AnswersAlgebra 2Systems of Inequalities

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1
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Which graph represents the solution of y is less than or equal to x squared minus 1 and x is greater than y squared minus 3 ?

A
Image with description On a coordinate plane, a parabola opens to the right and goes through (6, 3), has vertex (negative 3, 0), and goes through (6, negative 3). Another parabola opens down and goes through (2, negative 5), has vertex (0, negative 1), and goes through (2, negative 5). Everything inside of the first parabola and outside of the second parabola is shaded.
B
Image with description On a coordinate plane, a parabola opens to the right and goes through (6, 3), has vertex (negative 3, 0), and goes through (6, negative 3). Another parabola opens up and goes through (negative 2, 3), has vertex (0, negative 1), and goes through (2, 3). Everything inside of the first parabola and outside of the second parabola is shaded.
C
Image with description On a coordinate plane, a parabola opens to the right and goes through (6, 3), has vertex (negative 3, 0), and goes through (6, negative 3). Another parabola opens down and goes through (2, negative 5), has vertex (0, negative 1), and goes through (2, negative 5). Everything inside of the first parabola and second parabola is shaded.
D
Image with description On a coordinate plane, a parabola opens to the right and goes through (6, 3), has vertex (negative 3, 0), and goes through (6, negative 3). Another parabola opens up and goes through (negative 2, 3), has vertex (0, negative 1), and goes through (2, 3). Everything inside of the first parabola and second parabola is shaded.
2
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The sum of the squares of two different numbers is less than or equal to 49 Twice one of the numbers squared is less than the other number. Which system of inequalities represents these criteria?

A
x squared plus y squared is greater than or equal to 49 and x squared is less than 2 y
B
x squared plus y squared is less than or equal to 49 and x squared is less than 2 y
C
x squared plus y squared is greater than or equal to 49 and 2 x squared is less than y
D
x squared plus y squared is less than or equal to 49 and 2 x squared is less than y
3

Which graph represents the solution to the system of inequalities? x squared minus 4 y squared is less than 16; y is less than 2 to the x-th power

A
Image with description On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 2), (negative 4, 0), and (0, 2). Everything above the curve and inside of the ellipse is shaded.
B
Image with description On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). An ellipse has center (0, 0) and goes through (4, 0), (0, negative 2), (negative 4, 0), and (0, 2). Everything below the curve and inside of the ellipse is shaded.
C
Image with description On a coordinate plane, a curve approaches the x-axis in quadrant 2 and then increases up through (0, 1) and (2, 4). A parabola opens to the right and goes through (9, 4), has vertex (4, 0), and goes through (9, negative 4). Another parabola opens to the left and goes through (negative 9, 4), has vertex (negative 4, 0), and goes through (negative 9, negative 4). Everything outside of the parabola and above the curve is shaded.
D
Image with description A left-opening dashed parabola has a vertex at left-parenthesis 0 comma negative 4 right-parenthesis and passes through left-parenthesis negative 6 comma 2 right-parenthesis and left-parenthesis negative 6 comma negative 2 right-parenthesis. A right-opening dashed parabola has a vertex at left-parenthesis 0 comma 4 right-parenthesis and passes through left-parenthesis 6 comma 2 right-parenthesis and left-parenthesis 6 comma negative 2 right-parenthesis. A dashed curve extends along the horizontal axis from left-parenthesis negative 10 comma 0 right-parenthesis to left-parenthesis negative 2 comma 0 right-parenthesis and then rises through left-parenthesis 0 comma 1 right-parenthesis and left-parenthesis negative 2 comma 2 right-parenthesis. The region outside the parabolas and below the curve is shaded one color. The region outside the parabolas and above the curve is shaded a second color. The region inside the parabolas and below the curve is shaded a third color.
4

Which graph represents the solution of x squared plus y squared is less than 25 and y squared is less than 6 x ?

A
Image with description On a coordinate plane, a circle has center (0, 0) and radius 5. A parabola open right and goes through (6, 6), has vertex (0, 0) and goes through (6, negative 6). Everything inside of the circle and inside of the parabola is shaded.
B
Image with description On a coordinate plane, a circle has center (0, 0) and radius 5. A parabola open right and goes through (6, 6), has vertex (0, 0) and goes through (6, negative 6). Everything outside of the circle and inside of the parabola is shaded.
C
Image with description On a coordinate plane, a circle has center (0, 0) and radius 5. A parabola open right and goes through (6, 6), has vertex (0, 0) and goes through (6, negative 6). Everything inside of the circle and outside of the parabola is shaded.
D
Image with description On a coordinate plane, a circle has center (0, 0) and radius 5. A parabola open right and goes through (6, 6), has vertex (0, 0) and goes through (6, negative 6). Everything outside of the circle and outside of the parabola is shaded.
5

Three times the square of a number is greater than a second number. The square of the second number increased by 6 is greater than the first number. Which system of inequalities represents these criteria?

