Solve the problem.
136)
The three points (x1, y1), (x2, y2), and (x3, y3) are collinear if
x1y11
x2y21
x3y31
= 0. Are the points (–1, –3),
(0, 10), and (–3, –27) collinear?
136)
A)
Yes
B)
No
Solve the system using matrices.
137)
x+y+z=0
x–y+3z =8
2x +y+z=2
137)
A)
no solution or
B)
{(1, –3, 2)}
C)
infinitely many solutions; dependent equations
D)
{(2, –3, 1)}
Solve the system by the substitution method or the addition method. Identify a system with no solution or infinitely
many solutions, using set notation to express the solution set.
138)
x = – 9y +9
3x –7y = – 7
138)
A)
no solution or
B)
{(x, y) x = – 9y +9}
C)
{(1, 0)}
D)
{(0, 1)}
Solve the system using matrices. If there is no solution or if there are infinitely many solutions and a system’s equations
are dependent, so state.
139)
3x +6y =30
3x +2y =46
139)
A)
infinitely many solutions; dependent equations
B)
no solution or
C)
{(18, –4)}
D)
{(–18, 3)}
Evaluate the determinant.
140)
–4–2 3
2 0 –5
1 0 –1
140)
A)
14
B)
–6
C)
–14
D)
6
Solve the problem.
141)
A company is planning to produce and sell a new video game console. The fixed cost will be
$240,000 and it will cost $150 to produce each console. Each video game console will be sold for
$300. Write the revenue function, R, from the sale of x video game consoles.
141)
A)
R(x) =240,000 +150x
B)
R(x) =150x
C)
R(x) =240,000 –300x
D)
R(x) =300x
Solve the system by the substitution method.
142)
4x +y=16
12x+3y =48
142)
A)
{(0, 16)}
B)
C)
{(5, –4)}
D)
{(x, y) 4x + y =16}
Solve the system by any method.
143)
0.3x – 0.7y = – 1.8
0.6x + 0.5y =2.1
143)
A)
(1.7, 3.3)
B)
(1, 2)
C)
(1.7, 2)
D)
(1, 3)
Solve the problem.
144)
A college student earned $5300 during summer vacation working as a waiter in a popular
restaurant. The student invested part of the money at 10% and the rest at 7%. If the student
received a total of $440 in interest at the end of the year, how much was invested at 10%?
144)
A)
$2300
B)
$3000
C)
$757
D)
$2650
Determine whether the given ordered pair is a solution to the system.
145)
(5, –2)
2x +y=8
4x + 2y=16
145)
A)
solution
B)
not a solution
Perform the matrix row operation and write the new matrix.
146)
4–8–20
4 1 –3
1
4R1
146)
A)
1 –2–5
4 1 –3
B)
1 –2–5
5–1–8
C)
1 –2–5
11
4–3
4
D)
1 –2–20
4 1 –3
Use Cramer’s rule to solve the system or to determine that the system is inconsistent or contains dependent equations.
147)
6x +y=32
6x +y=44
147)
A)
{(24, 8)}
B)
{(20, 26)}
C)
inconsistent; no solution or
D)
dependent equations; infinitely many solutions
Solve the problem.
148)
Given the cost function, C(x), and the revenue function, R(x), write the profit function from
producing and selling x units of the product.
C(x) =4000x +99,000
R(x) =13,000x
148)
A)
P(x) = – 9000x –99,000
B)
P(x) =9000x –99,000
C)
P(x) = – 9000x +99,000
D)
P(x) =9000x +99,000
Solve the system by graphing.
149)
3x + y =17
3x + y =26
149)
A)
B)
{(x, y) 3x + y =17}
C)
{(9, 8)}
D)
{(6, 14)}
Solve the problem.
150)
A twin–engined aircraft can fly 1360 miles from city A to city B in 5 hours with the wind and make
the return trip in 8 hours against the wind. What is the speed of the wind?
150)
A)
85 mph
B)
68 mph
C)
34 mph
D)
51 mph
Solve the system by the substitution method.
151)
x+y= – 7
x–y=17
151)
A)
B)
{(5, –12)}
C)
{(5, 12)}
D)
{(x, y) x + y = – 7}
Solve the system. If there is no solution or if the system’s equations are dependent, so state.
