Question 1

Graph the solution set. $$12 x + 6 y > 24$$

Accepted Answer

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

Question 2

Find the x- and y-intercepts of the ellipse $$\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 144 } = 1$$

Accepted Answer

The answer of Find the x- and y-intercepts of the...

Question 3

Solve the system by the addition method. $$\begin{array} { l } 
2 x ^ { 2 } + 2 y ^ { 2 } = 18 \
2 y - x = 12
\end{array}$$

Accepted Answer

A)  $\{ ( 9,6 ) , ( - 9 , - 6 ) \}$ 
B)  $\{ ( 0,0 ) \}$ 
C)  $\{ ( 18,6 ) , ( - 18,6 ) \}$ 
D)  { } 
A)  $\{ ( 9,6 ) , ( - 9 , - 6 ) \}$ 
B)  $\{ ( 0,0 ) \}$ 
C)  $\{ ( 18,6 ) , ( - 18,6 ) \}$ 
D)  { }

Question 4

Solve the system of nonlinear equations by the addition method. $$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 12 \
x ^ { 2 } - y ^ { 2 } = 2
\end{array}$$

Accepted Answer

The answer of Solve the system of nonlinear equations by...

Question 5

Write the distance formula.

Accepted Answer

The answer of Write the distance formula....

Question 6

Write an equation that represents the graph of the circle.

Accepted Answer

A)  $( x + 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 4$ 
B)  $( x + 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 16$ 
C)  $( x - 2 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 16$ 
D)  $( x - 2 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 4$ 
A)  $( x + 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 4$ 
B)  $( x + 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 16$ 
C)  $( x - 2 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 16$ 
D)  $( x - 2 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 4$

Question 7

How would the solution set for $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } \leq 1$ change for the strict inequality $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } < 1 ?$

Accepted Answer

A)  The ellipse $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ would be drawn as a dashed curve. 
B)  The ellipse $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ would be drawn as a solid curve. 
C)  The hyperbola $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ would be drawn as a solid curve. 
D)  The hyperbola $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ would be drawn as a dashed curve. 
A)  The ellipse $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ would be drawn as a dashed curve. 
B)  The ellipse $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ would be drawn as a solid curve. 
C)  The hyperbola $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ would be drawn as a solid curve. 
D)  The hyperbola $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ would be drawn as a dashed curve.

Question 8

Use the equation of the ellipse to identify the center (h, k). $$\frac { ( x + 2 ) ^ { 2 } } { 36 } + \frac { ( y + 4 ) ^ { 2 } } { 4 } = 1$$

Accepted Answer

The answer of Use the equation of the ellipse to...

Question 9

Graph the hyperbola centered at (h, k) by following these guidelines. First locate the center. Then draw the reference rectangle relative to the center (h, k). Using the reference rectangle as a guide, sketch the hyperbola. $$\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$$

Accepted Answer

The answer of Graph the hyperbola centered at (h, k)...

Question 10

Write an equation of a circle centered at $\left( - \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)$ with a radius of $3 \sqrt { 5 }$.

Accepted Answer

A)  $\left( x - \frac { 2 } { 3 } \right) ^ { 2 } + \left( y + \frac { 1 } { 3 } \right) ^ { 2 } = 45$ 
B)  $\left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \left( y - \frac { 1 } { 3 } \right) ^ { 2 } = 45$ 
C)  $\left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \left( y - \frac { 1 } { 3 } \right) ^ { 2 } = 3 \sqrt { 5 }$ 
D)  $\left( x - \frac { 1 } { 3 } \right) ^ { 2 } + \left( y + \frac { 2 } { 3 } \right) ^ { 2 } = 3 \sqrt { 5 }$ 
A)  $\left( x - \frac { 2 } { 3 } \right) ^ { 2 } + \left( y + \frac { 1 } { 3 } \right) ^ { 2 } = 45$ 
B)  $\left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \left( y - \frac { 1 } { 3 } \right) ^ { 2 } = 45$ 
C)  $\left( x + \frac { 2 } { 3 } \right) ^ { 2 } + \left( y - \frac { 1 } { 3 } \right) ^ { 2 } = 3 \sqrt { 5 }$ 
D)  $\left( x - \frac { 1 } { 3 } \right) ^ { 2 } + \left( y + \frac { 2 } { 3 } \right) ^ { 2 } = 3 \sqrt { 5 }$

Question 11

Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right. 
$y = ( x + 1 ) ^ { 2 } - 7$

Accepted Answer

A)  Vertical axis of symmetry; opens downward 
B)  Horizontal axis of symmetry;  opens right 
C)  Vertical axis of symmetry; opens upward 
D)  Horizontal axis of symmetry; opens left 
A)  Vertical axis of symmetry; opens downward 
B)  Horizontal axis of symmetry;  opens right 
C)  Vertical axis of symmetry; opens upward 
D)  Horizontal axis of symmetry; opens left

Question 12

Solve the system by the substitution method. $$\begin{array} { l } 
y = 7 x ^ { 2 } - 14 x \
y = 7 x
\end{array}$$

Accepted Answer

A)  $\{ ( 0,0 ) , ( 3,21 ) \}$ 
B)  $\{ ( 3,21 ) \}$ 
C)  $\{ ( 0,0 ) \}$ 
D)  {  } 
A)  $\{ ( 0,0 ) , ( 3,21 ) \}$ 
B)  $\{ ( 3,21 ) \}$ 
C)  $\{ ( 0,0 ) \}$ 
D)  {  }

