ce (

m)

0

25

50

75

Time (s)

B

Ay

x1 2 3 4 5 6 7

y

xO

y � � x � 312

y � �2x

(�2, 4)


R19-R50 C1-13 SA-865108 11/6/03 8:04 PM Page R37

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23.

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

31.

33a. y � x � 1, y � ��32

�x � 2

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

37. (0, 3) 39. (2, �5)

41. 0.4 43. �0.5�

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

15. 17.

19. 21.

23. 25.

27. 29.

31. 1 33. �78

� 35. undefined 37. increase of 8 m/s

39. 41.

43. y � �x � 3

45. Sample answer:

Att

end

ance

2500

2400

0

260027002800

29003000

Year2000 20022001 2003

y

x

y

xO

y � x � 2 13

y

xO

y � x � 4

y

xO

x � y � �2

(0, �2)

(�2, 0)

y

xO

(�4, 0)x � �4

y

xO

y � �x � 3

(0, �3)

(�3, 0)

y

xO

(�2, 0)

(0, 2)

y � x � 2

y

xO

x � y � 4

y

xO

y � 3x � 2

y

xO

y � �x

y

xO

y � x � 4

y

xOy � �2x � 1

y � �x � 3(2, �5)

y

xO

y � x � 3

x � 0

(0, 3)

Eco

no

Raf

ts

10

0

20

30

Super Rafts5 10 15

100x � 40y � 1500

y

x

2000

3000

1000

0

4000

5000

6000

3000 6000

y

x

Sale

s ($

)

Costs ($)

y � x � 3000


R19-R50 C1-13 SA-825200 3/5/03 11:54 AM Page R38

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47. (3, 3)

49. no solution

51. (4, 4)53. 55.

Chapter 9 Real Numbers and Right Triangles

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

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

5. �8 7. 3.9 9. 8 11. 44.9 mi 13. 6 15. �5 17. notpossible 19. 14 21. 18, �18 23. 1.5 25. 7.5 27. �9.329. 15.8 31. �1.7 33. 70.7 35. 9 37. �7 39. 1441. �17 43. �2 45. 6 47. 14.8 mi 49. 9; Since 64 � 65 � 81, �64� � �65� � �81�. Thus it follows that 8 � �65� � 9. So, 9 is greater than �65�. 51a. 10.4 in.51b. 14.2 cm 51c. 8.4 m 53. 10 55. 2 57. Sampleanswer: A number that has a rational square root will havean ending digit of 0, 1, 4, 5, 6, or 9. The last digit is theending digit in one of the squares from 1–100. There arejust six ending digits. 59. D 61. Sample answer: additionand subtraction 63. a

65. 67. (5, 7) 69. (�4, �3)

71. �23

� 73. 9 75. It can

be written as a fraction.

77. It can be written as �34

�.

79. It can be written as �61

�.

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

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

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

9. �130�, 3�

35

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

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

31. always 33. � 35. � 37. � 39. �65

�, �4�, 2.1�, 5�14

�

41. �10�12

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

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

79. 81. 83.


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

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

21.acute

23.acute

25.obtuse

27. obtuse155˚

95˚

65˚40˚

55˚

7:4510:003:00

Area �64 in2

Area �56 in2

y

xO

�10 �9 �8 �7 �6 �5 �4 �3 �2 �1

�1.69�

y

xO

y � �x � 4y

xO

y � 3x � 1

y

xO

3x � y � 1

y � �3x � 5

y

xO

(3, 3)

y � xy � 3


R19-R50 C1-13 SA-825200 3/5/03 11:55 AM Page R39

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29.acute

31a. obtuse 31b. right 31c. acute33. Intense: about 68°; Moderate:about 104°; Light: 72°; No standardroutine: about 47°; Don’t exerciseregularly: about 68° 35. 24

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

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

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

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

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

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

�624� � �

22a2� Divide each side by 2.

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

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

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

12

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

27. �11�12

�, �5�

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

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


1. Sample answer: corresponding sides:

�XA

YB� � �

YBC

Z� � �

AX

CZ�

3. �1x5� � �

69

�; 10 5. 6 km 7. �x4

� � �150�; 8 9. �

1x8� � �

2105�; 24

11. �x3

� � �47.2�; 5 13. always 15. 68 yd 17. 6 ft 19. Sample

answer: 4 units by 6 units by 8 units and 1 unit, 1.5 units,

2 units 21. A 23. 3.6 25. 7.1 27. 77.4 29. �14

� 31. 1�12

�

33. 0.7143 35. 0.225

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

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

•

The height of the ramp is about 2 feet.

