Question 1

Determine whether the transverse axis of the hyperbola $$\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = - 1$$ is horizontal or vertical.

Accepted Answer

The answer of Determine whether the transverse axis of the...

Question 2

Graph the solution set. $$y > 4 ^ { x }$$

Accepted Answer

The answer of Graph the solution set. \[y > 4...

Question 3

Identify the center and radius of the circle. $$\left( x - \frac { 5 } { 7 } \right) ^ { 2 } + y ^ { 2 } = 8$$

Accepted Answer

A)  Center $= \left( \frac { 5 } { 7 } , 0 \right) ; r = 8$ 
B)  Center $= \left( 0 , \frac { 5 } { 7 } \right) ; r = 8$ 
C)  Center $= \left( - \frac { 5 } { 7 } , 0 \right) ; r = 2 \sqrt { 2 }$ 
D)  Center $= \left( \frac { 5 } { 7 } , 0 \right) ; r = 2 \sqrt { 2 }$ 
A)  Center $= \left( \frac { 5 } { 7 } , 0 \right) ; r = 8$ 
B)  Center $= \left( 0 , \frac { 5 } { 7 } \right) ; r = 8$ 
C)  Center $= \left( - \frac { 5 } { 7 } , 0 \right) ; r = 2 \sqrt { 2 }$ 
D)  Center $= \left( \frac { 5 } { 7 } , 0 \right) ; r = 2 \sqrt { 2 }$

Question 4

Find the midpoint of the line segment. (You can check your answer by plotting the midpoint on the graph).

Accepted Answer

A)  $\left( \frac { 3 } { 2 } , \frac { 7 } { 2 } \right)$ 
B)  $( 1,4 )$ 
C)  $\left( \frac { 4 } { 3 } , \frac { 1 } { 3 } \right)$ 
D)  $\left( \frac { 3 } { 2 } , \frac { 15 } { 4 } \right)$ 
A)  $\left( \frac { 3 } { 2 } , \frac { 7 } { 2 } \right)$ 
B)  $( 1,4 )$ 
C)  $\left( \frac { 4 } { 3 } , \frac { 1 } { 3 } \right)$ 
D)  $\left( \frac { 3 } { 2 } , \frac { 15 } { 4 } \right)$

Question 5

Identify the center and radius of the circle. $$( x + 8 ) ^ { 2 } + ( y - 9 ) ^ { 2 } = 121$$

Accepted Answer

A)  Center $= ( - 8,9 ) ; r = 11$ 
B)  Center $= ( 8,9 ) ; r = 11$ 
C)  Center $= ( 8 , - 9 ) ; r = 11$ 
D)  Center $= ( - 8,9 ) ; r = 121$ 
A)  Center $= ( - 8,9 ) ; r = 11$ 
B)  Center $= ( 8,9 ) ; r = 11$ 
C)  Center $= ( 8 , - 9 ) ; r = 11$ 
D)  Center $= ( - 8,9 ) ; r = 121$

Question 6

The cross sections of a certain satellite dish are parabolic in shape. A cross section through the vertex can be described by the equation $d ( x ) = \frac { 14 } { 25 } x ^ { 2 } - \frac { 14 } { 5 } x$ where d(x) is the depth of the dish (in feet) at a distance of x ft from the edge of the dish. How deep Is the satellite dish?

Accepted Answer

A)  The satellite dish is $6 \frac { 1 } { 4 } \mathrm { ft }$ deep. 
B)  The satellite dish is $5 \mathrm { ft }$ deep. 
C)  The satellite dish is $3 \frac { 1 } { 2 } \mathrm { ft }$ deep. 
D)  The satellite dish is $2 \frac { 4 } { 5 } \mathrm { ft }$ deep. 
A)  The satellite dish is $6 \frac { 1 } { 4 } \mathrm { ft }$ deep. 
B)  The satellite dish is $5 \mathrm { ft }$ deep. 
C)  The satellite dish is $3 \frac { 1 } { 2 } \mathrm { ft }$ deep. 
D)  The satellite dish is $2 \frac { 4 } { 5 } \mathrm { ft }$ deep.

Question 7

Graph the solution set. $$y \leq - x ^ { 2 }$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 8

Identify the center and radius of the circle and then graph the circle. $$\left( x - \frac { 7 } { 2 } \right) ^ { 2 } + y ^ { 2 } = 8$$

Accepted Answer

The answer of Identify the center and radius of the...

Question 9

Give the coordinates of the vertices for the following hyperbola.   [The fundamental rectangle and asymptotes are shown in dashed lines.]

Accepted Answer

A)  (6, 5), (6, -1), (-4, -1), and (-4, 5) 
B)  (1, 2) 
C)  (5, 1) and (-1, 1) 
D)  (1, 5) and (1, -1) 
A)  (6, 5), (6, -1), (-4, -1), and (-4, 5) 
B)  (1, 2) 
C)  (5, 1) and (-1, 1) 
D)  (1, 5) and (1, -1)

Question 10

Determine if the equation represents an ellipse or a hyperbola. $$\frac { ( x - 3 ) ^ { 2 } } { 4 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$$

Accepted Answer

A)  Hyperbola 
B)  Ellipse 
A)  Hyperbola 
B)  Ellipse

Question 11

Write an equation of a circle whose center is (20, 4) and that passes through the point (21, -5).