152)
x+y+z=7
x–y–3z =21
3x +3y +3z =15
152)
A)
no solution or
B)
{(5, –2, 4)}
C)
infinitely many solutions; dependent equations
D)
{(5, 4, –2)}
Determine if the given ordered triple is a solution of the system.
153)
(1, –1, 2)
5x + 3y + z =8
2x – 4y – z =7
3x + y + 5z =10
153)
A)
solution
B)
not a solution
154)
(2, –3, 4)
x – y + z =9
x + y + z =3
x + y – z = – 5
154)
A)
solution
B)
not a solution
Solve the problem.
155)
A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 5 bags of potato
chips for $10.00. Another customer buys 4 hot dogs and 4 bags of potato chips for $14.00. Find the
cost of each item.
155)
A)
$1.00 for a hot dog; $2.50 for a bag of potato chips
B)
$2.50 for a hot dog; $1.00 for a bag of potato chips
C)
$2.50 for a hot dog; $1.25 for a bag of potato chips
D)
$2.75 for a hot dog; $1.25 for a bag of potato chips
156)
A retired couple has $120,000 to invest to obtain annual income. They want some of it invested in
safe Certificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 10% per
year. How much should they invest in each to realize exactly $10,400 per year?
156)
A)
$80,000 at 10% and $40,000 at 6%
B)
$90,000 at 10% and $30,000 at 6%
C)
$70,000 at 6% and $50,000 at 10%
D)
$80,000 at 6% and $40,000 at 10%
157)
A bank teller has 53 $20 and $10 bills in her cash drawer. The value of the bills is $710. How many
$20 bills are there?
157)
A)
35 $20 bills
B)
18 $20 bills
C)
33 $20 bills
D)
20 $20 bills
Use Cramer’s rule to solve the linear system.
158)
4x +2y –z=37
x–2y +4z =2
3x +y+z=29
158)
A)
{(6, 8, 3)}
B)
{(6, –8, –3)}
C)
{(8, 3, 8)}
D)
{(7, 6, 3)}
Solve the system by graphing.
159)
3x –2y =4
–6x +4y =7
159)
A)
{(1, 2)}
B)
{(2, 1)}
C)
D)
{(x, y) 3x – 2y = 4}
Solve the problem.
160)
Julie and Eric row their boat (at a constant speed) 32 miles downstream for 4 hours, helped by the
current. Rowing at the same rate, the trip back against the current takes 8 hours. Find the rate of the
current.
160)
A)
3 mph
B)
2 mph
C)
1.5 mph
D)
6 mph
Solve by eliminating variables using the addition method.
161)
x + y + z = – 8
x – y +2z = – 10
4x + y + z = – 17
161)
A)
no solution or
B)
infinitely many solutions; dependent equations
C)
{(–3, –1, –4)}
D)
{(–4, –1, –3)}
Solve the system. If there is no solution or if the system’s equations are dependent, so state.
162)
x–y+4z = – 3
5x +z=0
x+4y +z=12
162)
A)
{(0, 3, 0)}
B)
infinitely many solutions; dependent equations
C)
no solution or
D)
{(0, 0, 3)}
Solve the problem.
163)
The equation of a line passing through two distinct points (x1, y1) and (x2, y2) is given by
x y 1
x1y11
x2y21
= 0. Use the determinant to write an equation for the line passing through (6, –4) and
(9, –7). Express the line’s equation in standard form.
163)
A)
3x + 3y – 6 = 0
B)
–3x – 3y – 6 = 0
C)
–7x + 6y – 36 = 0
D)
–4x + 9y – 42 = 0
164)
A couple have bought a new house and are comparing quotes from two moving companies for
moving their furniture. Company A charges $80 for the truck and $45 per hour for the movers.
Company B charges $70 for the truck and $65 per hour for the movers. Create a cost equation for
each company where y is the total cost and x is the number of hours of labor. Write a system of
equations.
164)
A)
y =80x +45
y =70x +65
B)
y =45x +80
y =65x +70
C)
45y =80x
65y =70x
D)
45y = x +80
65y = x +70
Solve the system by the substitution method.
