Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
Solve.
75)
Using data from 2010-2012, the annual number of cars sold at a certain dealership can be modeled
by the formula y =3x +4, where y is the number of cars, in thousands, sold x years after 2010.
According to this formula, in which years will the number of cars sold exceed 40 thousand?
75)
A)
Years after 2026
B)
Years after 2022
C)
Years after 2024
D)
Years after 2020
Solve.
76)
Mrs. White crochets hats and afghans for a church fundraising bazaar. The bazaar sells the hats for
$14 each and the afghans for $7 each. Let x = the number of hats sold and y = the number of
afghans sold. Write the objective function that describes the total income from the sale of hats and
afghans.
76)
A)
z =14x +7y
B)
z =7x +14y
C)
z =7x -14y
D)
z =14x -14y
Solve. Use interval notation to express the range.
77)
The formula for converting Celsius temperature, C, to Fahrenheit temperature, F, is
F =9
5C + 32.
If Fahrenheit temperature ranges from 5° to 77°, inclusive, what is the range for the Celsius
temperature?
77)
A)
(41, 171)
B)
[41, 171]
C)
(-15, 25)
D)
[-15, 25]
Solve the compound inequality. Other than , graph the solution set on a number line.
78)
0 3x +4
2<3
78)
A)
-4
3, 2
3
B)
-4
3,2
3
C)
-4
3, 2
3
D)
-4
3,2
3
42
Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the
solution set in interval notation.
79)
8<2x 14
79)
A)
(4, 7]
B)
[4, 7)
C)
(-, 4] (7, )
D)
(-, 4) [7, )
Solve.
80)
ABC phone company charges $20 per month plus 8¢ per minute of phone calls. XYZ phone
company charges $8 per month plus 10¢ per minute of phone calls. How many minutes of phone
calls in a month make XYZ phone company the better deal?
80)
A)
More than 60 minutes
B)
Less than 600 minutes
C)
More than 600 minutes
D)
Less than 60 minutes
Find the value of the objective function at each corner of the graphed region. Use this information to answer the question.
81)
Objective Function z = - x - 9y
What is the maximum value of the objective function?
81)
A)
-47
B)
-22
C)
-30
D)
-38
Graph the solution set of the system of inequalities or indicate that the system has no solution.
82)
y 1
2 x 6
x - 2y -2
x + y 6
82)
A)
B)
44
C)
D)
Solve and graph the solution set on a number line.
83)
|x + 3| > 0
83)
A)
(-3, 3)
B)
(-, -3) (-3, )
C)
D)
(-3, )
Graph the inequality.
45
84)
y <1
5x
84)
A)
B)
C)
D)
Solve. Use interval notation to express the range.
85)
The formula C =1.5x +17 represents the estimated future cost of yearly attendance at State
University, where C is the cost in thousands of dollars x years after 2010. Use a compound
inequality to determine in which years attendance costs will range from 27.5 to 33.5 thousand
dollars.
85)
A)
[2018, 2020]
B)
[2018, 2022]
C)
[2017, 2021]
D)
[2016, 2020]
Solve the problem.
86)
A candy company has 140 pounds of cashews and 185 pounds of peanuts which can be combined
into two different mixes. The deluxe mix is half cashews and half peanuts and sells for $6 per
pound. The economy mix is one-third cashews and two-thirds peanuts and sells for $5.60 per
pound. How many pounds of each mix should be prepared for maximum revenue?
86)
A)
95 pounds of deluxe mix and 45 pounds of economy mix
B)
190 pounds of deluxe mix and 135 pounds of economy mix
C)
140 pounds of deluxe mix and 0 pounds of economy mix
D)
285 pounds of deluxe mix and 90 pounds of economy mix
Solve the linear inequality. Other than , graph the solution set on a number line.
87)
8(x +5) 7(x - 4) + x
87)
A)
[7, )
B)
( , 7]
C)
( , )
D)
47
Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the
solution set in interval notation.
88)
-3x -9 or 3x >9x - 6
88)
A)
(-, 1) [3, )
B)
(1, 3]
C)
(-, 1] (3, )
D)
Solve.
89)
The length
of a metal rod used in manufacturing cars must not differ from the standard s by more
than 0.7 inches. The manufacturing engineers express this as |- s| 0.7.If the standard s is 13.7,
solve the inequality for the length
. Express the answer in set-builder notation.
89)
A)
{ 13 14.4 }
B)
{ 14.4 15.1 }
C)
{ 14.4 or 15.1 }
D)
{ 13 or 14.4 }
Find the solution set for the equation.
90)
4x + 3
9=3
90)
A)
- 6
B)
6, -15
2
C)
15
2
D)
Solve the inequality. Other than , graph the solution set on a number line.
91)
x -4
15 x -4
18 +1
90
91)
A)
(-, 5]
B)
(5, )
C)
(-, 5)
D)
[5, )
Solve.
92)
The radius r of a plastic tube used in manufacturing a child's toy must not differ from the standard
s by more than 5 millimeters. The manufacturing engineers express this as |r - s| 5. If the
standard s is 23, solve the inequality for the radius r. Express the answer in set-builder notation.
