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.
181)
The sum of two numbers is –14 and their product is –32. Find the numbers.
181)
A)
2 and 16; –2 and –16
B)
–2 and 16
C)
2 and –16
D)
2 and –16; –2 and 16
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.
182)
Objective Function z =6x + 6y
Constraints x 0
0 y 5
2x + 3y 12
2x + 3y 20
182)
A)
Maximum: –24; at (4, 0)
B)
Maximum: 60; at (10, 0)
C)
Maximum: 36; at (6, 0)
D)
Maximum: 42; at (2, 5)
Solve the system by the substitution method.
183)
xy =42
x2+y2=85
183)
A)
{(–6, –7), (–7, –6), (–6, 7), (–7, 6)}
B)
{(6, 7), (–6, –7), (6, –7), (–6, 7)}
C)
{(6, 7), (–6, –7), (7, 6), (–7, –6)}
D)
{(6, 7), (7, 6), (6, –7), (7, –6)}
Write the partial fraction decomposition of the rational expression.
184)
8x –32
(x – 1)(x –9)
184)
A)
3
x – 1 +5
x –9
B)
2
x – 1 +6
x –9
C)
7
x – 1 +1
x –9
D)
3
x – 1 +
–5
x –9
The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.
185)
At the break–even point both cost and revenue are what?
185)
A)
$2700
B)
$2250
C)
$750
D)
$1500
Solve the problem.
186)
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.]
186)
A)
x = – 2, y =0, z = – 4
B)
x = – 3, y = – 1, z = – 2
C)
x = – 5, y =1, z = – 2
D)
x = – 2, y = – 1, z = – 3
187)
An–Mei owns a business making and selling jackets. She has a fixed cost of $720. It costs $66 to
produce each jacket. The selling price is $78 per jacket. Let x represent the number of jackets
produced and sold and write the cost function, C, and revenue function, R.
187)
A)
C(x) =66x +720x
R(x) =78x
B)
C(x) =66x +720
R(x) =78x
C)
C(x) =66 +78x
R(x) =720x
D)
C(x) =66 +720x
R(x) =78
The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.
188)
Is there a profit when 395 binoculars are produced?
188)
A)
Yes
B)
No
Solve the problem.
189)
A steel company produces two types of machine dies, part A and part B. The company makes a
$3.00 profit on each part A that it produces and a $6.00 profit on each part B that it produces. Let
x = the number of part A produced in a week and y = the number of part B produced in a week.
Write the objective function that describes the total weekly profit.
189)
A)
z =6x +3y
B)
z =3(x –6) +6(y –3)
C)
z =3x +6y
D)
z =9(x + y)
Solve the system by the addition method.
190)
2x + 5y =2
–7x – 3y =22
190)
A)
{(–4, –2)}
B)
{(4, 2)}
C)
{(4, –2)}
D)
{(–4, 2)}
81
Write the partial fraction decomposition of the rational expression.
191)
15x – 40
x2– 5x + 6
191)
A)
6
x – 3 +9
x – 2
B)
5
x – 3 +10
x – 2
C)
5
x + 3 +10
x + 2
D)
5
x – 3 +
–10
x – 2
Graph the solution set of the system of inequalities or indicate that the system has no solution.
192)
x2+ y264
x + y > 1
192)
A)
B)
82
C)
D)
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
193)
3x + 5
(x – 3)(x + 1)
193)
A)
A
x – 3 +B
x + 1 +C
(x – 3)(x + 1)
B)
A
x – 3 +B
x + 1 +C
(x – 3)2(x + 1)2
C)
A
x – 3 +B
x + 1
D)
A
x – 3 +B
x + 1 +Cx + D
(x – 3)(x + 1)
Solve the system of equations by the substitution method.
194)
5x –3y =49 –5x
3x +7y = x +6y +5
194)
A)
49
10 , 0
B)
{(0, 49)}
C)
{(4, 3)}
D)
{(4, –3)}
Find the maximum or minimum value of the given objective function of a linear programming problem. The figure
illustrates the graph of feasible points.
195)
Objective Function: z = – x – 8y
Find maximum.
195)
A)
maximum: –34
B)
maximum: –27
C)
maximum: –20
D)
maximum: –42
Write the partial fraction decomposition of the rational expression.
