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6.1.1

6-7. See below:
a. x = 6 +
b. y =
y
x−9
c. r =

6-8. See below:
. 6(13x – 21) = 78x – 126
a. (x + 3)(x – 5) = x2 – 2x – 15
b. 4(4x2 – 6x + 1) = 16x2 – 24x + 4
c. (3x – 2)(x + 4) = 3x2 + 10x – 8

6-9. There is a moderately strong negative association, meaning that the more a
student watches TV, the lower his/her grade point average is predicted to be. 52% of
the variability in GPAs can be explained by a linear relationship with number of hours
spent watching TV. However, we are careful not to imply a cause. Watching less TV
will not necessarily cause a rise in GPA.

6-10. See below:
. arithmetic
a. t(n) = 4n + 3
b. No, n = 26.5.

6-11. Yes; both points makes the equation true.

6-12. If x = the width, 2(x) + 2(3x – 1) = 30, width is 4 inches, length is 11 inches.
6.1.2

6-15. See below:
a. y = −2x +
b. y = 4x −

6-16. See below:
. a=0
a. m = –2
b. x = 10
c. t = 2

6-17. They will be the same after 20 years, when both are $1800.

6-18. See below:
. –43
a. 58.32

6-19. See below:
. (–1, 9)
a. Possible response: Reflect over the y-axis and then rotate clockwise (or
counterclockwise) 180º around the origin.

6-20. (3, 5)
6.1.3

6-25. See below.
a. In 7 weeks.
b. George will score more with 1170 points, while Sally will have 970.

6-26. See below.
. no solution
a. x = 13

6-27. (–1, 3)

6-28. From an earlier lesson, association does not mean that one variable caused the
other. One possible lurking variable is per capita wealth: wealthier nations may tend
to have more TVs and also better health care.

6-29. See below.
. 17, 14, 11, ...; an = 20 – 3n
a. 20, 10, 5, ...; an = 40( )n

6-30. See below.
. x=3
a. x = 1
6.1.4

6-38. See below.
a. The units of measurement, centimeters. Side #2 = x, Side #3 = 2x − 1
b. x + x + (2x − 1) = 31
c. x = 8, so Side #1 = Side #2 = 8cm and Side #3 = 2 · 8 – 1 = 15cm.

6-39. 1,600,000 miles per day; 66,666.6 miles per hour.

6-40. She combined terms from opposite sides of the equation. Instead, line 4 should
read 2x = 14, so x = 7 is the solution.

6-41. See below.
. geometric
a. 55 = 3125
b. an = 5n

6-42. c

6-43. AC2 = 32 + 72 = 58, AC =
≈ 7.62. The length of
because the original measurements were whole numbers.
6.2.1

6-49. See below.
a. a + c = 150
b. 14.95c + 39.99v = 84.84

6-50. 3 – m miles

6-51. See below.
.
a.
b.
c. y = –bx

6-52. Lakeisha, Samantha, Carly, Barbara, and Kendra

6-53. 5 years

6-54. See below.
. –3, –1, 1, 3, 5
a. 3, –6, 12, –24, 48
is rounded up to 8
6.2.2

6-60. Let d = distance walked (miles); d = 3t and (66 – d) = (15)(2t), or,
3t + (15)(2t) = 66; t = 2; 4 hours on the bus.

6-61. See below.
a. ii
b. 4 touchdowns and 9 field goals

6-62. See below.
. See answers in bold in table and line on graph.
x
y
–3
3
–2
1
–1
–1
0
–3
a.

1
–5
2
–7
3
–9
Yes; (–3, 3) and (–2, 1) both make this equation true.
6-63. See below.
. geometric
a. curved
b. t(n) =
(5)n

6-64. Katy is correct; the 6x − 1 should be substituted for y because they are equal.

6-65. See below.
.
a. b4
b. 9.66 × 10–1
c. 1.225 × 107

6-66. See below.
. Calculate the output for the input that is 6 times w.
a. Calculate the output for the input that is 2 less than h.
b. 10 more than 4 times the output of f when the input is a.
6.2.3

6-73. From the graph, x ≈ 3.7 and y ≈ 6.3, when students look at the table of values
they can justify that since f(3) = 5.5 and g(3) = 4.95 and then f(4) = 6.6 and g(4) =
6.85 that the two functions must have the same value between x= 3 and x = 4 and that
value must be between 5.5 and 6.6.

6-74. See below.
a. h = 2c − 3
b. 3h + 1.5c = 201
c. 28 corndogs were sold.

