AnswersMO-Algebra II AMixed Degree Systems

Mixed Degree Systems Answers

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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)
2
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Consider the following system of equations.Which statement describes why the system has infinite solutions?

Question illustration
A
The equations represent parabolas that result in graphs that do not intersect.
B
The equations represent circles that result in graphs that do not intersect.
C
The equations represent parabolas that result in the same graph.
D
The equations represent circles that result in the same graph.
3

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.
4

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
5

The center of a circle is at the origin on a coordinate grid. The vertex of a parabola that opens upward is at (0, 9). If the circle intersects the parabola at the parabola’s vertex, which statement must be true?

A
The maximum number of solutions is one.
B
The maximum number of solutions is three.
C
The circle has a radius equal to 3.
D
The circle has a radius less than 9.
6

How many solutions exist for the mixed-degree system graphed below?

Question illustration
A
zero
B
one
C
two
D
three
7

What are the solutions to the following system?

Question illustration
A
(0, 2)
B
(1, –2)
C
and
Option C
D
and
Option D
8

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
9

Which system is equivalent to ?

Question illustration
A
StartLayout Enlarged left-brace 1st row y = negative 2 y squared minus 2 2nd row x = y minus 2 EndLayout
Option A
B
StartLayout Enlarged left-brace 1st row y = negative 2 y squared + 2 2nd row x = y + 2 EndLayout
Option B
C
StartLayout Enlarged left-brace 1st row y = negative 2 y squared minus 8 y minus 8 2nd row x = y + 2 EndLayout
Option C
D
StartLayout Enlarged left-brace 1st row y = negative 2 y squared + 8 y minus 8 2nd row x = y minus 2 EndLayout
Option D
10

Parabola A can be represented using the equation (x + 3)2 = y, while line B can be represented using the equation y = mx + 9. Isabel claims one solution to the system of two equations must always be the vertex of parabola A. Which best describes the reasonableness of her claim?

A
Isabel is correct because the y-intercept of line B is (0, 9) and the value of y when x = 0 in parabola A is 9.
B
Isabel is correct because the y-intercept of line B is (9, 0) and the value of x when y = 0 in parabola A is 9.
C
Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.
D
Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the x-intercept of the equations, not the vertex.

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