(PDF) CPM Algebra 1 HW Solutions - PBworkscwalter.pbworks.com/w/file/fetch/50279248/CPM Algebra 1 HW... · CPM Algebra 1 HW Solutions.pdf Author: cwalter Created Date: 1/27/2012 1:34:46 - PDFSLIDE.NET (2023)

  • Algebra Connections 28

    Chapter 5

    Lesson 5.1.1

    5-1. b. x + 4 and x + 2 c. x2 + 6x + 8 = (x + 2)(x + 4)

    5-2. a. (x +1)(x + 2) b. 3(2x + 5) c . (2x + 3)(x + 2)

    d. (x +1)(3x +1) e. (2x + 6)(x + 2) or (2x + 4)(x + 3)

    f. 2y(y + 3) g. (y + x)(y + 2) h. (x +1)(y +1)

    i. (x + y +1)(x + y + 2) j. (2y +1)(x + 2)

    5-4. 77 + 56 + 33+ 24 = 190 5-5. y = 7x + 5

    5-6. (2x + 4)(x + 2) = 2x2 + 8x + 8 5-7. Answers vary.

    5-8. No, he is not correct. Parallel lines do not have a pointof intersection. 5-9. 62,000 votes

    Lesson 5.1.2

    5-10. a. (2x + 3)(x + 2) = 2x2 + 7x + 6 b. (y + x + 2)(x + 4) =xy + x2 + 6x + 4y + 8

    5-11. a. 8x2 b. 2x2 + 7x + 3 c. 2x2 +10x

    d. 4x2 + 4x +1 e. 2x2 + xy

    f. 2x2 + 2xy + 9x + 5y +10 g. 6x +10 h. 2xy + y2 + 3y

    5-13. a. 12x2 +10x b. 24x + 6 c. 12xy + 9y d. 70xy + 77y2

    5-15. a. (x +1)(x + 3) = x2 + 4x + 3 b. (2x +1)(x + 2) = 2x2 +5x + 2

    5-16. a. 238 b. 112 5-17. a. Multiply by 6 b. x = 15 c. x = 45-18. a. m = 3 b. (0, 2) c. y = 3x ! 2

    5-19. 10,000 + 1,500x = 18,000 + 1,300x, x = 40 months 5-20.x-intercepts are (1.5, 0) and (1, 0), y-intercept is (0, 3).

  • Answer Key 29

    Lesson 5.1.3

    5-21. a. !18x +12 b. 4x2 ! 2x

    c. 50t !15t2 d. !32 + 24k ! 4y

    5-22. (4x + 5)(2x + 3) = 8x2 + 22x +15

    5-23. The area inside each smaller rectangle of the genericrectangle corresponds to the tiles in the same portions of therectangle in problem 5-22.

    5-24. a. (3)(y + 5) = 3y +15 b. (x)(2x) = 2x2

    c. (x + 5)(2x ! 3) = 2x2 + 7x !15 d. (4y ! 7)(6y !1) = 24y2 !46y + 7

    5-25. a. 3x2 +17x +10 b. 10y2 !11y ! 35

    c. 18xy ! 33x d. 15w2 ! wp ! 2p2 ! 20w + 8p

    5-26. a. y(x + 3) = xy + 3y b. (x +12)(x + 5) = x2 +17x + 60

    c. (x ! 2)(2x ! 3y + 5) = 2x2 ! 3xy + x + 6y !10

    d. Multiple answers possible

    5-27. a. 2x2 +17x + 30 b. 3m2 ! 4m !15

    c. 12x2 ! 59x ! 5 d. 6 ! 7y ! 5y2

    5-28. a. 6 b. 16 c. 1.5 d. 8

    5-29. a. 4, 0 b. 16, 6 c. 2, 14 d. 20, 1 5-30. a. y = !2x +1 b.x: (0.5, 0), y: (0, 1) c. y = !2x

    5-31. 30 ounces 5-32. These expressions are equivalent becauseof the Commutative Properties of Addition

    and Multiplication.

  • Algebra Connections 30

    Lesson 5.1.4

    5-33. a. 12x2 + 8x ! 55 b. !30x2 + 6x

    c. !y2 + 4y +12 d. 48 !16m2

    5-34. This can be built with 3 rows, each containing 2 x-tilesand 1 unit tile

    a. 4

    b. 3(24 + 1) = 84 5 5-35. A and C are correct. 5-36. x = !25-37. a. x = 9 b. x = 0 c. y = 6

    d. x = !3.5 e. x = 2 f. x = ! 103

    5-38. a. 1 b. 5 c. 2.5 d. 8 5-39. The equation in part (b) hasno solution. Possible reason: There are the same number

    of x-terms on each side of the equation, so if you try to solve,you end up with an equation such as 11 = 14 , which isimpossible.

    5-40. Rena is correct.