92)
A)
{ rr 18 or r 28 }
B)
{ r r 13 or r 18 }
C)
{ r13 r 18 }
D)
{ r18 r 28 }
93)
Chi is assigned to construct a triangle with the measure b of the base and the measure h of the
height differing by no more than 0.2 centimeters. Express the relationship between b and h as an
inequality involving absolute value.
93)
A)
|b - h| 0.2
B)
|b + h| 0.2
C)
|h - b| > 0.2
D)
|b - h| < 0.2
Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the
solution set in interval notation.
94)
-5x < - 15 and x +5>4
94)
A)
B)
(3, )
C)
(-1, 3)
D)
(-, -1) (3, )
Solve.
95)
Yvette has up to $2000 to invest and has chosen to put her money into telecommunications and
pharmaceuticals. The telecommunications investment is to be no more than 4 times the
pharmaceuticals investment. Write a system of inequalities to describe the situation. Let x represent
the amount (in dollars) invested in telecommunications and y represent the amount (in dollars)
invested in pharmaceuticals.
95)
A)
x + y =2000, y 4x, x 0, y 0
B)
x + y 2000, 4x y, x 0, y 0
C)
x + y =2000, x 4y, x 0, y 0
D)
x + y 2000, x 4y, x 0, y 0
Solve and graph the solution set on a number line.
96)
x>8
96)
A)
(-8, 8)
B)
(-, -8) ( 8, )
C)
[-8, 8]
D)
(-, -8] [8, )
97)
|x + 4| <7
97)
A)
[-11, 3]
B)
(-, -11) (3, )
C)
D)
(-11, 3)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
51
98)
1 x <4
98)
A)
B)
C)
D)
Solve and graph the solution set on a number line.
99)
|2x + 3| 2
99)
A)
-1
2,
B)
-5
2, -1
2
C)
-5
2, -1
2
D)
, -5
2-1
2,
Solve. Use interval notation to express the range.
100)
Parts for an automobile repair cost $814. The mechanic charges $37 per hour. If you receive an
estimate for at least $962 and at most $1036 for fixing the car, what is the time interval that the
mechanic will be working on the job?
100)
A)
[1, 6]
B)
[1, 4]
C)
[4, 6]
D)
[26, 28]
Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the
solution set in interval notation.
101)
x 4 or x 5
101)
A)
(4, 5)
B)
[4, 5]
C)
D)
(-, 4] [5, )
An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region.
Use these values to determine the maximum value of the objective function and the values of x and y for which the
maximum occurs.
102)
Objective Function z =13x + 12y
Constraints 0 x 10
0 y 5
3x + 2y 6
102)
A)
Maximum: 36; at (0, 3)
B)
Maximum: 60; at (0, 5)
C)
Maximum: 130; at (10, 0)
D)
Maximum: 190; at (10, 5)
54
Solve and graph the solution set on a number line.
103)
|5x - 4| 7
103)
A)
, -3
511
5,
B)
-3
5, 11
5
C)
-3
5, 11
5
D)
, 11
5
Graph the inequality.
104)
x -1
104)
55
A)
B)
C)
D)
D)
Find the solution set for the equation.
105)
|x + 2| =8
105)
A)
{-6}
B)
{10, 6}
C)
D)
{-10, 6}
Graph the inequality.
56
106)
x + 4y 4
106)
A)
B)
C)
D)
57
Solve the inequality. Other than , graph the solution set on a number line.
107)
10x -53x -15
107)
A)
-, -10
7
B)
[-10, 7]
C)
(-10, 7)
D)
-, -10
7
Solve the compound inequality. Other than , graph the solution set on a number line.
108)
-3x + 1 7 or 4x + 3 -13
108)
A)
(-, )
B)
[-4, -2]
C)
[-2,)
D)
[-4, )
58
109)
7x - 4 -11 and 6x - 4 26
109)
A)
[-1, )
B)
[5, )
C)
[-1, 5]
D)
(-, -1] [5, )
An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region.
Use these values to determine the maximum value of the objective function and the values of x and y for which the
maximum occurs.
110)
Objective Function z =7x + 6y
Constraints x 0
0 y 6
x - y 5
x + 2y 14
110)
A)
Maximum: 50; at (2, 6)
B)
Maximum: 36; at (0, 6)
C)
Maximum: 35; at (5, 0)
D)
Maximum: 74; at (8, 3)
59
Solve and graph the solution set on a number line.
111)
|x + 5| - 6 1
111)
A)
(-12, 2)
B)
[-12, 2]
C)
[-12, 1]
D)
Find the union of the sets.
112)
{-6, -1, 2, 7} {-3, 0, 4, 9}
112)
A)
{-1, 0, 2}
B)
{-6, -3, -1, 0, 2, 4, 7, 9}
C)
{0}
D)
Find the solution set for the equation.
113)
|5x + 7| = |x + 9|
113)
A)
B)
1
2, -8
3
C)
-1
2, 8
3
D)
1
2, 5
6
114)
|x + 1| = 0
114)
A)
B)
{1}
C)
{-1}
D)
{1, -1}
60
