AnswersAlgebra IIMixed Degree Systems

Mixed Degree Systems — Quiz Answers

10 verified answers1 views
1
Free Preview

Consider the following system of equations. y is equal to 6 x squared plus 1 y is equal to x squared plus 4 Which statement describes why the system has two solutions?

A
Each graph has one y -intercept, which is a solution.
B
The graphs of the equations intersect the x -axis at two places.
C
The graphs of the equations intersect each other at two places.
D
Each graph has one vertex, which is a solution.
2
Free Preview

Parabola cap A can be represented using the equation open paren x plus 3 close paren squared is equal to y , while line cap b can be represented using the equation y is equal to m x plus 9 Isabel claims one solution to the system of two equations must always be the vertex of parabola cap A Which best describes the reasonableness of her claim?

A
Isabel is incorrect because the point of intersection between line cap b and parabola cap A that can be determined is the y -intercept of the equations, not the vertex.
B
Isabel is correct because the y -intercept of line cap b is open paren 9 comma 0 close paren and the value of x when y is equal to 0 in parabola cap A is 9 .
C
Isabel is incorrect because the point of intersection between line cap b and parabola cap A that can be determined is the x -intercept of the equations, not the vertex.
D
Isabel is correct because the y -intercept of line cap b is (0, 9) and the value of y when x is equal to 0 in parabola cap A is 9 .
3

A system of equations is shown. {y^2+x^2=20y=−x^2 Plot the real solutions to the system of equations. Plot each point on the coordinate grid.

Answer:

point; -2; -4; 2

4

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

A
The circle has a radius less than 9 .
B
The maximum number of solutions is three.
C
The maximum number of solutions is one.
D
The circle has a radius equal to 3 .
5

Consider the following system of equations. negative 10 x squared minus 10 y squared is equal to negative 300 5 x squared plus 5 y squared is equal to 150 Which statement describes why the system has infinite solutions?

A
The equations represent parabolas that result in the same graph.
B
The equations represent parabolas that result in graphs that do not intersect.
C
The equations represent circles that result in graphs that do not intersect.
D
The equations represent circles that result in the same graph.
6

What are the solutions to the following system? negative 2 x squared plus y is equal to negative 5 y is equal to negative 3 x squared plus 5

A
open paren 1 comma negative 2 close paren
B
open paren square root of 5 comma negative 10 close paren and open paren negative square root of 5 comma negative 10 close paren
C
open paren square root of 2 comma negative 1 close paren and open paren negative square root of 2 comma negative 1 close paren
D
open paren 0 comma 2 close paren
7

What are the solutions of the following system? 10 x squared minus y is equal to 48 2 y is equal to 16 x squared plus 48

A
open paren 6 comma 312 close paren and open paren negative 6 comma negative 264 close paren
B
open paren 2 square root of 3 comma 120 close paren and open paren negative 2 square root of 3 comma negative 72 close paren
C
open paren 2 square root of 3 comma 120 close paren and open paren negative 2 square root of 3 comma 120 close paren
D
open paren 6 comma 312 close paren and open paren negative 6 comma 312 close paren
8

Which graph shows the following system? x squared plus y is equal to 2 x squared plus y squared is equal to 9

A
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 6 to 6 with an interval of 1 unit. The circle has a center at (0 comma 3) and a radius of 3 units. The parabola opens up and has a vertex at (0 comma 2), and it passes through (negative 1 comma 3), and (1 comma 3).
B
Image with description On a coordinate plane, the scale on the x and y axis ranges from negative 6 to 6 with an interval of 1 unit. The circle has a center at (0 comma 3) and a radius of 3 units. The parabola opens down and has a vertex at (0 comma 2), and it passes through (negative 1 comma 1), and (1 comma 1).
C
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 6 to 6 with an interval of 1 unit. The circle has a center at the origin and a radius of 3 units. The parabola opens down and has a vertex at (0 comma 2), and it passes through points (negative 1 comma 1), and (1 comma 1).
D
Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 6 to 6 with an interval of 1 unit. The circle has a center at the origin and a radius of 3 units. The parabola opens up and has a vertex at (0 comma negative 2), and it passes through (1 comma negative 1), and (negative 1 comma negative 1).
9

Tom determines that the system of equations has two solutions, one of which is located at the vertex of the parabola. Equation 1: open paren x minus 3 close paren squared is equal to y minus 4 Equation 2: y is equal to negative x plus b In order for Tom’s thinking to be correct, which qualifications must be met?

A
b must equal 7 and a second solution to the system must be located at the point open paren 1 comma 8 close paren .
B
b must equal 1 and a second solution to the system must be located at the point open paren 4 comma 5 close paren .
C
b must equal 1 and a second solution to the system must be located at the point open paren 3 comma 4 close paren .
D
b must equal 7 and a second solution to the system must be located at the point open paren 2 comma 5 close paren .
10

During a pumpkin launching contest, two pumpkins are launched at the same time. The path of pumpkin A is modeled by the equation y is equal to negative 0 point 0 1 x squared plus 0 point 3 2 x plus 4 The path of pumpkin B is modeled by the equation y is equal to negative 0 point 0 1 x squared plus 0 point 1 8 x plus 5 If x represents the distance the pumpkin traveled in feet and y represents height of the pumpkin in feet, what does the intersection point of the equations represent?

A
the height at which the pumpkins reach their greatest horizontal distance from the launch site
B
the horizontal distance of the pumpkins from the launch site when their heights are the same
C
the horizontal distance of the pumpkins from the launch site when they reach the ground
D
the starting height of the pumpkins when they are at the launch site

Did you find these answers helpful?

More from this Course

Quiz
10 verified answers

Quiz

Quiz
10 verified answers

Quiz

Quiz
10 verified answers

Quiz

Mixed Degree Systems — Quiz Answers — Algebra II