AnswersDHS Algebra 2 VLinear Programming

Linear Programming — Unit test Answers

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Mr. Lee asks a student to solve the following system of linear equations.Which ordered pair (p, q) is the solution to the system?

Question illustration
A
Option
Option A
B
Option
Option B
C
(0, 2)
D
(2, 0)
2
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The constraints of a problem are listed below. What are the vertices of the feasible region?

Question illustration
A
(0, 0), (0, 3), (2, 3), (5, 0)
B
(0, 0), (0, 5), (2, 3), (5, 0)
C
(0, 0), (2, 3), (5, 0)
D
(0, 3), (0, 5), (2, 3)
3

Which statement about the following system of inequalities is true?

Question illustration
A
The solution contains points in one quadrant of the coordinate plane.
B
The solution contains points in two quadrants of the coordinate plane.
C
The solution contains points in three quadrants of the coordinate plane.
D
The solution contains points in all four quadrants of the coordinate plane.
4

The constraints of a problem are listed below. What are the vertices of the feasible region?

Question illustration
A
(0, 0), (0, 2.5), (1.5, 2), (3, 0)
B
(0, 0), (0, 4), (1.5, 2), (7.5, 0)
C
(0, 2.5), (1.5, 2), (4, 3)
D
(0, 4), (1.5, 2), (7.5, 0)
5

Consider the solution to the system of inequalities below.Which of the following functions could be added to the system without changing the solution set?

Question illustration
A
y = –2
B
y < –2
C
y < –3
D
y > –3
6

Which system of equations is consistent and dependent?

A
mc014-1.jpg
Option A
B
mc014-2.jpg
Option B
C
mc014-3.jpg
Option C
D
mc014-4.jpg
Option D
7

Brandi is downloading music for her MP3 player. Albums cost $10 each, and singles cost $1 each. She wants to purchase at least 5 singles but wants to spend no more than $25 total. If Brandi purchases x albums and y singles, which of the following is a possible combination of albums and singles that Brandi could purchase and stay within her guidelines?

Question illustration
A
5 albums and 2 singles
B
2 albums and 5 singles
C
2 albums and 10 singles
D
10 albums and 2 singles
8

What is the point of intersection when the system of equations below is graphed on the coordinate plane?

Question illustration
A
(1, –3)
B
(–1, 3)
C
(1, 3)
D
(–1, –3)
9

What is the value of w in the solution to the following system of linear equations?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

Evan washes two types of vehicles. It takes him 30 minutes to wash a car and 40 minutes to wash a truck. He charges $12 to wash a car and $15 to wash a truck. In 270 minutes, Evan made $105 washing cars and trucks. How many trucks did Evan wash?

A
2 trucks
B
3 trucks
C
4 trucks
D
5 trucks
11

Solve the system of equations below by graphing. What are the approximate solutions rounded to the nearest tenth?

Question illustration
A
(–6.2, –4) and (5, 0.6)
B
(–4, –6.2) and (0.6, 5)
C
(–2.4, 2.4) and (3.7, –12.8)
D
(2.4, –2.4) and (–12.8, 3.7)
12

Solve the system of equations below by graphing. What is the solution rounded to the nearest hundredth?

Question illustration
A
(–2.25, –1.5)
B
(–1.5, –2.25)
C
(–0.82, –0.68)
D
(–0.68, –0.82)
13

Which ordered pair (r, s) is the solution to the given system of equations?

Question illustration
A
(1, 8)
B
(3, 8)
C
(1, –2)
D
(8, 3)
14

A school district needs to arrange transportation for at least 360 students for a field trip. The district can use large buses or small buses. The large buses hold 60 students each and have an operating expense of $300 for the day. The small buses hold 45 students each and have an operating expense of $200 for the day. The district only has chaperones for, at most, seven buses. What is the minimum cost for the transportation for the field trip if each bus has chaperones?

A
$1,400
B
$1,600
C
$1,700
D
$1,800
15

What is the value of y in the solution to the following system of linear equations?

Question illustration
A
3
B
5
C
8
D
12
16

Raj tried to solve the system below. Raj’s Work What error did Raj make?

Question illustration
A
Raj forgot to multiply the value of x by 9 when solving for the value of y.
B
Raj subtracted 120 from both sides when he solved for the value of x.
C
Raj forgot the negative sign when substituting –15 + 9x for y.
D
Raj found the value of –y instead of y.
17

The equations –a – 7b = 14 and –4a – 14b = 28 represent a system of linear equations. Which statement correctly explains how to eliminate the variable b when solving the system of equations?

A
Multiply the first equation by –2 and add it to the second equation. Then solve the resulting equation, –2a = 0.
B
Multiply the first equation by 2 and add it to the second equation. Then solve the resulting equation, –2a = 0.
C
Divide the second equation by –4 and add it to the first equation.
D
Divide the second equation by 4 and add it to the first equation.
18

Which statement describes the system of equations?

Question illustration
A
The system has infinitely many solutions.
B
The system has no solution.
C
The system has one solution .
Option C
D
The system has one solution .
Option D
19

A cell phone carrier offers two plans for text messaging. Plan A costs $20 per month plus $0.05 per text. Plan B costs $10 per month plus $0.10 per text. For how many text messages per month are the plans the same cost?

A
20
B
30
C
200
D
300

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