45. C 47. �1�12

�, �12

�� 49. (�3, �4) 51. a � �6

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

33. (0, �2) 35. �AH

BJ

� � �BJKC�; 10 37. 1.3333

Chapter 10 Two-Dimensional Figures

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

15. 10.7 17. 10�16

� 19. 3�78

� 21. 5�38

� 23. 6�29

�

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

sin 6° � �1x9�

19(sin 6°) � x2.0 � x

6˚ x ft19 ft

B C

A X

Y Z

y

xO

(�3, 1)

(2, �1)

( , 0)Midpoint

B

A 12 �

30˚ 120˚30˚

38˚


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

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

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

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

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

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

7. A�(�2, 5), B�(1, 3), 9. D��1, 3�12

��, E��3, 4�12

��, C�(�2, 0);

G��1, �1�12

��, F��3, ��12

��;

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

Q�(0, 0);

15. 17.

19. translation

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

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

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

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

scooter represents a translation, and the skateboardrepresents reflection.

27. C 29. D�F� 31. 110°33. x � 9.6;

35. 113 37. 47 39. 106

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

7.0 8.0 9.0 10.0

y

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y

xO A

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B

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E' A'

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M'

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T

S'

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D'

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C

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U T

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J

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

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

31. B 33. 35. M�A� 37. 14.439. 28.52

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


1. Sample answer:

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

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

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

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

•

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


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

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

• Sample answer:

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

47. quadrilateral 49. 16.4x 51. 33.9 53. 18.1

Pages 536–538 Lesson 10-71. Multiply 2 times � times the radius. 3. Mark; since thediameter of the circle is 7 units, its radius is 3.5 units. Thus,the area of the circle is � · (3.5)2 or 38.5 square units.5. 50.3 m; 201.1 m2 7. 8.2 km; 5.3 km2 9. about 9.1 mi2

11. 40.8 in.; 132.7 in2 13. 131.9 km; 1385.4 km2 15. 79.8 m;506.7 m2 17. 22.9 cm; 41.9 cm2 19. 96.6 in; 742.6 in2

21. 1.5 m 23. 13 cm 25. about 3979 mi 27. d 29. a31. about 26 times 33. are safe: 25.4 in2; are unsafe: 24.2 in2;don�t know: 14.0 in2 35. 4 37. C 39. 125° 41. 235°43. 125° 45. 62.5° 47. Sample answer: S�P�, S�Q��, R�P��49. 144° 51. 38 m2 53. x � �7 55. 150.5

Page 538 Practice Quiz 21. 112.86 cm2 3. 32 m2 5. 29.5 in.; 69.4 in2


1. Sample answer:

3. 49.5 yd2 5. 2 7. 72 ft2 9. 56.1 cm2 11. 18.3 in2

13. 45 ft2 15. 86.8 yd2 17. 85 units2 19. 6963.5 yd2

21. Sample answer: Separate the area into a rectangle and atrapezoid. 23. 68,679 mi2 25. You can use polygons tofind the area of an irregular figure by finding the area ofeach individual polygon and then finding the total area ofthe irregular figure. Answers should include the following.•

• To find the area of the irregular figure shown above, thefigure can be separated into two rectangles and a triangle.

27. C 29. 44.0 cm, 153.9 cm2 31. 540° 33. 1080°35. �24xy

Pages 544–548 Chapter 10 Study Guide and Review1. supplementary 3. corresponding angles 5. equilateral7. 109° 9. 71° 11. �H 13. R�S� 15. G�F�

8 in.

3 in.

y

xO

G

E

D

F

D'

F'

G'

E'


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17. 19. 112; 112° 21. 70; 70°;70° 23. 11 yd2

25. hexagon; 720°27. decagon; 1440°29. 13.2 m; 13.9 m2

31. 118 in2 33. 863.4 cm2

Chapter 11 Three-Dimensional Figures

Page 553 Chapter 11 Getting Started1. yes; triangle 3. no 5. 17 7. 7 9. 155 11. yes 13. yes15. yes

Pages 559–561 Lesson 11-11. Five planes form a square pyramid because the solid hasfive faces. An edge is formed when two planes intersect; avertex is formed when three or four planes intersect.3. triangular pyramid; any one of the following faces can be considered a base: RST, QRS, QST, QRT; Q�R�, Q�S�, Q�T�, R�T�, R�S�, S�T�; Q, R, S, T 5. intersecting7.