A
1 third x squared is greater than y and y squared plus 6 is less than x
B
3 x squared is greater than y and y squared plus 6 is less than x
C
3 x squared is greater than y and y squared plus 6 is greater than x
D
1 third x squared is greater than y and y squared plus 6 is greater than x
6

Which point is a solution to the system of inequalities? y is greater than or equal to one half x squared plus 4; y is less than the square root of x plus 2 plus 6

A
open paren 2 comma 8 close paren
B
open paren negative 2 comma 6 close paren
C
open paren 0 comma 4 close paren
D
open paren 1 comma 9 close paren
7

Which graph represents the solution of the fraction with numerator open paren y plus 2 close paren squared and denominator 4 plus the fraction with numerator open paren x minus 3 close paren squared and denominator 9 is less than 1 and y is less than or equal to square root of x minus 1 end root minus 4 ?

A
Image with description On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 1), (5.5, negative 2), (3, negative 5), and (0.5, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and below the curve is shaded.
B
Image with description On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 0), (6, negative 2), (3, negative 4), and (0, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and above the curve is shaded.
C
Image with description On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 1), (5.5, negative 2), (3, negative 5), and (0.5, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and above the curve is shaded.
D
Image with description On a coordinate plane, an ellipse has center (3, negative 2) and goes through (3, 0), (6, negative 2), (3, negative 4), and (0, negative 2). A curve starts at (1, negative 4) and goes up through (2, negative 3) and (11, negative 1). Everything inside of the ellipse and below the curve is shaded.
8

Which graph shows the solution to the system of inequalities? y is greater than or equal to x squared plus 3; y is greater than or equal to 3 times the absolute value of x minus 3 plus 1

A
Image with description On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 3), and goes through (2, 7). An absolute value function opens up goes through (0, 10), has point (3, 1), and goes through (6, 10). Everything inside of the parabola and outside of the absolute value function is shaded.
B
Image with description On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 3), and goes through (2, 7). An absolute value function opens up goes through (0, 10), has point (3, 1), and goes through (6, 10). Everything inside of the parabola and inside the absolute value function is shaded.
C
Image with description On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 3), and goes through (2, 7). An absolute value function opens up goes through (0, 10), has point (3, 1), and goes through (6, 10). Everything outside of the absolute value function and parabola is shaded.
D
Image with description On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 3), and goes through (2, 7). An absolute value function opens up goes through (0, 10), has point (3, 1), and goes through (6, 10). Everything outside of the parabola and inside of the absolute value function is shaded.
9

One half the square of a number is less than a second number. The sum of 3 and the opposite of the second number is greater than the square of the first number. Which graph represents the solution set?

A
Image with description On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything inside the first parabola and inside the second parabola is shaded.
B
Image with description On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything inside of the first parabola and outside of the second parabola is shaded.
C
Image with description On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything outside of both parabolas is shaded.
D
Image with description On a coordinate plane, a parabola opens up and goes through (negative 4, 8), has vertex (0, 0), and goes through (4, 8). Another parabola goes through (negative 3, negative 7), has vertex (0, 3), and goes through (3, negative 7). Everything outside of the first parabola and inside the second parabola is shaded.
10

Which graph represents the solution of x squared plus 9 y squared is less than or equal to 81 and y squared plus 2 is less than x ?

A
Image with description On a coordinate plane, an ellipse has center (0, 0) and goes through (9, 0), (0, negative 3), (negative 9, 0) and (0, 3). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and inside of the parabola is shaded.
B
Image with description On a coordinate plane, an ellipse has center (0, 0) and goes through (3, 0), (0, negative 9), (negative 3, 0), and (0, 9). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and outside of the parabola is shaded.
C
Image with description On a coordinate plane, an ellipse has center (0, 0) and goes through (3, 0), (0, negative 9), (negative 3, 0), and (0, 9). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and inside of the parabola is shaded.
D
Image with description On a coordinate plane, an ellipse has center (0, 0) and goes through (9, 0), (0, negative 3), (negative 9, 0) and (0, 3). A parabola opens to the right and goes through (6, 2), has vertex (2, 0), and goes through (6, negative 2). Everything inside of the ellipse and outside of the parabola is shaded.

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