A)
B)
C)
D)
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.
140)
Objective Function z =5x – 2y
Constraints x 0
0 y 4
x – y 7
x + 2y 10
140)
A)
B)
C)
D)
Solve the system of equations.
141)
y– 5z= – 6
5x + y + 3z= – 10
4x + 2z= – 12
141)
A)
{(–4, 4, 2)}
B)
{(–4, 9, 3)}
C)
{(–2, 6, –2)}
D)
{(–2, 5, –2)}
Solve the problem.
142)
The equation that represents the proper traffic control and emergency vehicle response availability
in a small city is 2P + 3F
23, where P is the number of police cars on active duty and F is the
number of fire trucks that have left the firehouse in response to a call. In order to comply with
staffing limitations, the equation 2P + F
17 is appropriate. The number of police cars on active
duty and the number of fire trucks that have left the firehouse in response to a call cannot be
negative, so P 0 and F
0. Graph the regions satisfying all the availability and staffing
requirements, using the horizontal axis for P and the vertical axis for F. If 6 police cars are on active
duty and 4 fire trucks have left the firehouse in response to a call, are all of the requirements
satisfied?
142)
A)
B)
62
C)
D)
Solve by the method of your choice.
143)
x2+y2=13
–2x +y2=5
143)
A)
B)
C)
D)
Solve the problem.
144)
Steve invests in a circus production. The cost includes an overhead of $44,000, plus production
costs of $6000 per performance. A sold–out performance brings in $10,000. Determine the dollar
amount coming in and going out at the break–even point.
144)
A)
$110,000
B)
$66,000
C)
$27,500
D)
$11
145)
A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 4 hot dogs, 3 bags
of potato chips, and 2 soft drinks for $8.50. The price of a hot dog is $0.75 more than the price of a
bag of potato chips. The cost of a soft drink is $1.50 less than the price of two hot dogs. Find the cost
of each item.
145)
A)
$1.25 for a hot dog; $1.00 for a bag of potato chips; $0.50 for a soft drink
B)
$1.25 for a hot dog; $0.50 for a bag of potato chips; $1.00 for a soft drink
C)
$0.50 for a hot dog; $1.25 for a bag of potato chips; $1.00 for a soft drink
D)
$1.50 for a hot dog; $0.75 for a bag of potato chips; $1.00 for a soft drink
Graph the inequality.
146)
x + y < – 6
146)
A)
B)
64
C)
D)
Solve the problem.
147)
Find the values of a, b, and c such that the graph of the quadratic equation y = ax2+ bx + c passes
through the points (–3, –25), (2, 5), and (3, –1).
147)
A)
B)
C)
D)
Solve the system by the addition method.
148)
x – 4y = – 15
8x – 5y =42
148)
A)
{(8, 7)}
B)
{(9, 6)}
C)
{(–9, 7)}
D)
Solve the system of equations.
149)
x – y + 5z = – 3
4x + z =0
x + 3y + z =9
149)
A)
{(0, 3, 0)}
B)
{(3, 0, 0)}
C)
{(0, 0, 3)}
D)
{(0, 3, –3)}
65
Solve the system by the addition method.
150)
x2–y2=25
9x2+25y2=225
150)
A)
{(0, 3), (0, –3)}
B)
{(0, 5), (0, –5)}
C)
{(5, 0), (–5, 0)}
D)
{(3, 0), (–3, 0)}
Graph the inequality.
151)
y log(x + 5)
151)
A)
B)
C)
D)
66
Write the partial fraction decomposition of the rational expression.
152)
x –2
(x –5)(x –4)
152)
A)
2
x –5+
–3
x –4
B)
3
x –5+2
x –4
C)
3
x –5+
–2
x –4
D)
–2
x –5+3
x –4
D)
Solve the problem.
153)
A real estate investor is examining a triangular plot of land. She measures each angle of the field.
The sum of the first and second angles is 78° more than the measure of the third angle. If the
measure of the third angle is subtracted from the measure of the second angle, the result is twice
the measure of the first angle. Find the measure of each angle. (Note: The sum of the angles of a
triangle is 180°.)
153)
A)
First angle is 26°, second angle is 103°, third angle is 51°
B)
First angle is 30°, second angle is 105°, third angle is 45°
C)
First angle is 24°, second angle is 103°, third angle is 49°
D)
First angle is 32°, second angle is 99°, third angle is 49°
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
154)
3x + y <3
3x + y >1
154)
67
D)
A)
B)
C)
D)
D)
Write the partial fraction decomposition of the rational expression.
155)
–3x2– 13x – 12
(x + 2)(x + 1)2
155)
A)
B)
C)
D)
D)
Graph the inequality.
68
156)
x > – 9
156)
A)
B)
C)
D)
Solve the system by the addition method.
157)
y =x2+ 6
y = – x2+ 10
157)
A)
B)
C)
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
158)
–x +3y < – 15
x 2
158)
A)
B)
C)
D)
70
Graph the inequality.
159)
–3x – 4y 12
159)
A)
B)
C)
D)
Solve by the method of your choice.