9. rectangular prism; LMNP, QRST or LPTQ, MNSR orPNST, LMRQ; LMNP, QRST, LPTQ, MNSR, PNST, LMRQ; L�M�, M�N�, N�P�, P�L�, L�Q�, M�R�, N�S�, P�T�, Q�R�, R�S�, S�T�, T�Q�; L, M, N,P, Q, R, S, T 11. triangular pyramid; any one of thefollowing faces can be considered a base: WXY, WYZ,WZX, XYZ; W�X�, W�Y�, W�Z�, X�Z�, X�Y�, Y�Z�; W, X, Y, Z 13. W�R�15. skew 17. top 19. rectangular and pentagonal prisms23. Never; only three or more planes can intersect in asingle point. 25. Sometimes; three planes may intersect ina line. Or, the planes may be parallel and not intersect at all.27. Two-dimensional figures form three-dimensionalfigures. Answers should include the following.• Two-dimensional figures have length and width and

therefore lie in a single plane. Three-dimensional figureshave length, width, and depth.

• Two-dimensional figures form the faces of three-dimensional figures.

29. D 31. 37.7 cm; 113.1 cm2 33. 0.5000 35. c � 8

37. n � �11 39. y � 1�34

� 41. 14 in2 43. 6.5 cm2

Pages 565–567 Lesson 11-21. Sample answer: Finding how much sand is needed to filla child’s rectangular sandbox; measure the length, width,and height, and then multiply to find the volume.3. 183.6 cm3 5. 1608.5 ft3 7. 282.7 yd3 9. 198.9 ft11. 512 cm3 13. 748 in3 15. 88.0 ft3 17. 225 mm3

19. 18.6 m3 21. 6.2 m 23. 1728 25. 1,000,000 27. 11.5 in.

29. The volume will be greater if the height is 8�12

� inches.

By using the formula for circumference, you can find theradius and volume of each cylinder. If the height is

8�12

� inches, the volume is 86.5 in3; if the height is 11 inches,

the volume is 67.7 in3. 31. C 33. Sample answer: Q�T� and Y�Z� 35. x � �8 37. 25 39. 4 41. 28

Pages 570–572 Lesson 11-31. The base is a circle.3. Sample answer: V � 134.0 cm3

5. 37.7 cm3 7. 378 ft3 9. 91,636,272 ft3

11. 412 cm3 13. 150 in3 15. 78.5 m3

17. 270.8 cm3 19. 565.5 m3 21. 44.0 m3

23a. 2.4 ft3 23b. 314.4 lb

25. The volume of a pyramid is one-third the volume of aprism with the same base and height. Answers shouldinclude the following.• The height of the pyramid and prism are equal. The

bases of the pyramid and prism are squares with equalside lengths. Therefore, their base areas are equal.

• The formula for the volume of a pyramid is one-thirdtimes the formula for the volume of a prism.

27. B 29. 904.8 cm3 31. 107.5 mm3 33. 10.1 in3

35. 7.8 37. 36

Page 572 Practice Quiz 11. triangular prism 3. 12.6 cm3 5. �11,545,353 ft3

Pages 575–577 Lesson 11-41. Sample answer: The surface of a solid is two-dimensional. Its area is the sum of the face areas, which aregiven in square units. 3. 150 ft2 5. 571.8 in2 7. 140.7 mm2

9. 282 in2 11. 264 m2 13. 1885.0 ft2 15. 294 ft2

17. 628.3 in2 19. 264.0 in2 21. 754 ft2 23. The surfacearea is 4 times greater. 25. D 27. square or rectangle

29. rectangle 31. 565.5 in3 33. 15.21 35. 1.3 37. 3�14

�

Pages 580–582 Lesson 11-51. Slant height is the altitude of a triangular face of apyramid; it is the length from the vertex of a cone to theedge of its base. Height of a pyramid or cone is the altitudeof the whole solid. 3. Sample answer: An architect mightuse the formulas to calculate the amount of materialsneeded for parts of a structure. 5. 42.9 m2 7. 336 ft2

9. 96.3 in2 11. 62.4 in2 13. 339.3 in2 15. 311.9 m2

17. 506.6 mm2 19. Style 8M has 29 in2 more plastic.21. 339 ft2; 4 squares 23. Many building materials arepriced and purchased by square footage. Architects usesurface area when designing buildings. Answers shouldinclude the following.• Surface area is used in covering building exteriors and in

designing interiors. • It is important to know surface areas so the amounts and

costs of building materials can be estimated.25. C 27. 5541.8 mm2 29. 7 ft2 31. 25.1 in3 33. infinitelymany solutions 35. 3 37. 3 39. 3.15

Pages 586–588 Lesson 11-61. Sample answer: The cones are similarbecause the ratioscomparing their radiiand slant heights are

equal: �23

� � �75.5�.