Accepted Answer

The answer of Write an equation of a circle whose...

Question 12

Solve the system by the substitution method. $$\begin{array} { l } 
y = - 2 x ^ { 2 } + 39 \
x = \sqrt { y }
\end{array}$$

Accepted Answer

A)  $\{ ( 13 , \sqrt { 13 } ) \}$ 
B)  $\{ ( \sqrt { 13 } , 13 ) \}$ 
C)  $\{ ( 0,0 ) ( \sqrt { 13 } , 13 ) \}$ 
D)  $\{ ( 0,1 ) , ( 0,13 ) \}$ 
A)  $\{ ( 13 , \sqrt { 13 } ) \}$ 
B)  $\{ ( \sqrt { 13 } , 13 ) \}$ 
C)  $\{ ( 0,0 ) ( \sqrt { 13 } , 13 ) \}$ 
D)  $\{ ( 0,1 ) , ( 0,13 ) \}$

Question 13

Graph the solution set to the system of nonlinear inequalities. $$\begin{array} { l } 
\frac { x ^ { 2 } } { 9 } - y ^ { 2 } \leq 1 \
x ^ { 2 } + y ^ { 2 } \leq 16
\end{array}$$

Accepted Answer

The answer of Graph the solution set to the system...

Question 14

Use the distance formula to find the distance between the two points. (-2, 18) and (4, 10)

Accepted Answer

A)  10 
B)  14 
C)  100 
D)  $\sqrt { 14 }$ 
A)  10 
B)  14 
C)  100 
D)  $\sqrt { 14 }$

Question 15

Sketch the system of equations. Then solve the system by the substitution method. $$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 100 \
7 y - x = 50
\end{array}$$

Accepted Answer

The answer of Sketch the system of equations. Then solve...

Question 16

Determine if the equation represents an ellipse or a hyperbola. $$\frac { ( x - 2 ) ^ { 2 } } { 64 } - \frac { ( y - 5 ) ^ { 2 } } { 100 } = 1$$

Accepted Answer

A)  Ellipse 
B)  Hyperbola 
A)  Ellipse 
B)  Hyperbola

Question 17

Use the equation in standard form to graph the hyperbola. $$\frac { ( y - 2 ) ^ { 2 } } { 9 } - ( x + 1 ) ^ { 2 } = 1$$

Accepted Answer

The answer of Use the equation in standard form to...

Question 18

Write an equation of a circle centered at (-2, -8) with a diameter of 2.

Accepted Answer

A)  $( x + 2 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 1$ 
B)  $( x + 2 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 4$ 
C)  $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 4$ 
D)  $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 1$ 
A)  $( x + 2 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 1$ 
B)  $( x + 2 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 4$ 
C)  $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 4$ 
D)  $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 1$

Question 19

A coordinate system is placed at the center of a house with the positive x-axis pointing east, and the positive y-axis pointing north. A pest-deterrent device that uses high-frequency sound waves is Placed in an electrical outlet 15 ft west and 8 ft south of the center of the house. If the device has a Range of 11 feet, write an inequality that represents the points on the coordinate system affected by The device.

Accepted Answer

A)  $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \geq 11$ 
B)  $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \leq 121$ 
C)  $( x + 15 ) ^ { 2 } + ( y + 8 ) ^ { 2 } \leq 121$ 
D)  $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \leq 11$ 
A)  $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \geq 11$ 
B)  $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \leq 121$ 
C)  $( x + 15 ) ^ { 2 } + ( y + 8 ) ^ { 2 } \leq 121$ 
D)  $( x - 15 ) ^ { 2 } + ( y - 8 ) ^ { 2 } \leq 11$

Question 20

Use the equation of the parabola in standard form y = a(x - h)2 + k to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. $$y = - x ^ { 2 } - 2 x + 2$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Determine whether the transverse axis of the hyperbola $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = - 1$ is horizontal or vertical.

Graph the solution set. $y > 4 ^ { x }$

Identify the center and radius of the circle. $\left( x - \frac { 5 } { 7 } \right) ^ { 2 } + y ^ { 2 } = 8$

Find the midpoint of the line segment. (You can check your answer by plotting the midpoint on the graph).

Identify the center and radius of the circle. $( x + 8 ) ^ { 2 } + ( y - 9 ) ^ { 2 } = 121$

Graph the solution set. $y \leq - x ^ { 2 }$

Identify the center and radius of the circle and then graph the circle. $\left( x - \frac { 7 } { 2 } \right) ^ { 2 } + y ^ { 2 } = 8$

Give the coordinates of the vertices for the following hyperbola. [The fundamental rectangle and asymptotes are shown in dashed lines.]

Determine if the equation represents an ellipse or a hyperbola. $\frac { ( x - 3 ) ^ { 2 } } { 4 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$

Write an equation of a circle whose center is (20, 4) and that passes through the point (21, -5).

