C)
D)
Solve the system of equations.
137)
x – y + z = – 7
x + y + z =1
x + y – z =9
137)
A)
B)
C)
{(1, –4, 4)}
D)
Write the partial fraction decomposition of the rational expression.
138)
2x2– x –19
x(x + 1)(x – 1)
138)
A)
19
x+
–9
x + 1 +8
x – 1
B)
19
x+
–8
x + 1 +9
x – 1
C)
19
x+
–8
x + 1 +
–9
x – 1
D)
19
x+8
x + 1 +
–9
x – 1
Solve the system by the addition method.
139)
x2+y2=81
x2–y2=81
139)
A)
B)
C)
{(0, 9)}
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
140)
(x + 5)2+(y + 2)2>16
(x + 5)2+(y + 2)2< 36
140)
A)
B)
C)
D)
Solve the system by the substitution method.
141)
x2+y2= 13
x – y = 1
141)
A)
B)
C)
{(–2, 3), (–3, 2)}
D)
Write the partial fraction decomposition of the rational expression.
142)
11x2+ 21x + 40
(x + 4)(x2+ 6)
142)
A)
6
x + 4 +5x + 1
x2+ 6
B)
6
x + 4 +5x – 1
x2+ 6
C)
6
x + 4 +5
x + 6 +1
(x + 6)2
D)
6
x + 4 +5
x2+ 6
Graph the solution set of the system of inequalities or indicate that the system has no solution.
143)
y < – x +8
y >7x – 3
143)
63
A)
B)
C)
D)
Graph the inequality.
144)
x > – 9
144)
64
A)
B)
C)
D)
Solve the problem.
145)
A bank teller has 46 $10 and $20 bills in her cash drawer. The value of the bills is $820. How many $
10 bills are there?
145)
A)
B)
C)
12 $10 bills
D)
Write the partial fraction decomposition of the rational expression.
146)
13x + 2
(x – 1)(x2+ x + 1)
146)
A)
5
x – 1 +
–5x +3
x2+ x + 1
B)
–5
x – 1 +5x +3
x2+ x + 1
C)
5
x – 1 +3x – 5
x2+ x + 1
D)
5
x – 1 +
–5
x + 1 +3
x – 1
147)
27 –5x
x(x –3)2
147)
A)
–3
x+3
x –3+4
(x –3)2
B)
3
x+
–3
x –3+4
(x –3)2
C)
3
x+
–3
x –3+8
(x –3)2
D)
3
x+4
x –3+
–3
(x –3)2
Solve the problem.
148)
Benjamin never has more than 20 hours free during the week. He is trying to make a weekly plan
for dividing his free time between reading and working out. He wants to spend at least 8 hours per
week reading. Write a system of inequalities to describe the situation. Let x represent the number of
hours for reading and y represent the number of hours for working out.
148)
A)
B)
C)
x + y 20
x 8y
x 0
y 0
D)
Write the partial fraction decomposition of the rational expression.
149)
12x + 3
x3– 1
149)
A)
5
x – 1 +
–5
x + 1 +2
x – 1
B)
5
x – 1 +
–5x +2
x2+ x + 1
C)
–5
x – 1 +5x +2
x2+ x + 1
D)
5
x – 1 +2x – 5
x2+ x + 1
Solve the system by the addition method.
150)
2x + 7y =12
2x + 2y =22
150)
A)
B)
C)
{(–2, 13)}
D)
Solve the problem.
151)
A basketball player scored 22 points in a game. The number of three–point field goals the player
made was 12 less than three times the number of free throws (each worth 1 point). Twice the
number of two–point field goals the player made was 5 more than the number of three–point field
goals made. Find the number of free–throws, two–point field goals, and three–point field goals that
the player made in the game.
151)
A)
5 free throws; 3 two–point field goals; 4 three–point field goals
B)
6 free throws; 4 two–point field goals; 6 three–point field goals
C)
5 free throws; 5 two–point field goals; 5 three–point field goals
D)
5 free throws; 4 two–point field goals; 3 three–point field goals
152)
Ms. Adams received a bonus check for $12,000. She decided to divide the money among three
different investments. With some of the money, she purchased a municipal bond paying 5.5%
simple interest. She invested twice the amount she paid for the municipal bond in a certificate of
deposit paying 4.3% simple interest. Ms. Adams placed the balance of the money in a money
market account paying 3.3% simple interest. If Ms. Adams’ total interest for one year was $480, how
much was placed in each account?
152)
A)
municipal bond: $1750
certificate of deposit: $3500
money market: $6750
B)
municipal bond: $1500
certificate of deposit: $3000
money market: $7500
C)
municipal bond: $2500
certificate of deposit: $5000
money market: $4500
D)
municipal bond: $2000
certificate of deposit: $4000
money market: $6000
Write the partial fraction decomposition of the rational expression.
153)
x
(x –3)(x –4)
153)
A)
B)
C)
–3
x –3+4
x –4
D)
Solve the system by the addition method.
154)
x2– 3y2= 1
2x2+ 3y2=11
154)
A)
{(1, 2), (–1, –2)}
B)
{(2, 1), (–2, –1)}
C)
{(1, 2), (–1, 2), (1, –2), (–1, –2)}
D)
{(2, 1), (–2, 1), (2, –1), (–2, –1)}
Solve the problem.