5 m 7.5 m

2 m3 m

8 cm

4 cm

sidefronttop

y

xO

H H'

J J'I I'


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3. no 5. x � 33�13

� ft 7. 525 m 9. 2,976,750 m3 11. yes

13. yes 15. x � 7 m, y � 18 m 17. Sometimes; bases mustbe the same polygon and the corresponding side lengthsmust be proportional. 19. always; same shape, diametersor radii are proportional 21. 2003 or 8,000,000 timesgreater 23. If the ratios of corresponding lineardimensions are equal, the solids are similar. Answersshould include the following.• For example, if the ratio comparing the heights of two

cylinders equals the ratio comparing their radii, then thecylinders are similar.

• A cone and a prism are not similar.

25. C 27. 184 ft2 29. 65° 31. ��59

� 33. 19.3 35. 6.0

37. 9.4

Page 588 Practice Quiz 21. 166 mm2 3. 9.4 m2 5. Yes; their correspondingdimensions are proportional.

Pages 592–594 Lesson 11-71. Josh; the first two 0s are not significant because they areplaceholders for the decimal point. The 0 between 2 and 5is significant because it is between two significant digitsand shows the actual value in the thousandths place.3. Sample answer: 0.012 or 2500 5. 3 7. 3 9. 7.1 L

11. 544.5 in2 13. �312� in. 15. 3 17. 2 19. 1 21. 4

23. 45 in. 25. 2 ft2 27. 84.47 m 29. 49.5 cm 31. 26 m2

33. b; The precision unit of ruler a is �18

� inch. The precision

unit of ruler b is �116� inch. 35. No, the numbers are

estimated to the nearest 0.1 million. 37. 12,400,000; 339. Not necessarily, because the actual size of the 2.0 mmwrench can range from 1.95 mm to 2.05 mm and the actualsize of the 2 mm bolt can range from 1.5 mm to 2.5 mm. So,the bolts could be larger than the corresponding wrenches.41. A 43. 0.05 mi; between 132.75 mi and 132.85 mi45. 26.5 cm2 47. 14.8 m2

Pages 595–598 Chapter 11 Study Guide and Review1. false; lateral area 3. false; slant height 5. false; cylinder7. true 9. rectangular prism; QRST, UVWX or QTXU,RSWV or QRVU, TSWX; QRST, UVWX, QTXU, RSWV, QRVU, TSWX; Q�R�, R�S�, S�T�, T�Z�, U�V�, V�W�, W�X�, X�U�, Q�U�, T�X�, S�W�, R�V�; Q, R, S, T, U, V, W, X 11. rectangular pyramid; YNPZ; AYZ, AZP, ANP, ANY, YNPZ; A�Y�, A�Z�, A�P�, A�N�, Y�Z�, Z�P�, P�N�, N�Y�; A, Y, Z, P, N 13. 0.8 mm3 15. 4 ft3

17. 1721.9 cm3 19. 548.7 mm2 21. 45 in2 23. 37.1 in2

25. yes 27. 19.0 cm 29. 0.9 m 31. 973 ft2

Chapter 12 More Statistics andProbability

Page 605 Chapter 12 Getting Started

1. 16; 15; none 3. 5.3, 5.8, 6.5 5. �13

� 7. �12

� 9. �12

� 11. �12

�

13. �18

� 15. �16

� 17. �16

�

Pages 608–611 Lesson 12-11. Sample answer: The age of the youngest President at thetime of his inauguration was 42 and the age of the oldestPresident to be inaugurated was 69. However, most of thePresidents were 50 to 59 years old at the time of theirinauguration.

3. Stem Leaf

0 6 71 2 5 52 03 54 0 1 20 � 20

11. 13.

15.

29c. Sample answer: It would be easier to find the mode ina stem-and-leaf plot because the value or values that occurmost often are grouped together. 31. C 33. no35. 62.8 ft; 314.2 ft2 37. 247% 39. 0.65% 41. 57.1%43. 1.6% 45. 6 47. 1.1

Pages 614–616 Lesson 12-21. The range describes how the entire set of data isdistributed, while the interquartile range describes how themiddle half of the data is distributed. 3. Sample answer:{8, 9, 13, 25, 26, 26, 26, 27, 28, 30, 35, 40} 5. 27; 6 7. 24 h9. 77; 39 11. 50; 10 13. 25; 15.5 15. 22 17. Feb.: 13.5;July: 8 19. National League: 42, 44, 48, 38, 10; AmericanLeague: 39, 44, 49, 39, 10 21a. Sample answer: {43, 49, 50,50, 58, 60, 60, 66, 70, 70, 71, 78} 21b. Sample answer: {15, 18, 20, 20, 44, 60, 60, 64, 70, 70, 75, 79} 21c. Sampleanswer: The first set of data has a smaller interquartilerange, thus the data in the first set are more tightlyclustered around the median and the data in the second aremore spread out over the range. 23. C

25. Stem Leaf

0 91 2 4 5 82 1 73 7 37 � $37


5. 50, 99 7. Sample answer: Thelowest score was 50. The highestscore was 99. Most of the scoreswere in the 70–79 interval.9. Chicken; whereas chickensandwiches have 8–20 grams offat, burgers have 10–36 grams offat.

