Selected Answers for

Core Connections Algebra

2 Core Connections Algebra

Lesson 3.1.1 3-6. a: 1

h2 b: x7 c: 9k10

d: n8 e: 8y3 f:28x3y6 3-7. a: incorrect, x100 b: correct c: incorrect, 8m6n45 3-8. 3-9. Let x = number of weeks. 150 +10x 3-10. a: 9 b: –4 c: –1 d: 12 3-11. a: – 7

10 b: –2 23 c: 3 13 d: –3

Lesson 3.1.2 3-19. b, c, d, f 3-20. a: 14 b: 1 c: 1

52= 125 d: 1

x2

3-21. a: x = 3 b: x = 6 c: x = 2 d: x = 4 3-22. a: m = – 13 b: y = – 13 x – 2 3-23. Let x = number of weeks. 1500 ! 35x = 915; x = 17 weeks 3-24. y = 3x –1

x

y

Selected Answers 3

Lesson 3.2.1 3-33. a: 4x2 + 6x +13 b: 5y2 + 8x +19

c: 9x2 + x + 44 d: 5y2 + 6xy + 30 3-34. a: x = –8 b: x = 1 3-35. A pair of parallel lines. 3-36. Let x = the number of votes for candidate B, x + (x – 15,000) = 109,000. 62,000 votes 3-37. a: 1 19 b: –13 3

10 c: –14 1720 d: –7 16 3-38. y = 1

2 x +1 3-39. a: 4x + 2y + 6 b: 2x + 4 c: 4y + 2x + 6 d: 2y + 2x + 6 3-40. Possible equation: 2 + (!2x)! (4 ! x) = 2 + (!3)! (x ! 2) or

2 + (!2x)! (!x)! 4 = 2 + !3! x ! (!2) 3-41. a: x = 8 b: c: It is the point where the lines intersects the x-axis on the graph. It is the x-value when y = 0 in the table. 3-42. a: 16 b: 2 c: undefined d: 0 3-43. B 3-44. a: 15x2 b: 8x c: 6x2 d: 7x

x –2 0 2 4 6 8 10 y –5 –4 –3 –2 –1 0 1

x

y

4 Core Connections Algebra

Lesson 3.2.2 3-48. 77 + 56 + 33 + 24 = 190 square units 3-49. (2x + 4)(x + 2) = 2x2 + 8x + 8 3-50. a: Multiply by 6. b: x = 15 c: x = 4 3-51. a: m = 3 b: (0, –2) c: y = 3x – 2 3-52. 10, 000 +1500x = 18, 000 +1300x , x = 40 months 3-53. The x-intercepts are (1.5, 0) and (–1, 0); the y-intercept is (0, –3).

Lesson 3.2.3 3-58. a: (x +1)(x + 3) = x2 + 4x + 3 b: (2x +1)(x + 2) = 2x2 + 5x + 2 3-59. a: 238 square units b: 112 square units 3-60. a: x = 6 b: x = 16 c: x = 15 d: x = 8 3-61. 30 ounces 3-62. y = 2

3 x – 3 3-63. a: –15 1

12 b: –5 14 c: 17 d: –10 58

x –2 –1 0 1 2 3 y 7 0 –3 –2 3 12

x

y

Selected Answers 5

Lesson 3.2.4 3-70. a: 2x2 +17x + 30 b: 3m2 – 4m –15

c: 12x3 + x2 – 60x – 5 d: 6 – 7y – 5y2 3-71. y = –2x +13 3-72. a: After 3 hours b: 8 3-73. (–2, –1) See graph at right. 3-74. They are not. An odd number added to an odd number is an even number. 3-75. a: –15x b: 64 p6q3 c: 3m8

Lesson 3.3.1 3-81. a: –20xy – 32y2 b: –36x + 90xy c: x4 + 3x3 + 3x2 ! 6x !10 3-82. Yes, for even numbers. On a number line, if you start at any multiple of two and add a

multiple of two (an even number), you will always be stepping up the number line in multiples of two; you will always land on an even number. No for odd numbers. For example, 3 + 5 = 8; the sum of two odd numbers is not always odd.

3-83. (x – 5)(x + 3) = x2 – 2x –15 3-84. a: x = 8 or x = –2 b: x = ±7 c: x = 1 or x = –3 d: no solution 3-85. a: b: c: d: 3-86. a: 12 b: 59 c: 7 d: 9 e: –13 f: –5

x

y

– 4 4 –1

3

16 – 4 – 4

–8

–33 11 –3

8

–7 –1 7

6

6 Core Connections Algebra

Lesson 3.3.2 3-93. a: x = ±7 b: x = ±16 c: x = 3, –17 d: x = ±53.1 3-94. a: x = 6 + 2

3 y b: y = 32 x – 9 c: r = d

t d: r = C2!

3-95. a: 5 59 b: –11 1735 c: 6 3049 d: 1 163350 3-96. a: y = –11 b: y = – 34 x + 21 3-97. See graph at right. (2, –5) 3-98. a: x4y3 b: xy c: –6x6 d: 8x3 3-99. a: x = 10 or x = !16 b: x = 9

2 , !112

c: x = ! 13 or x = ! 1

3 d: no solution 3-100. a: 5x2 – 30x b: –54y + 27y2 3-101. a: 2x(x + 5) = 2x2 +10x b: (2x + 3)(x + 5) = 2x2 +13x +15 3-102. a: x = 5 b: x = 2 c: y = 0 d: x = 38 3-103. a: 4x2 +17x +15 b: –6x3 – 20x2 –16x

c: –3xy + 3y28x – 8y d: 3xy + 5y2 – 22y –12x + 8 3-104. a: x = y+5

2 b: w = p–9–3 c: m = (4n+10)

2 d: y = –3x

x

y

Selected Answers 7

Lesson 3.3.3 3-107. a: x = 0 b: x = 8 c: x = 1 d: x = –3, 13 3-108. y = 3x – 5 3-109. y = 1

5 x + 7 3-110. a: – 1924 b: 4 56 c: 75 = 1

25

d: – 83 = –223 e: –3 7

12 f: 2 27 3-11. a: 6(13x – 21) = 78x –126 b: (x + 3)(x – 5) = x2 – 2x –15

c: 4(4x2 – 6x +1) = 16x2 – 24x + 4 d: (3x – 2)(x + 4) = 3x2 +10x – 8 3-112. a: 15x3y b: y c: x5 d: 8

x3