165)
5x –2y = – 1
x+4y =35
165)
A)
{(3, 9)}
B)
C)
{(x, y) x + 4y = 35}
D)
{(3, 8)}
Solve the problem.
166)
Ron attends a party. He wants to limit his food intake to 103 g protein, 93 g fat, and 135 g
carbohydrate. According to the health conscious hostess, the marinated mushroom caps have 3 g
protein, 5 g fat, and 9 g carbohydrate; the spicy meatballs have 14 g protein, 7 g fat, and 15 g
carbohydrate; and the deviled eggs have 13 g protein, 15 g fat, and 6 g carbohydrate. How many of
each snack can he eat to obtain his goal?
166)
A)
4 mushrooms; 2 meatballs; 7 eggs
B)
8 mushrooms; 5 meatballs; 3 eggs
C)
2 mushrooms; 7 meatballs; 4 eggs
D)
7 mushrooms; 4 meatballs; 2 eggs
Solve the system by the substitution method or the addition method. Identify a system with no solution or infinitely
many solutions, using set notation to express the solution set.
167)
y –5x =4
5y =25x +20
167)
A)
{(x, y) y – 5x =4}
B)
{(–1.5, –1)}
C)
no solution or
D)
{(1, 1)}
Perform the matrix row operation and write the new matrix.
168)
4–4 1 1
–5 0 3 –2
–1 5 –3–1
–5R1+R2
168)
A)
–25 20 –2–7
–5 0 3 –2
–1 5 –3–1
B)
4–4 1 1
–25 20 –2–7
–1 5 –3–1
C)
29 –4–14 11
–5 0 3 –2
–1 5 –3–1
D)
4–4 1 1
15 –20 8 3
–1 5 –3–1
48
Solve the problem.
169)
Given the cost function, C(x), and the revenue function, R(x), find the dollar amount coming in and
going out at the break–even point. Round to the nearest dollar if necessary.
C(x) =9000x +70,000
R(x) =16,000x
169)
A)
$10
B)
$44,800
C)
$90,000
D)
$160,000
Determine whether the system is inconsistent, dependent, or neither.
170)
4x + y – 4z = – 7
–x + 2y + 2z = – 3
–6x – 6y + 4z =20
170)
A)
inconsistent
B)
dependent
C)
neither
Solve the problem.
171)
One number is 3 less than a second number. Twice the second number is 32 more than 4 times the
first. Find the two numbers.
171)
A)
–14 and –11
B)
–12 and –9
C)
10 and 13
D)
–13 and –10
Use Cramer’s rule to solve the linear system.
172)
6x–6y –3z = – 3
3x +9y –6z =18
5x –5y +3z =3
172)
A)
{(3, 0, 1)}
B)
{(2, 1, 2)}
C)
{(2, –2, –1)}
D)
{(2, 2, 1)}
Solve the problem.
173)
Andrea is having her yard landscaped. She obtained an estimate from two landscaping companies.
Company A gave an estimate of $180 for materials and equipment rental plus $65 per hour for
labor. Company B gave an estimate of $240 for materials and equipment rental plus $50 per hour
for labor. Create a cost equation for each company where y is the total cost of the landscaping and x
is the number of hours of labor. Determine how many hours of labor will be required for the two
companies to cost the same.
173)
A)
8 hr
B)
3 hr
C)
7 hr
D)
4 hr
174)
Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must
be sold to break even.
C(x) =66x +1190
R(x) =83x
174)
A)
72 units
B)
12 units
C)
70 units
D)
71 units
Solve the system by the addition method.
175)
4x +y=15
16x+4y =60
175)
A)
{(5, –5)}
B)
C)
{(0, 15)}
D)
{(x, y) 4x + y =15}
Solve the problem.
176)
Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in.
The length of the garden is 11 feet more than 6 times the width. He needs 92 feet of fencing to do
the job. Find the length and width of the garden.
176)
A)
length: 35 ft; width: 4 ft
B)
length: 47 ft; width: 6 ft
C)
length: 80 3
7 ft; width: 11 4
7 ft
D)
length: 41 ft; width: 5 ft
Evaluate the determinant.