Stem Leaf

1 32 6 8 3 4 945 2 36 2 2 77 7 98 4 77 � 77

Stem Leaf

40 0 0 54142 5434445 0 6464748 0 4 7495051 052 0...62 5...76 47778 9 764 � 764

Stem Leaf

0 6 6 81 0 1 4 6 82 0 2 53 2 745 0 37 � 37

17. never 19. 35% 21. Sampleanswer: In the most populatedU.S. cities, about 27 to 35% of thepeople exercise daily. 23. 525. The average number of gameswon by the teams in the Big EastConference is less than theaverage number of games wonby the teams in the Big TenConference. 29a. Sampleanswer: It would be easier to findthe median in a stem-and-leafplot because the data arearranged in order from least togreatest. 29b. Sample answer: Itwould be easier to find the meanin a table because once you findthe sum, it may be easier to countthe number of items in a table.

27. 461.8 cm3 29. 1.6 ft31. {0.2, 0.3, 0.6, 0.8, 1.2, 1.4, 1.5}33. {9.8, 9.9, 10.5, 10.9, 11.2, 11.4}

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Pages 619–621 Lesson 12-31. lower quartile, least value; upper quartile, greatest value3. Sample answer: {28, 30, 52, 68, 90, 92}

5.

7. Sample answer: The length of the box-and-whisker plotshows that the winning times of the men’s marathons arenot concentrated around a certain time. 9. The most fuel-efficient SUV and the least fuel-efficient sedan both average22 miles per gallon.

11.

13.

15.

17. 50% 19. Sample answer: The least number of gameswon for NFC is 3 and the least number of games won forthe AFC is 1. The most number of games won for the NFCis 12 and the most number of games won for the AFC is 13.In addition, for both conferences, the median number ofgames won is about 9. 21. A box-and-whisker plot wouldclearly display any upper and lower extreme temperaturesand the median temperature. Answers should include thefollowing.•

• Sample answer: Tampa has a median temperature of 73and Caribou has a median temperature of 40.5. Whereasthe highest average temperature for Tampa is 82, thehighest average temperature for Caribou is 66.

• Sample answer: You can easily see how the temperaturesvary.

23. C 25. 4

27. Stem Leaf

1 42 1 4 73 94 8 24 � 24

Pages 625–628 Lesson 12-41. Sample answer: Because the intervals are continuous.

3.

5. the number of states that have a certain number of rollercoasters 7. The numbers between 10 and 34 are omitted. 9. 2 or more national monuments

11.

13.

15. 13 17. 37.5% 19. Dallas 21. true 23. false 25. true27. A 29. absolute frequency: 2, 9, 17, 12, 7, 2; relative

frequency: �429�, �

499�, �

1479�, �

1429�, �

17

�, �429�; cumulative frequency:

2, 11, 28, 40, 47, 49

Touchdowns in a Season

4

6

2

0

8

Nu

mb

er o

f Pl

ayer

s

10

Number of Touchdowns

114–130

148–164

97–113

131–147

165–181

80–96

Weekly Study Time

0

87654321

Nu

mb

er o

f St

ud

ents

12

109

11

Time (hr)

10–127–94–60–3 13–15

Pet Survey

10–127–94–61–3

468

10

20

18161412

20

Nu

mb

er o

f Pa

rtic

ipan

ts

22

13–15Number of Pets

Caribou, ME

Tampa, FL

10 20 30 40 50 60 70 80 900

26.0 28.0 30.0 32.0 34.0 36.0

50 70 90 110 130 150 170

60 70 80 90 100 110 120 130

14 18 22 26 30 34 38 42 46 50


29. 14

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31.

33. 44; 15 35. Sample answer: Brand B costs one-thirdmore than brand C.


1. Stem Leaf

1 6 8 9 92 0 2 6 8 8 83 0 24 0 2 3 5 5678 6 9 55 � 55

3.

5.