196)
11x2– x –20
x3– x
196)
A)
20
x+
–4
x + 1 +5
x – 1
B)
20
x+
–5
x + 1 +4
x – 1
C)
20
x+4
x + 1 +
–5
x – 1
D)
20
x+
–4
x + 1 +
–5
x – 1
Solve by the method of your choice.
197)
x3+ y = 0
10x2– y = 0
197)
A)
{(0, 0), (10, –1000)}
B)
{(–1, 1), (–10, 1000)}
C)
{(0, 0), (–10, 100)}
D)
{(0, 0), (–10, 1000)}
84
Write the partial fraction decomposition of the rational expression.
198)
–28x + 4
(x – 3)2(x2+ 1)
198)
A)
2
x – 3 +
–8
(x – 3)2+
–2x + 2
x2+ 1
B)
2
x – 3 +
–8
(x – 3)2+
–2
x2+ 1
C)
–6x – 2
(x – 3)2+
–2x + 2
x2+ 1
D)
2
x – 3 +
–6
(x – 3)2+
–2x – 2
x2+ 1
Solve the system by the addition method.
199)
5x +32y =32
7x –4y = – 4
199)
A)
{(1, 0)}
B)
{(0, 1)}
C)
{(0, 0)}
D)
{(1, 1)}
Graph the solution set of the system of inequalities or indicate that the system has no solution.
200)
y < x + 1
6x +6y >18
200)
A)
B)
85
C)
D)
Solve the system of equations.
201)
x –y + 3z =5
3x + z =2
x + 3y +z =5
201)
A)
{(2, 1, 0)}
B)
{(1, 0, 2)}
C)
{(0, 1, 2)}
D)
{(2, 0, 1)}
Graph the inequality.
202)
y <1
4x
202)
86
A)
B)
C)
D)
Solve the system of equations by the substitution method.
203)
y=5x – 4
2y + 6x= – 24
203)
A)
{(–1, –9)}
B)
{(1, –9)}
C)
{(–9, –1)}
D)
Explanation:
Decide if the system of equations in two variables is linear or nonlinear.
204)
xy = – 8
x +9y =3
204)
A)
Nonlinear
B)
Linear
Explanation:
Explanation:
Solve the problem.
205)
A candy company has 130 pounds of cashews and 170 pounds of peanuts which they combine into
two different mixes. The deluxe mix has half cashews and half peanuts and sells for $7 per pound.
The economy mix has one third cashews and two thirds peanuts and sells for $5.40 per pound.
How many pounds of each mix should be prepared for maximum revenue?
205)
A)
90 pounds of deluxe and 40 pounds of economy
B)
270 pounds of deluxe and 80 pounds of economy
C)
180 pounds of deluxe and 120 pounds of economy
D)
130 pounds of deluxe and 0 pounds of economy
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.
206)
y = – 4x + 9
20x + 5y =45
206)
A)
B)
{(0, 9)}
C)
{(x, y) | 4x + y =9}
D)
{(0, 0)}
Solve the problem.
207)
A volunteer wants to crochet beach hats and baby afghans for a church fund–raising bazaar. She
needs 4 hours to make a hat and 7 hours to make an afghan and she has 28 hours available. Write
an inequality that describes the situation and use the inequality to decide whether she can make 9
hats and 9 afghans in the time allowed. Let x represent the number of hats and y the number of
afghans that she makes.
207)
A)
4x +7y 28; yes
B)
4x +7y 28; no
C)
4x +7y 28; yes
D)
4x +7y 28; no
208)
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?
208)
A)
municipal bond: $1750
certificate of deposit: $3500
money market: $6750
B)
municipal bond: $2000
certificate of deposit: $4000
money market: $6000
C)
municipal bond: $1500
certificate of deposit: $3000
money market: $7500
D)
municipal bond: $2500
certificate of deposit: $5000
money market: $4500
Graph the inequality.
209)
y >x2+ 3
209)
A)
B)
89
C)
D)
90
Answer Key
Testname: C5
Answer Key
Testname: C5
Answer Key
Testname: C5
93
Answer Key
Testname: C5
Answer Key
Testname: C5