160)
x2+y2=68
(x –5)2+y2=73
160)
A)
B)
C)
D)
Solve the system by the addition method.
161)
2x2+ y2= 66
x2+ y2= 41
161)
A)
B)
C)
D)
Solve the system by the substitution method.
162)
x – y =5
(x – 2)2+(y + 5)2= 20
162)
A)
B)
C)
D)
Determine if the given ordered triple is a solution of the system.
163)
(2, 5, 3)
x – y + z =0
x + y + z =10
x + y – z =4
163)
A)
B)
164)
(5, –2, –5)
4x + 5y + z = – 25
2x – 3y – z = – 9
5x + y + 4z = – 7
164)
A)
B)
Solve the system by the substitution method.
165)
15x – y =55
y =x2+ 1
165)
A)
B)
C)
D)
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.
166)
Objective Function z =15x + 14y
Constraints 0
x
10
0
y
5
3x + 2y 6
166)
A)
B)
C)
D)
73
Solve the problem.
167)
In the town of Milton Lake, the percentage of women who smoke is increasing while the percentage
of men who smoke is decreasing.
Let x represent the number of years since 1990 and y represent the percentage of women in Milton
Lake who smoke. The graph of y against x includes the data points (0, 17.5) and (14, 21.56). Let x
represent the number of years since 1990 and y represent the percentage of men in Milton Lake
who smoke. The graph of y against x includes the data points (0, 29.7) and (13, 27.1).
Determine when the percentage of women who smoke will be the same as the percentage of men
who smoke. Round to the nearest year. What percentage of women and what percentage of men (to
the nearest whole percent) will smoke at that time?
[Hint: first find the slope–intercept equation of the line that models the percentage, y, of women
who smoke x years after 1990 and the slope–intercept equation of the line that models the
percentage, y, of men who smoke x years after 1990]
167)
A)
2013; 25%
B)
2017; 24%
C)
2015; 25%
D)
2019; 24%
168)
You invested $18,000 and started a business selling vases. Supplies cost $16 per vase and you are
selling each vase for $34. Determine the number of vases, x, that must be produced and sold to
break even.
168)
A)
347 units
B)
1001 units
C)
1002 units
D)
1000 units
D)
Graph the inequality.
169)
y >2x
169)
74
D)
A)
B)
C)
D)
170)
x2+y2>1
170)
A)
B)
75
C)
D)
Solve the problem.
171)
An office manager is buying used filing cabinets. Each small file cabinet costs $4, takes up 7 square
feet of floor space, and holds 9 cubic feet of files. Each large file cabinet costs $9, takes up 10 square
feet of floor space, and holds 15 cubic feet of files. The total cost cannot exceed $94, and the office
has no more than 130 square feet of floor space available for the cabinets. How many of each file
cabinet should the manager buy to maximize storage capacity? What is the maximum storage
capacity?
171)
A)
16 small file cabinets and 0 large file cabinets; 144 cubic feet
B)
0 small file cabinets and 16 large file cabinets; 240 cubic feet
C)
6 small file cabinets and 10 large file cabinets; 240 cubic feet
D)
10 small file cabinets and 6 large file cabinets; 180 cubic feet
D
Solve the system by the addition method.
172)
2x + 20y = – 144
11x + 5y =48
172)
A)
{(–8, 8)}
B)
{(11, –11)}
C)
{(–5, 8)}
D)
{(8, –8)}
D
76
C
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
173)
7x – 5
x2+ 9x + 18
173)
A)
B)
C)
D)
Solve the system by the addition method.
174)
5x2– 4y2= – 99
2x2+ 2y2=90
174)
A)
B)
C)
D)
Solve the system of equations.
175)
x + y + z =1
x – y + 5z = – 21
2x +2y +2z =3
175)
A)
{(–4, 3, 2)}
B)
{(2, 3, –4)}
C)
{(–4, 2, 3)}
D)
Solve the problem.
176)
Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 6 hours to
make a hat and 4 hours to make an afghan, and she has no more than 52 hours available. She has
material for no more than 11 items and no more than 8 afghans. The bazaar will sell the hats for $13
each and the afghans for $7 each. How many of each should she make to maximize the income for
the bazaar? What is the maximum income?
176)
A)
B)
C)
D)
Write the partial fraction decomposition of the rational expression.
177)
2x3+4x2
(x2+ 5)2
177)
A)
B)
C)
D)
Solve the system by the substitution method.
178)
9x2+6y2=24
y = x +2
178)
A)
B)
C)
D)
Solve the system of equations by the substitution method.
179)
2y =x + 32
2x + 4y=0
179)
A)
{(–16, –8)}
B)
{(–16, 8)}
C)
{(16, 7)}
D)
{(8, –16)}
Solve the problem.
180)
Find the dimensions of a rectangle whose perimeter is 32 feet and whose area is 63 square feet.
180)
A)
6 feet by 8 feet
B)
7 feet by 9 feet
C)
6 feet by 10 feet
D)
8 feet by 8 feet