Pages 631–633 Lesson 12-51. Sample answer: inconsistent vertical scale and break invertical scale 3. Graph A has a break in the vertical scale.5. From the vertical scale, you can see that the number of

area codes in 1999 is about 1.5 times the number of areacodes in 1996. The graph is misleading because the drawingof the phone for 1999 is about 3 times the size of the phonefor 1996. Also, there is a break in the vertical scale.7. Graph B 9. Graph B; the vertical scale used makes thedecrease in the unemployment rates appear more drastic.11a. Sample answer:

11b. Sample answer:

13. B15.

17. 20.3 m2 19. �16

� or 16�23

�% 21. �56

� or 83�13

�%

23. �56

� or 83.3�%

Pages 637–639 Lesson 12-61. Sample answer: Both methods find the number ofoutcomes. Using the Fundamental Counting Principle isfaster and uses less space; using a tree diagram shows whateach outcome is. 3. First find the number of outcomespossible. The possible outcomes are taco-chicken, taco-beef,

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Commuter Train Passengers

Am

ou

nt

(mill

ion

s)

450

46

47

48

49

50

51

5352

54

5556

57

5859

Year’96 ’97 ’98 ’99

Commuter Train Passengers

Am

ou

nt

(mill

ion

s)

50

10

15

20

25

30

35

4540

50

5560

Year’96 ’97 ’98 ’99

60–6950–59

40–4930–39

20–29

10–19

0–9

Freq

uen

cy

70–79

80–89

Cost ($)

4

6

2

0

3

5

1

7

9

10

8

Costs

0 10 20 30 40 50 60 70 80 90 100

Average Lengthof U.S. States

900–1199

600–899

300–599

1–299

Nu

mb

er o

f St

ates

1200–1499

Length (mi)

8

12

4

0

16

24

20

10

14

6

2

18

26

22

3032

28

Source: The World Almanac


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taco-bean, burrito-chicken, burrito-beef, and burrito-bean,for a total of 6 outcomes. Two of the outcomes have chicken

filling, so the probability of chicken filling is �26

� or �13

�. 5. �116�

7. �14

� 9. 9

11.

8 outcomes13.

15. 36 outcomes 17. 24 outcomes19. 1024 outcomes 21. �

158� 23. �100

1,000�

25. Either; the probability of rollingeither odd or even is one-half.27. Sample answer: any two lettersfollowed by any four digits 29. D31. Sample answer: Vertical scale thatdoes not start at zero. 33. 11–20

35. 37.

39. 15 41. 28

Pages 643–645 Lesson 12-71. Sample answer: How many 3-digit numbers can be madefrom the digits 1, 2, 3, and 4 if no digit is repeated?3. Sarah; five CDs from a collection of 30 is a combinationbecause order is not important. 5. P; 120 ways 7. C; 84 ways 9. 220 pizzas 11. P; 24 flags 13. C; 105 ways15. P; 1320 ways 17. C; 364 ways 19. 40,32021. 39,916,800 23. 36 handshakes 25. 3003 ways

27. 10 combinations 29. �25

� 31. When order is not

important, duplicate arrangements are not included in thenumber of arrangements. Answers should include thefollowing.• When order was not important there were half as many

pairs. • Order is important when you arrange things in a line;

order is not important when you choose a group ofthings.

33. C 35. Yes; the vertical axis does not include zero.37. Q 39. I 41. 1:8 43. 11:2

Page 645 Practice Quiz 21. Sample answer: Bars are different widths.3. 256 outcomes 5. 15 segments

Pages 648–649 Lesson 12-81. Write a ratio comparing the ways the event can occur tothe ways the event cannot occur. 3. Hoshi; the probabilityof rolling a 2 is 1 out of 6. The odds of rolling a 2 are 1 in 5.5. 1:2 7. 5:1 9. 1:2 11. 2:1 13. 1:1 15. 1:3 17. 5:7

19. 31:5 21. 1:17 23. 5:4 25. 9:4 27. �81

192� 29. 47:53

31. No; 512 is the total number of possible outcomes, so itcould not be a number in the odds of winning. 33. A35. 6 ways37. ; a � 6

39. ; y � �3

41. �13

� 43. �516�

Pages 653–655 Lesson 12-91. Independent and dependent events are similar becauseboth are a connection of two or more simple events and theprobability of the compound event is found by multiplyingthe probabilities of each simple event. They are differentbecause the second event in a dependent event isinfluenced by the outcome of the first event. Therefore, the probability of the second event used in calculating theprobability of the compound event is dependent on theoutcome of the first event. 3. The result of the 1st event

must be taken into account. 5. �112� 7. �

134� 9. �

34

� 11. �310�

13. �15

� 15. �911� 17. �

1901� 19. �

3564� 21. �

58

� 23. �37

� 25. 1 27. �29

�

29. 0.16 31a. Sample answer: 3 red, 2 white, and 4 blue31b. Sample answer: The numerator must be 24. Any

combination of 3, 2, and 4 will have a probability of �211�.

