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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) = 2×2 + 8x + 8 5-7. Answers vary.
5-8. No, he is not correct. Parallel lines do not have a point of intersection. 5-9. 62,000 votes
Lesson 5.1.2
5-10. a. (2x + 3)(x + 2) = 2×2 + 7x + 6 b. (y + x + 2)(x + 4) = xy + x2 + 6x + 4y + 8
5-11. a. 8×2 b. 2×2 + 7x + 3 c. 2×2 +10x
d. 4×2 + 4x +1 e. 2×2 + xy
f. 2×2 + 2xy + 9x + 5y +10 g. 6x +10 h. 2xy + y2 + 3y
5-13. a. 12×2 +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) = 2×2 + 5x + 2
5-16. a. 238 b. 112 5-17. a. Multiply by 6 b. x = 15 c. x = 4
5-18. 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. 4×2 ! 2x
c. 50t !15t2 d. !32 + 24k ! 4y
5-22. (4x + 5)(2x + 3) = 8×2 + 22x +15
5-23. The area inside each smaller rectangle of the generic rectangle corresponds to the tiles in the same portions of the rectangle in problem 5-22.
5-24. a. (3)(y + 5) = 3y +15 b. (x)(2x) = 2×2
c. (x + 5)(2x ! 3) = 2×2 + 7x !15 d. (4y ! 7)(6y !1) = 24y2 ! 46y + 7
5-25. a. 3×2 +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) = 2×2 ! 3xy + x + 6y !10
d. Multiple answers possible
5-27. a. 2×2 +17x + 30 b. 3m2 ! 4m !15
c. 12×2 ! 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 because of the Commutative Properties of Addition
and Multiplication.
Algebra Connections 30
Lesson 5.1.4
5-33. a. 12×2 + 8x ! 55 b. !30×2 + 6x
c. !y2 + 4y +12 d. 48 !16m2
5-34. This can be built with 3 rows, each containing 2 x-tiles and 1 unit tile
a. 4
b. 3(2·4 + 1) = 8·4 – 5 5-35. A and C are correct. 5-36. x = !2 5-37. a. x = 9 b. x = 0 c. y = 6
d. x = !3.5 e. x = 2 f. x = !10
3
5-38. a. –1 b. 5 c. –2.5 d. 8 5-39. The equation in part (b) has no 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 is impossible.
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 table below.
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 ! 5
2y c. y = 6x !11
d. x can be any number e. x = !1
3y + 2 f. p = m
2+ 4
g. y = x ! 3 h. q = !37
3
5-50. a. 4×2 +17x +15 b. !6×2 ! 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 the two 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 = 1
2x ! 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 , after 2.5 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 vary b. No c. When ratios are of corresponding parts, the ratios are equal
d. The ratios used will vary. One example: 68100
=x
527. Therefore,
x = 358.36 , so Mr. Mears would probably receive roughly 358 votes from
Carina’s 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. answers vary
5-70. a. x2 + 9x + 20 b. 2y2 + 6y
5-71. a. 3×2 + 5x +13 b. 5×2 +16x + 5 c. !x2 + 4x + 6
d. 5x e. 4×2 !11x ! 2
3–3
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. 50
1240=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 whole day)
5-75. 15 units
5-76. 74
184=
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 even numbers 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 the product is (2m)(2n) = 2(2mn) , which is even.
5-82. a. 2x(x + 5) = 2×2 +10x b. (2x + 5)(x + 3) = 2×2 +13x +15
Lesson 5.2.3
5-85. a. x2 +10x +16 b. 2m2 + 70m + 600
c. xy +10x d. 6×2 +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 = !3
2x + 6 d. y = !
2
3x + 2