6-75. Yes; adding equal values to both sides of an equality preserves the equality.

6-76. See below.
. x = 2.2
a. x = 6
b. x = −10.5
c. x = 0

6-77. an = t(n) = 32( )n

6-78. See below.
. y = –3x + 7
a. y = –x –
6.3.1

6-84. See below.
a. (5, 3)
b. (2, –6)

6-85. See below.
. You end up with 10 = 10. Some students may conclude that it is all real numbers or
infinite solutions.
a. The two lines are the same.
b. Since the equations represent the same line when graphed, any coordinate pair
(x, y) will solve both equations.

6-86. See below.
. Let p represent the number of pizza slices and b represent the number of burritos
sold. Then 2.50p + 3b = 358 and p = 2b − 20.
a. 82 pizza slices were sold.

6-87. See below.
. 1.05
a. 20(1.05)5 = $25.52
b. t(n) = 20(1.05)n; 20 represents the current (initial) cost and 1.05 represents the
percent increase.

6-88. See below.
.
; x = 5.5 hours
a. 90 = 1.5r, r = 60 mph, 330 = 60t, t = 5.5 hours
b. yes

6-89. See below.
.
a. xy6
b. 1.2 × 109
c. 8 × 103
6.3.2

6-95. See below.
a. (3, 1)
b. (0, 4)
c. (10, 2)
d. (–4, 5)

6-96. They are both correct. The equations represent the same line, and so both
coordinate pairs are solutions to both equations.

6-97. 3 hours

6-98. an = t(n) = 4 · 3n

6-99. See below.
. x=2
a. x = 4

6-100. See below.
. b = y − mx
a. x =
b. t =
c. t =
6.3.3

6-106. See below.
a. 6x2 − x − 2
b. 6x3 − x2 − 12x − 5

6-107. See below.
. (–5, 1)
a. (3, 1)
b. no solution

6-108. See below.
. not a function, D: –3 ≤ x ≤ 3 and
R: –3 ≤ y ≤ 3
a. a function, D: –2 ≤ x ≤ 3, R: –2 ≤ x ≤ 2

6-109. r ≈ 0; Answers will vary for LSRL, but the average number of pairs
appears to be about 3.8, which is an LSRL of y = 3.8.

6-110. See below.
. 3x – 18º = 74º; x = 30.67º
a. 3x – 9º = x + 25º; x = 17º; m∠2 = 3(17º) – 9º = 42º

6-111. See below.
. m = –12
a. x = –24
b. x =
6.4.1

6-116. See below.
a. (0,
)
b. (−6, 2)
c. no solution
d. (11, −5)

6-117. 2n = p and n + p = 168; 56 nectarines are needed.

6-118. See below.
. Yes, because these expressions are equal.
a. 5(3y) + y = 32, y = 2, x = 3.5

6-119. an = t(n) = 6n − 2

6-120. y = − x + 6

6-121. See below.
. 2x2 + 6x
a. 3x2 − 7x − 6
b. y = 3
c. x = 2
6.4.2

6-134. See below.
a. infinitely many solutions
b. ( , − )
c. (1, 2)
d. (8, 7)

6-135. See below.
. It is a line. It can be written in y = mx + b form.
a. Answers will vary. Possible solutions: (0, 2), (1, 5), (2, 8), …
b. y = 3x + 2; Yes, because the points are the same.

6-136. See below.
. p: y = 2x + 8; q: y = –
x+3
a. Yes, because (–2, 4) is the point of intersection.
b. The slopes indicate that the lines are perpendicular.
c. (–2, 4)

6-137. See below.
. 5, –10, 20, –40, 80
a. an = –

(–2)n
6-138. See below.
. x2 + 9x + 20
a. 2y2 + 6y

6-139. See below.
. M'(–3, 3), J'(–1, 1), N'(–1, 6)
a. M"(3, 3), J"(1, 1), N"(1, 6)
b. 5 square units

6-140. n + d = 30 and 0.05n + 0.10d = 2.60, so n = 8. There are 8 nickels.

6-141. C

6-142. See below.
. no solution
a. x = 5, y = 2

6-143. See below.
. x = −5
a. y = 2x − 3
b. no solution
c. y = −3x + 5

6-144. See below.
. 0.85
a. 1500(0.85)4 ≈ $783
b. an = 1500(0.85)n; 1500 represents the current (initial) cost. 0.85 represents a
15% decrease.

6-145. Let s = number of slices on an extra-large pizza; 4s + 3 = 51 . An extra-large
pizza has 12 slices.