Download Integrated 1 Chapter 2 2.1.1 • 2-7. • 2

Integrated 1
Chapter 2
2.1.1
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2-6. y = 7x + 5
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2-7.
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2-8. See below.
a. 2
b. −4
c. −5, −2, 0, 2, 4
d. −2
e. 13
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2-9. See below.
a. 60
b. 127
c. 0
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2-10.
2.1.2
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2-18.
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2-19. 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 = 4, which is impossible.
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2-20. See below.
a. −10
b. −4
c. undefined
d. 2
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2-21. No solution; you cannot divide by 0.
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2-22. See below.
a. 2
b. −37
c. −5
d. −6
2.1.3
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2-29. See the "Suggested Lesson Activity" for possible answers.
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2-30. See below.
a. Line a: y = 2x − 2,
Line b: y = 2x + 3
b. It would lie between lines a and b, because its y-intercept is at (0, 1).
c. It would slant downward but would have the same y-intercept as the line from part (b).
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2-31. Approximately 79%
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2-32. See below.
a. 2.4 x 108
b. 1.4 x 10−9
c. 2.25 x 10−2
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2-33. See below.
a. −15x
b. 64p6q3
c. 3m8
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2-34. Graphs (a) and (b) have a domain of all real numbers, while graphs (a) and (c) have a range
of all real numbers. Graphs (a) and (b) are functions
2.1.4
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2-40. See below.
a. m =
b. m = −
, b =(0, −4)
, b =(0, 3)
c. m = 0, b =(0, −5)
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2-41. See below.
a. m = –2
b. m = 0.5
c. undefined
d. m = 0
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2-42. See below.
a. correct
b. 7.89 x 104
c. 3.15 x 103
d. correct
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2-43. See below.
a. 4
b. 16
c. y = 4x + 16
d. It would get steeper.
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2-44. See below.
a. While walking double (or triple) the distance, they would encounter double (or triple) the
number of dogs. If they walked zero blocks, they would encounter zero dogs. The dogs
in the area are evenly spread out along the blocks.
b.
; x ≈ 36.83 so 37 dogs would be reasonable.
c. ≈ 1.42 dogs per block
2.2.1
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2-47. A very strong positive nonlinear association with no apparent outliers.
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2-48. The number of people must be whole numbers, and Mikko probably did not keep track of
parts of burgers, so the points should not be connected; that is, there is no possible data between
the points. If a line is drawn to model the trend, it should be straight rather than go through all
the points.
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2-49. See below.
a. m =
b. (0, −4)
c. See graph at right.
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2-50. See below.
a. −15
b. −4
c. 3
d. −m2
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2-51. x ≠ 5 because the denominator cannot be 0.
2.2.2
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2-58. See below.
a. The dependent variable is y (distance in meters) and the independent variable is x (time in
seconds).
b. See graph below. Mark won the race, finishing in 5 seconds.
c. Barbara: y =
x + 3, Mark: y = 4x
d. 5 meters every 2 seconds, or
meters per second.
e. 2 seconds after the start of the race, when each is 6 meters from the starting line.
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2-59. b, c, d, f
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2-60. See below.
a. 43
b. 25.5
c. 17.5
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2-61. y = 2x + 3
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2-62. See graph below.
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2-63. a: The slope represents the change in height of a candle per minute, m = 0 cm per minute,
b: The slope represents the gallons per month of water being removed from a storage tank, m = –
900 gallons per month.
a.
b.
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2-64. −3
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2-65. See below.
a. 9
b.
or 0.15625
c.
d.
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2-66. $50 per week, A = 50w + 100, A = (50)(52) + 100 = 2700
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2-67. See below.
a. y = –2x + 1
b. x: (0.5, 0), y: (0,1)
2.2.3
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2-71. See below.
a. (4, 0) and (0, –2)
b. (8, 0) and (0, 4)
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2-72. See below.
.
x = 12
a. w = 0
b. x = –8
c. no solution
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2-73. See below.
a. It is the slope of the line of best fit drawn on the graph. Its units are mpg/1000 pounds.
b. It is the y-intercept of the line of best fit. Its units are mpg.
c. Moderately strong negative linear association with no apparent outliers.
d. About 25 mpg
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2-74. See below.
a. Growth = 5, Fig 0 = 3
b. Growth = –2, y-intercept = 3
c. Growth = 3, y-intercept = –14
d. Growth = –5, y-intercept = 3
e. Pattern A
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2-75. See below.
Days (x)
0
2
4
6
8
Height cm (y)
30
27
24
21
18
a. No. On Day 0 the height is not 0. If the number of days is doubled (or tripled), the height is not
doubled (or tripled).
b. See answers in bold in table.
c.
or –1.5 cm/day
d. y = –
x + 30
2.2.4
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2-81. See the “Suggested Lesson Activity”.
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2-82.
measurement, the car uses about 2 gallons of gas.
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2-83. See below.
= 1.95 gallons. Considering precision of
a. 3, (0, 5)
b.
, (0, 0)
c. 0, (0, 3)
d. 4, (0, 7)
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2-84. The sum of the first four planets’ distances = 3.597x108 miles, which is less than the
distance to Jupiter.
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2-85. See below.
a.
–1
b. –
c.
d.
e. The line travels downward from left to right, so m = –1.
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2-86. f(x) = 4x + 4
2.3.1
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2-93. See the "Suggested Lesson Activity" for possible answers.
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2-94. See below.
a. y = 1.5x + 0.5
b. Answers vary, but solutions should lie on y = 1.5x + 0.5. Possible points: (0, 0.5), (1, 2),
(10, 15.5)
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2-95. $213.33 per second
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2-96. There is no association between number of pets and age.
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2-97. Answers vary. Typical responses:
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2-98. See below.
, x3x-5, and (x-1)2
a. 4
b. 3
c. 1
d. 2
2.3.2
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2-102. y = 7x + 9
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2-103. See below.
a. −8
b. 1
c. −2
d. 17
e. −45
f. 125
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2-104. ≈ 73 feet/second
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2-105. See below.
a. See graph below. u = 37 – 13.7p where p is the price in dollars and u is the number of
unpopped kernels. The slope represents the change in price for each unpopped kernel.
The y-intercept
intercept represents the number of unpopped kernels in a free (unpopped) bag.
b. ≈ 21 kernels
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2-106. See graph below.
2.3.3
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2-108. See below:
y=
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–4
2-109. m = 3
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2-110. He should thaw out 3 pounds of hamburger.
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2-111. See below:
a.
–6
b.
–2
c.
–
d. undefined
e. x = 2.25
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2-112. See below:
a.
b.
or –2.5 pounds/month.
y=–
+ 120, where x = months and y = pounds