AnswersTX-Algebra II A-CRMixed Degree Systems

Mixed Degree Systems Answers

10 verified answers
1
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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
2
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How many solutions exist for the system of equations in the graph?

Question illustration
A
one
B
two
C
three
D
four
3

Which equation is part of solving the system by substitution?

Question illustration
A
4(y + 11)2 – 3y2 = 8
B
4(11 – y)2 – 3y2 = 8
C
4(y – 11)2 – 3y2 = 8
D
4(–11y)2 – 3y2 = 8
4

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
5

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
6

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.
7

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
8

What are the solutions to the following system?

Question illustration
A
(0, 2)
B
(1, –2)
C
and
Option C
D
and
Option D
9

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)
10

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.

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