AnswersMO-Algebra II AMixed Degree Systems

Mixed Degree Systems — Unit test Answers

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Galena is solving the following system.Step 1: She multiplies equation (3) by 3 and adds it to equation (1). Step 2: She multiplies equation (3) by –7 and adds it to equation (2). Which statement explains Galena’s mistake?

Question illustration
A
She added equation (1) instead of equation (2) in step 1.
B
She did not multiply equation (3) in step 1 by the correct value.
C
She did not multiply equation (3) in step 2 by the correct value.
D
She added equation (2) instead of equation (1) in step 2.
2
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Given that (3, 2, –6) and (–2, 5, 1) are solutions of two equations in a system of three linear equations, which of the following is true about the system?

A
The system can only be consistent and independent.
B
The system can be either inconsistent and independent or consistent and dependent.
C
The system can be either inconsistent and dependent or consistent and independent.
D
The system can only be inconsistent and dependent.
3

A pair of weak earthquakes is modeled by a system of inequalities. One earthquake occurred roughly 20 km east and 14 km north of the center of Columbia, NC. The quake could be felt from 25 km away. A couple days later, another earthquake occurred 8 km west and 3 km north of the center of Columbia and could be felt from 14 km away. If Columbia is located at (0, 0) on a coordinate grid, the system of inequalities represents this scenario.

Question illustration
A
4 km west and 12 km south
B
6 km west and 4 km north
C
2 km east and 10 km north
D
6 km east and 8 km north
4

Which classification describes the following system of equations?

Question illustration
A
inconsistent and dependent
B
consistent and dependent
C
consistent and independent
D
inconsistent and independent
5

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
mc022-2.jpg
Option A
B
mc022-3.jpg
Option B
C
(0, 2)
D
(2, 0)
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

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)
8

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
9

Which graph represents the solution to the system of inequalities?

Question illustration
A
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 8), (negative 4, 0), and (0, 8). Everything inside of the ellipse and below the curve is shaded.
Option A
B
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 8), (negative 4, 0), and (0, 8). Everything inside of the ellipse and above the curve is shaded.
Option B
C
On a coordinate plane, a curve approaches the x-axis in quadrant 2 and increase through (0, 1) and (2, 9). An ellipse has center (0, 0) and goes through (8, 0), (0, negative 4), (negative 8, 0) and (0, 4). Everything inside of the ellipse and below the curve is shaded.
Option C
D
Option
Option D
10

Which classification describes the following system of equations?

Question illustration
A
inconsistent and dependent
B
consistent and dependent
C
consistent and independent
D
inconsistent and independent
11

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
12

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
13

What is one solution of the following system?

Question illustration
A
(–6, 0)
B
(–2, 4)
C
(0, –6)
D
(4, –2)
14

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

Question illustration
A
mc026-2.jpg
Option A
B
mc026-3.jpg
Option B
C
mc026-4.jpg
Option C
D
mc026-5.jpg
Option D
15

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)

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