    5-41. y = !2x +13

    5-42. a. After 3 hours b. 8

    5-43. (2, 1)

    5-44. No, on average he will make about 375 baskets.

  • Answer Key 31

    Lesson 5.1.5

    5-45. a. 5 feet, the y-intercept is the constant

    b. 4 feet per year, the rate is the coefficient of the x. 5-46.b. y = 3x + 5

    c. y-intercept is (0, 5); growth factor is 3. 5-47. See tablebelow.

    y =mx + b form Growth factor y-intercept

    a. y = x ! 7 1 (0, 7)

    b. y = x + 2 1 (0, 2)

    c. y = !5x ! 2 5 (0, 2)

    d. y = x 1 (0, 0)

    e. y = 0 0 (0, 0)

    f. y = !3x ! 4 3 (0, 4)

    5-48. a. y = 5 b. x = 5 ! 52y c. y = 6x !11

    d. x can be any number e. x = !13y + 2 f. p = m

    2+ 4

    g. y = x ! 3 h. q = !373

    5-50. a. 4x2 +17x +15 b. !6x2 ! 20x !16

    c. !3xy + 3y2 + 8x ! 8y d. 3xy + 5y2 ! 22y !12x + 8

    5-51. a. x =y+5

    2 b. w =

    p!9

    !3 c. m = 2n + 5 d. y = !3x

    5-52. y = 3+ 2x

    5-53. b. no solution

    c. there is no solution to the system of equations because thetwo lines do not intersect

    5-54. 100 4 = 25, 3,000 25 = 120 gallons

  • Algebra Connections 32

    Lesson 5.1.6

    5-55. a. x = 3 b. y = 12x ! 2 c. x = 3 d. y = ! 1

    2x + 4 e. x = 2

    f. y = !x + 3 g. x =y!4

    !3 h. x = 2 i. w = 3! 2v j. no solution

    5-57. a. x = 5 b. x = 2 c. y = 0 d. x = 38

    5-58. (x + 3)(x ! 5) = x2 ! 2x !15

    5-59. See graph at right.

    5-60. The numbers are 55 and 60. 5-61. a. 6x +10 = 10x , after2.5 hours b. 25 problems 5-62. ! 1222

    Lesson 5.2.1

    5-63. a. 18 b. 12 c. 4.5 d. 127

    5-64. a. 34 people b. Yes c. 238,085 votes 5-65. a. Ratios varyb. No c. When ratios are of corresponding parts, the ratios areequal

    d. The ratios used will vary. One example: 68100

    =x

    527. Therefore,

    x = 358.36 , so Mr. Mears would probably receive roughly 358votes from

    Carinas neighborhood.

    5-66. a. 217

    =x

    85, x = 10 minutes b. 8

    29=

    x

    1490, x ! 411 students

    5-67. 19.9 minutes 5-68. 9.6 weeks; 179.2 pounds 5-69. answersvary

    5-70. a. x2 + 9x + 20 b. 2y2 + 6y

    5-71. a. 3x2 + 5x +13 b. 5x2 +16x + 5 c. !x2 + 4x + 6

    d. 5x e. 4x2 !11x ! 2

    33

    4

    y

    x

  • Answer Key 33

    Lesson 5.2.2

    5-72. a. 30 b. 16 c. 32 d. .3

    5-73. See table below:

    # of Cans Weight (kg)

    50 0.77

    1,240 x

    b. 501240

    =0.77

    x, x ! 19.1 kg c. ! 31.9 kg

    5-74. a. $8 b. $74.95 c. 10 days (rounded up to nearest wholeday)

    5-75. 15 units

    5-76. 74184

    =x

    4, x ! 1.6 inches

    5-77. a. x = !5 b. y = 2x ! 3 c. no solution d. y = !3x + 5

    5-78. ! 574 times at bat

    5-79. a. 132

    =8

    x, x = 256 miles b.

    g

    118=1

    32, g ! 3.7 gallons

    5-80. a. (3, 5) 5-81. a. Yes, because the sum of two evennumbers is always an even number. If one even

    number is written as 2m and the other as 2n , then the sum is 2m+ 2n = 2(m + n) ,

    which is even.

    b. Yes, because the product of two even numbers is always even.If one even number is written as 2m and the other as 2n , then theproduct is (2m)(2n) = 2(2mn) , which is even.

    5-82. a. 2x(x + 5) = 2x2 +10x b. (2x + 5)(x + 3) = 2x2 +13x+15

    Lesson 5.2.3

    5-85. a. x2 +10x +16 b. 2m2 + 70m + 600

    c. xy +10x d. 6x2 +17x +12

    5-86. a. 0.08 feet or about 1 inch b. ! 42 feet

    5-87. a. 11.2 b. 7.5 c. 3.75 d. 0.25

    5-88. (2, -5)

    5-89. a. y = 4x ! 3 b. y = x + 3 c. y = ! 32x + 6 d. y = ! 2

    3x + 2

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