33. B 35. �23

� 37. 3:10 39. 17,576,000 41. 65° 43. 65°

45. 90° 47. 40.6 49. 16

Pages 658–662 Chapter 12 Study Guide and Review1. b 3. c 5. d 7.

9. 23; 7 11. 22; 10 13. 80°F 15. 50% 17. Graph A

19. 16 outcomes 21. C; 364 ways 23. C; 21 ways 25. 3:5

27. 1:3 29. �310�

Chapter 13 Polynomials and Nonlinear Functions

Page 667 Chapter 13 Getting Started1. 1 3. 2 5. 0 7. 5a � 20 9. �4 � 32n 11. 27b � 27c13. yes 15. yes

�3 �2 �1 0 21�5 �4�6

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S

B

SB

N

SN

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W

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B

YB

N

YN

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B

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N

BN

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12 outcomes

Stem Leaf

4 5 55 0 0 5 5 6 0 0 0 0 07 5 5 58 5 5 75 � 75¢

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Pages 670–672 Lesson 13-11. The degree of a monomial is the sum of the exponents ofits variables. The degree of a polynomial is the same as thedegree of the term with the greatest degree. 3. Tanisha; the degree of a binomial is the degree of the term with thegreater degree. 5. yes; monomial 7. yes; binomial9. yes; trinomial 11. 0 13. 1 15. 4 17. 2 19. yes;binomial 21. yes; monomial 23. no 25. yes; trinomial27. no 29. yes; trinomial 31. 0 33. 3 35. 5 37. 5 39. 341. 5 43. Always; any number is a monomial.45. 2x � 2y � z � xy 49. Polynomials approximate real-world data by using variables to represent quantities thatare related. Answers should include the following.• Heat index is found by using a polynomial in which one

variable represents the percent humidity and anothervariable represents the temperature.

• Heat index cannot be approximated using a linearequation because the values do not change at a constantrate.

51. C 53. mutually exclusive; �23

� 55. 70 in3

57. (x � 2x) � 4 59. (6n � 3n) � (2 � 5)61. (s � 5s) � (t � 3t)

Pages 676–677 Lesson 13-21. x2 and 2x2; 5x and �4x; 2 and 7 3. Hai; the terms havethe same variables in a different order. 5. 7a2 � 9a � 47. 13x � 4y 9. 4x2 � 3x � 2 11. 3x � 313. 11x2 � 5xy � 4y2 15. 4x � 14 17. 8y � 2r19. 5x2 � xy � y 21. 7x2 � 9x � 5 23. 5a � 4b; �3125. 4a � 6b � c; 14 27. 56 29. 23x � 12 31. 42x � 2233. Use algebra tiles to model each polynomial andcombine the tiles that have the same size and shape.Answers should include the following.• Algebra tiles that represent like terms have the same size

and shape. • When adding polynomials, a red tile and a white tile that

have the same size and shape are zero pairs and may beremoved. The result is the sum of the polynomials.

35. B 37. 2 39. �123� 41. �

236� 43. 15c � (�26)

45. 1 � (�2x) 47. (n � rt) � (�r2)

Pages 680–681 Lesson 13-31. Subtracting one polynomial from another is the same asadding the additive inverse. 3. 4r 5. 5x � 27. 3x2 � 3x � 8 9. 7x � 5 units 11. �2n2 � 6n13. y2 � 7y � 10 15. 15w2 � 2w � 10 17. 4x � 319. �2t � 2 21. 3a2 � 2b2 23. 9n2 � n � 1225. 2x2 � 2xy � 3y2 27. x � y � 68 � (x � y); �34°F29. In subtracting polynomials and in subtractingmeasurements, like parts are subtracted. Answers shouldinclude the following.• To subtract measurements with two or more units,

subtract the like units. To subtract polynomials with twoor more terms, subtract the like terms.

• For example, to subtract 1 foot 5 inches from 3 feet 8 inches, subtract the feet 3 � 1 and subtract the inches 8 � 5. The difference is 2 feet 3 inches.