155)
As the price of a product increases, the demand for that product decreases. However, at higher
prices, suppliers are willing to produce greater quantities of the product. The weekly supply and
demand models for a certain type of television are as follows:
Demand: N = – 4p +780
Supply: N =2.6p
where p is the price in dollars per television.
Find the price at which supply and demand are equal. At this price, how many televisions can be
supplied and sold each week?
155)
A)
B)
C)
$557.14; 1449
D)
Solve the system by the addition method.
156)
x2– 3y2– 1 = 0
4x2+ 3y2– 19 = 0
156)
A)
{(1, 2), (–1, 2), (1, –2), (–1, –2)}
B)
{(2, 1), (–2, –1)}
C)
{(2, 1), (2, –1), (–2, 1), (–2, –1)}
D)
{(–1, 2), (1, –2)}
Graph the inequality.
157)
y >x2+ 3
157)
A)
B)
69
C)
D)
Solve the problem.
158)
The Family Fine Arts Center charges $20 per adult and $10 per senior citizen for its performances.
On a recent weekend evening when 511 people paid admission, the total receipts were $7020. How
many who paid were senior citizens?
158)
A)
191 senior citizens
B)
230 senior citizens
C)
281 senior citizens
D)
320 senior citizens
Graph the inequality.
159)
y log(x + 5)
159)
70
A)
B)
C)
D)
Write the partial fraction decomposition of the rational expression.
160)
–28x + 4
(x – 3)2(x2+ 1)
160)
A)
2
x – 3 +
–8
(x – 3)2+
–2x + 2
x2+ 1
B)
–6x – 2
(x – 3)2+
–2x + 2
x2+ 1
C)
2
x – 3 +
–8
(x – 3)2+
–2
x2+ 1
D)
2
x – 3 +
–6
(x – 3)2+
–2x – 2
x2+ 1
Graph the solution set of the system of inequalities or indicate that the system has no solution.
71
161)
x2+ y281
y >3x
161)
A)
B)
C)
D)
72
Solve the system by the substitution method.
162)
2y – x =10
x2+y2–100 = 0
162)
A)
{(10, 0), (–10, 0), (6, 8)}
B)
{(–10, 0), (6, 8)}
C)
0, 5, 8, 9
D)
0, 5, 0, – 5 , 8, 9
Solve the problem.
163)
A rectangular lot whose perimeter is 440 feet is fenced along three sides. An expensive fencing
along the lot’s length costs $25 per foot , and an inexpensive fencing along the two side widths costs
only $10 per foot. The total cost of the fencing along the three sides comes to $5150. What are the
lot’s dimensions?
163)
A)
Length 143 ft; Width 77 ft
B)
Length 300 ft; Width 140 ft
C)
Length 158 ft; Width 62 ft
D)
Length 150 ft; Width 70 ft
Graph the inequality.
164)
y >2x
164)
A)
B)
73
C)
D)
Solve the problem.
165)
You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and
eventually strikes the ground. A mathematical model can be used to describe the relationship for
the ball’s height above the ground, y, after x seconds. Consider the following data:
x, seconds after
ball is thrown
y, ball’s height, in feet,
above the ground
1114
3166
590
Find the quadratic function y = ax2+bx + c whose graph passes through the given points.
165)
A)
y = – 16x2+ 80x + 50
B)
y = – 16x2+90x +40
C)
y = – 10x2+ 100x + 24
D)
y = – 12x2+90x + 36
Graph the solution set of the system of inequalities or indicate that the system has no solution.
74
166)
y 2x – 4
x + 2y
7
y –2
x 1
166)
A)
B)
C)
D)
75
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
167)
5y =42 –4x
2x =46 –5y
167)
A)
{(5, –10)}
B)
{(–2, 10)}
C)
{(x, y) 4x +5y =42 }
D)
Write the partial fraction decomposition of the rational expression.
168)
15x – 40
x2– 5x + 6
168)
A)
B)
C)
6
x – 3 +9
x – 2
D)
A
Solve the problem.
169)
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.
169)
A)
B)
C)
$110,000
D)
C
Determine whether the given ordered pair is a solution of the system.
170)
(1, –4)
x + y = – 3
x – y =5
170)
A)
solution
B)
not a solution
A
B
Solve the system by the addition method.
171)
4x + 6y = – 42
2x – 4y =0
171)
A)
B)
C)
{(–6, –3)}
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
172)
x2+y281
5x + 2y 10
172)
A)
B)
C)
D)
Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear
equations. Solve the system and find the numbers.
173)
The sum of two numbers is –14 and their product is –32. Find the numbers.
173)
A)
2 and –16; –2 and 16
B)
2 and –16
C)
2 and 16; –2 and –16
D)
–2 and 16
Solve the problem.
174)
The sum of three numbers is –6. If the second number is subtracted from the sum of the first and
third numbers, the result is –4. If the third number is subtracted from the sum of the first and
second numbers, the result is –2. Find the three numbers.
[Hint: let x represent the first number, y the second number, and z the third number. Use the given
conditions to write and solve a system of equations.]
174)
A)
x = – 5, y =1, z = – 2
B)
x = – 3, y = – 1, z = – 2
C)
x = – 2, y = – 1, z = – 3
D)
x = – 2, y =0, z = – 4
Solve the system by the substitution method.
175)
9x2+6y2=24
y = x +2
175)
A)
0, –2, 8
5, 18
5
B)
0, –2, –8
5, 2
5
C)
0, 2, 8
5, 18
5
D)
0, 2, –8
5, 2
5
78