AnswersMO-Algebra II AMixed Degree Systems

Mixed Degree Systems Answers

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Which graph shows a system of equations with no solutions?

A
On a coordinate plane, the graphs of 2 circles are shown. Both circles have a center at (0, 0). The smaller circle is within the larger circle and the smaller circle has a radius that is 2 units smaller than the larger circle.
Option A
B
On a coordinate plane, a graph of a line and a parabola are shown. The line is horizontal to the x-axis at y = negative 5. The parabola opens up and its vertex on the line.
Option B
C
On a coordinate plane, the graphs of 2 circles are shown. Both circles are in quadrant 1, and they intersect each other.
Option C
D
On a coordinate plane, the graphs of 2 parabolas are shown. Both parabolas open up and they intersect each other at (0, 0). The first parabola has a vertex in quadrant 3 and the second parabola has a vertex in quadrant 4.
Option D
2
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How many solutions exist for the mixed-degree system graphed below?

Question illustration
A
zero
B
one
C
two
D
three
3

Pablo graphs a system of equations. One equation is quadratic and the other equation is linear. What is the greatest number of possible solutions to this system?

A
0
B
1
C
2
D
4
4

What are the solutions to the following system?

Question illustration
A
(0, 2)
B
(1, –2)
C
and
Option C
D
and
Option D
5

Which graph shows a system of equations with exactly one solution?

A
On a coordinate plane, a graph shows a smaller circle within a larger circle in quadrants 2 and 3. The larger circle is in both quadrants, but the smaller circle is in the middle of the larger circle in quadrant 2.
Option A
B
On a coordinate plane, the graph of a circle and a parabola are shown. The circle is in quadrant 3. The parabola has a vertex in quadrant 1 and goes through the circle in quadrant 3.
Option B
C
On a coordinate plane, the graph of a circle and a straight line are shown. The circle is in quadrant 1. The line has a negative slope and starts in quadrant 2, crosses the y-axis at (0, 3), and crossed the x-axis at (3, 0). The line does not go through the circle.
Option C
D
On a coordinate plane, the graphs of 2 parabolas are shown. One parabola opens down and the other opens up. They share the same vertex in quadrant 2.
Option D
6

The vertex of a parabola is in the first quadrant of a coordinate grid. A line with a negative slope passes through the origin. If the parabola and line intersect at the origin, which statement must be true?

A
The parabola opens downward.
B
The parabola opens upward.
C
The slope of the line is equal to –1.
D
The slope of the line is not equal to –1.
7

Consider the following system of equations.Which statement describes why the system has two solutions?

Question illustration
A
Each graph has one y-intercept, which is a solution.
B
Each graph has one vertex, which is a solution.
C
The graphs of the equations intersect the x-axis at two places.
D
The graphs of the equations intersect each other at two places.
8

How many solutions exist for the system of equations in the graph?

Question illustration
A
one
B
two
C
three
D
four
9

What are the solutions of the following system?

Question illustration
A
and
Option A
B
and
Option B
C
(6, 312) and (–6, 312)
D
(6, 312) and (–6, –264)
10

What are the solutions of the following system?

Question illustration
A
(0, –5) and (–5, 5)
B
(0, –5) and (5, –15)
C
(0, –5) and (–4, 3)
D
(0, –5) and (4, –13)

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