177)
124
205
124
177)
A)
52
B)
1
C)
0
D)
–20
Solve the system by graphing.
178)
3x +2y =42
4x +3y =59
178)
A)
{(x, y) 3x + 2y =42}
B)
C)
{(9, 8)}
D)
{(8, 9)}
Use matrices to determine whether the system is inconsistent, dependent, or neither.
179)
x + y + z =1
x – y + 2z =4
5x +5y + 5z = – 19
179)
A)
neither
B)
dependent
C)
inconsistent
Use Cramer’s rule to solve the linear system.
180)
4x –3y +4z =44
3y –3z = – 33
2x +3z =35
180)
A)
{(8, 2, 7)}
B)
{(4, 7, 4)}
C)
{(7, 4, 7)}
D)
{(7, –4, –7)}
Determine whether the system has exactly one ordered–pair solution, no solution, or infinitely many solutions.
181)
2x – 3y = – 8
2x – 3y =1
181)
A)
no solution
B)
one ordered–pair solution
C)
infinitely many solutions
Solve the system. If there is no solution or if the system’s equations are dependent, so state.
182)
3x –4y +4z =9
–15x+20y–20z= – 45
15x–20y+20z=45
182)
A)
no solution or
B)
{(–1, –4, –7)}
C)
infinitely many solutions; dependent equations
D)
{(–1, –7, –4)}
Determine if the given ordered triple is a solution of the system.
183)
(2, –5, 0)
x – y + 3z =11
2x + z =2
x + 3y + z = – 13
183)
A)
not a solution
B)
solution
Solve the problem.
184)
A store sells tents, sleeping bags, and camp stools. A customer buys a tent, 3 sleeping bags, and 3
camp stools for $174. The price of the tent is 9 times the cost of a camp stool. The cost of a sleeping
bag is $23 more than the cost of a camp stool. Find the cost of each item.
184)
A)
$63 for a tent; $30 for a sleeping bag; $7 for a camp stool
B)
$63 for a tent; $30 for a sleeping bag; $8 for a camp stool
C)
$72 for a tent; $30 for a sleeping bag; $8 for a camp stool
D)
$63 for a tent; $35 for a sleeping bag; $12 for a camp stool
185)
The Little Town Fine Arts Center charges $25 per adult and $13 per senior citizen for its
performances. On a recent weekend evening when 486 people paid admission, the total receipts
were $7746. How many who paid were senior citizens?
185)
A)
119 senior citizens
B)
367 senior citizens
C)
277 senior citizens
D)
209 senior citizens
186)
A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter Festival.
A serving bowl takes 3 hours to prepare, 2 hours to paint, and 10 hours to fire. A platter takes 16
hours to prepare, 3 hours to paint, and 4 hours to fire. A bread basket takes 4 hours to prepare, 16
hours to paint, and 7 hours to fire. If the workshop has 125 hours for prep time, 64 hours for
painting, and 108 hours for firing, how many of each can be made?
186)
A)
2 serving bowls, 7 platters, 6 bread baskets
B)
8 serving bowls, 7 platters, 3 bread baskets
C)
6 serving bowls, 2 platters, 7 bread baskets
D)
7 serving bowls, 6 platters, 2 bread baskets
Solve the system by any method.
187)
8x – 8y =8
24x – 24y =40
187)
A)
3
2, –3
2
B)
C)
(8, 40)
D)
{(x, y) 8x – 8y =8}
Solve the system using matrices. If there is no solution or if there are infinitely many solutions and a system’s equations
are dependent, so state.
188)
x–y+3z = – 4
2x +z=0
–x+y–3z =20
188)
A)
{(0, 0, 4)}
B)
no solution or
C)
infinitely many solutions; dependent equations
D)
{(3, 4, 0)}
B
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.
189)
More than how many binoculars must be produced and sold for the company to have a profit gain?
189)
A)
2700 binoculars
B)
750 binoculars
C)
2250 binoculars
D)
1500 binoculars
B
B
Answer Key
Testname: C3
55
Answer Key
Testname: C3
Answer Key
Testname: C3
Answer Key
Testname: C3