Solve the system by the substitution method. y=-2+39 x=

Graph the solution set to the system of nonlinear inequalities. -\leq1 +\leq16

Use the distance formula to find the distance between the two points. (-2, 18) and (4, 10)

Sketch the system of equations. Then solve the system by the substitution method. +=100 7y-x=50 $Sketch the system of equations. Then solve the system by the substitution method. \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 100 \\ 7 y - x = 50 \end{array}$

Determine if the equation represents an ellipse or a hyperbola. $\frac { ( x - 2 ) ^ { 2 } } { 64 } - \frac { ( y - 5 ) ^ { 2 } } { 100 } = 1$

Use the equation in standard form to graph the hyperbola. $\frac { ( y - 2 ) ^ { 2 } } { 9 } - ( x + 1 ) ^ { 2 } = 1$

Write an equation of a circle centered at (-2, -8) with a diameter of 2.

Use the equation of the parabola in standard form y = a(x - h)2 + k to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. $y = - x ^ { 2 } - 2 x + 2$

Linear Equations and Inequalities in One Variable

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Exam 9: Conic Sections

Determine whether the transverse axis of the hyperbola x225−y264=−1\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = - 125x2​−64y2​=−1 is horizontal or vertical.

Graph the solution set. y>4xy > 4 ^ { x }y>4x

Identify the center and radius of the circle. (x−57)2+y2=8\left( x - \frac { 5 } { 7 } \right) ^ { 2 } + y ^ { 2 } = 8(x−75​)2+y2=8

Find the midpoint of the line segment. (You can check your answer by plotting the midpoint on the graph).

Identify the center and radius of the circle. (x+8)2+(y−9)2=121( x + 8 ) ^ { 2 } + ( y - 9 ) ^ { 2 } = 121(x+8)2+(y−9)2=121

Graph the solution set. y≤−x2y \leq - x ^ { 2 }y≤−x2

Identify the center and radius of the circle and then graph the circle. (x−72)2+y2=8\left( x - \frac { 7 } { 2 } \right) ^ { 2 } + y ^ { 2 } = 8(x−27​)2+y2=8

Give the coordinates of the vertices for the following hyperbola. [The fundamental rectangle and asymptotes are shown in dashed lines.]

Determine if the equation represents an ellipse or a hyperbola. (x−3)24+(y−1)216=1\frac { ( x - 3 ) ^ { 2 } } { 4 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 14(x−3)2​+16(y−1)2​=1

Write an equation of a circle whose center is (20, 4) and that passes through the point (21, -5).

Solve the system by the substitution method. y=-2+39 x=

Graph the solution set to the system of nonlinear inequalities. -\leq1 +\leq16

Use the distance formula to find the distance between the two points. (-2, 18) and (4, 10)

Sketch the system of equations. Then solve the system by the substitution method. +=100 7y-x=50

Determine if the equation represents an ellipse or a hyperbola. (x−2)264−(y−5)2100=1\frac { ( x - 2 ) ^ { 2 } } { 64 } - \frac { ( y - 5 ) ^ { 2 } } { 100 } = 164(x−2)2​−100(y−5)2​=1

Use the equation in standard form to graph the hyperbola. (y−2)29−(x+1)2=1\frac { ( y - 2 ) ^ { 2 } } { 9 } - ( x + 1 ) ^ { 2 } = 19(y−2)2​−(x+1)2=1

Write an equation of a circle centered at (-2, -8) with a diameter of 2.

Use the equation of the parabola in standard form y = a(x - h)2 + k to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. y=−x2−2x+2y = - x ^ { 2 } - 2 x + 2y=−x2−2x+2

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

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Radicals and Complex Numbers

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Exponential and Logarithmic Functions and Applications

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

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Determine whether the transverse axis of the hyperbola $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = - 1$ is horizontal or vertical.

Graph the solution set. $y > 4 ^ { x }$

Identify the center and radius of the circle. $\left( x - \frac { 5 } { 7 } \right) ^ { 2 } + y ^ { 2 } = 8$

Identify the center and radius of the circle. $( x + 8 ) ^ { 2 } + ( y - 9 ) ^ { 2 } = 121$

Graph the solution set. $y \leq - x ^ { 2 }$

Identify the center and radius of the circle and then graph the circle. $\left( x - \frac { 7 } { 2 } \right) ^ { 2 } + y ^ { 2 } = 8$

Determine if the equation represents an ellipse or a hyperbola. $\frac { ( x - 3 ) ^ { 2 } } { 4 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$

Sketch the system of equations. Then solve the system by the substitution method. +=100 7y-x=50 $Sketch the system of equations. Then solve the system by the substitution method. \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 100 \\ 7 y - x = 50 \end{array}$

Determine if the equation represents an ellipse or a hyperbola. $\frac { ( x - 2 ) ^ { 2 } } { 64 } - \frac { ( y - 5 ) ^ { 2 } } { 100 } = 1$

Use the equation in standard form to graph the hyperbola. $\frac { ( y - 2 ) ^ { 2 } } { 9 } - ( x + 1 ) ^ { 2 } = 1$

Use the equation of the parabola in standard form y = a(x - h)2 + k to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph The parabola. $y = - x ^ { 2 } - 2 x + 2$