31. B 33. 12x � 3y 35. �t2 � 12t � 2 37. yes; binomial39. Stem Leaf

5 4 96 4 6 87 0 1 1 28 5 99 1 54 � 54

Page 681 Practice Quiz 11. 4 3. 3 5. 2x � 2 7. 8r � 3s 9. �3x � 5y

Pages 684–686 Lesson 13-41. False; the order in which numbers or terms aremultiplied does not change the product, by theCommutative Property of Multiplication; x(2x � 3) � 2x2 � 3x and (2x � 3)x � 2x2 � 3x. 3. Sampleanswer: 2x(x � 1) � 2x2 � 2x 5. a2 � 4a 7. 12x2 � 28x9. �15x2 � 35x � 45 11. 14n � 35 13. t2 � 9t15. �7a2 � 6a 17. 40n � 8n2 19. 3y3 � 6y 21. 5x2 � 5xy23. �14x2 � 35x � 77 25. 4c4 � 28c2 � 40c 27. –129. high school, 84 ft by 50 ft; college, 94 ft by 50 ft

31. 33. D 35. 7x � 137. 4y2 � 2y � 1439. 8x � 11y

(a � b)(c � d) � ac � ad � bc � bd41. Sample answer: The scales are labeled inconsistently or the bars on a bar graph are different widths.43. reflection

45.

Pages 689–691 Lesson 13-51. Sample answer: Determine whether an equation can bewritten in the form y � mx � b or look for a constant rate ofchange in a table of values. 3. Sample answer: populationgrowth 5. Nonlinear; graph is a curve. 7. Nonlinear;equation cannot be written as y � mx � b. 9. Linear; rateof change is constant. 11. Nonlinear; graph is a curve.13. Linear; graph is a straight line. 15. Nonlinear; graph isa curve. 17. Linear; equation can be written as y � 0.9x � 0. 19. Linear; equation can be written as

y � �34

�x � 0. 21. Nonlinear; equation cannot be written as

y � mx � b. 23. Linear; rate of change is constant.25. Nonlinear; rate of change is not constant.27. Nonlinear; the points (year, applications) would lie on acurved line, not on a straight line. Or, the rate of change isnot constant. 29. No, the difference between the yearsvaries, so the change is not constant. 31. A 33. 4t � 9t2

35. a2b � 2ab2 37. �x 39. acute

41. 43.

x

y

O

y � � x � 312

x

y

O

y � x � 4

a

�b

adac

bdbc

c � d


41. 8y2 43. 4m3 45. 10r5

0 �3 (0, �3)

1 �1 (1, �1)

2 5 (2, 5)

3 15 (3, 15)

x 2x2 � 3 (x, y)

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Page 691 Practice Quiz 21. 2c3 � 8c 3. 5a2 � a3 � 2a4 5. Nonlinear; equationcannot be written as y � mx � b.

Pages 694–696 Lesson 13-61. Sample answer: The graph of y � nx2 has line symmetryand the graph of y � nx3 does not. 3. Sample answer: y � x2 � 3; make a table of values and plot the points.

5. 7.

9. 11.

13. 15.

17. 19.

21.

23.

Both equations are functions because every value of x ispaired with a unique value of y.25. (0, 7)27. Similar shape; y � 3x2 is

more narrow.

29. Same shape; y � �2x2

is y � 2x2 reflected over thex-axis.

31. A � 50x � x2 33. 25 ft by 25 ft35. V � 0.2�r2 or V � 0.6r2

37. Formulas, tables, and graphs are interchangeable waysto represent functions. Answers should include thefollowing. • To make a graph, use a rule to make a table of values.

Then plot the points and connect them to make a graph. • To write a rule, find points that lie on a graph and make

a table of values using the coordinates. Look for apattern and write a rule that describes the pattern.

39. C 41. Sample answer: 18 units2 43. 10x � 2045. 24y � 21y2 47. y � 4x � 3

Pages 698–700 Chapter 13 Study Guide and Review1. trinomial 3. cubic 5. like terms 7. curve 9. yes;binomial 11. yes; monomial 13. yes; trinomial 15. no

r

V

V � 0.6r 2

1110987654321

0 3 5 761 2 4

y

xO

y � �2x 2

y � 2x 2

y

xO

y � x 2y � 3x 2

y

xO

y � �4x 3

y

xO

y � x 2 � 4

y

xO

12y � x 2 � 1

y

xO

y � x 3 � 1

y

xO

y � 2x 3

y

xO

y � �2x 3

y

xO

y � �x 2

y

xO

y � 3x 2

y

xO

y � x 3� 2

y

xO

y � �x 3

y

xO

y � �2x 2


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17. 1 19. 3 21. 6 23. 5 25. 8b � 3 27. 5y2 � 2y � 429. y2 � y � 1 31. 3x2 � 4x � 7 33. �x � 1 35. 20t � 1037. 6k2 � 3k 39. �18a � 2a3 41. Linear; graph is a straightline. 43. Nonlinear; rate of change is not constant. 45. 47.

49. y

xO

y � 2x 2 � 4

y

xO

y � x 3 � 1

y

xO

y � �3x 2


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