Question 13

Solve the system of nonlinear equations by the addition method. $$\begin{array} { l } 
7 y = - x + 7 \
x ^ { 2 } + 49 y ^ { 2 } = 49
\end{array}$$

Accepted Answer

A) { } 
B)  $\{ ( 7,0 ) ( 0 , - 1 ) \}$ 
C)  $\{ ( - 7,0 ) ( 0 , - 1 ) \}$ 
D)  $\{ ( 7,0 ) ( 0,1 ) \}$ 
A) { } 
B)  $\{ ( 7,0 ) ( 0 , - 1 ) \}$ 
C)  $\{ ( - 7,0 ) ( 0 , - 1 ) \}$ 
D)  $\{ ( 7,0 ) ( 0,1 ) \}$

Question 14

Solve the system by the substitution method. $$\begin{array} { l } 
x + y ^ { 2 } = 12 \
y + x = 6
\end{array}$$

Accepted Answer

The answer of Solve the system by the substitution method....

Question 15

Find the x- and y-intercepts of the ellipse $$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$$ = 1 and graph the ellipse.

Accepted Answer

The answer of Find the x- and y-intercepts of the...

Question 16

Find the center of a circle if a diameter of the circle has endpoints (-5, -4) and (-11, -2).

Accepted Answer

A)  (-8, -3) 
B)  (3, -1) 
C)  (3, -3) 
D)  (-8, -1) 
A)  (-8, -3) 
B)  (3, -1) 
C)  (3, -3) 
D)  (-8, -1)

Question 17

Graph the solution set to the system of inequalities. $$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } \geq 25 \
x ^ { 2 } + y ^ { 2 } \geq 16
\end{array}$$

Accepted Answer

A) 
  
B) {  } 
C) 
  
D) 
  
A) 
  
B) {  } 
C) 
  
D)

Question 18

Find all values of k so that the distance from (-10, 6) to (-7, k) is 5 units.

Accepted Answer

The answer of Find all values of k so that...

Question 19

Solve the system of nonlinear equations by the addition method. $$9 x ^ { 2 } + 8 x y = 64$$
$$x ^ { 2 } - x y = 9$$

Accepted Answer

A)  $\left\{ \left( - \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) , \left( \sqrt { 8 } , - \frac { \sqrt { 8 } } { 8 } \right) \right\}$ 
B)  $\left\{ \left( - \sqrt { 8 } , - \frac { \sqrt { 8 } } { 8 } \right) , \left( \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) \right\}$ 
C)  $\left\{ \left( - \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) , \left( \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) \right\}$ 
D) { } 
A)  $\left\{ \left( - \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) , \left( \sqrt { 8 } , - \frac { \sqrt { 8 } } { 8 } \right) \right\}$ 
B)  $\left\{ \left( - \sqrt { 8 } , - \frac { \sqrt { 8 } } { 8 } \right) , \left( \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) \right\}$ 
C)  $\left\{ \left( - \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) , \left( \sqrt { 8 } , \frac { \sqrt { 8 } } { 8 } \right) \right\}$ 
D) { }

Question 20

Determine if the three points define the vertices of a right triangle. (-1, -2), (-5, 6), (7, 2)

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Graph the solution set. $12 x + 6 y > 24$

Find the x- and y-intercepts of the ellipse $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 144 } = 1$

Solve the system by the addition method. 2+2=18 2y-x=12

Solve the system of nonlinear equations by the addition method. +=12 -=2

Write the distance formula.

Write an equation that represents the graph of the circle.

How would the solution set for $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } \leq 1$ change for the strict inequality $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } < 1 ?$

Use the equation of the ellipse to identify the center (h, k). $\frac { ( x + 2 ) ^ { 2 } } { 36 } + \frac { ( y + 4 ) ^ { 2 } } { 4 } = 1$

Graph the hyperbola centered at (h, k) by following these guidelines. First locate the center. Then draw the reference rectangle relative to the center (h, k). Using the reference rectangle as a guide, sketch the hyperbola. $\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$

Write an equation of a circle centered at $\left( - \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)$ with a radius of $3 \sqrt { 5 }$ .

Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right. $y = ( x + 1 ) ^ { 2 } - 7$

Solve the system by the substitution method. y=7-14x y=7x

Solve the system of nonlinear equations by the addition method. 7y=-x+7 +49=49

Solve the system by the substitution method. x+=12 y+x=6

Find the x- and y-intercepts of the ellipse $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$ = 1 and graph the ellipse.

Find the center of a circle if a diameter of the circle has endpoints (-5, -4) and (-11, -2).

Graph the solution set to the system of inequalities. +\geq25 +\geq16

Find all values of k so that the distance from (-10, 6) to (-7, k) is 5 units.

Solve the system of nonlinear equations by the addition method. $9 x ^ { 2 } + 8 x y = 64$ $x ^ { 2 } - x y = 9$

Determine if the three points define the vertices of a right triangle. (-1, -2), (-5, 6), (7, 2)

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

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Exam 9: Conic Sections

Graph the solution set. 12x+6y>2412 x + 6 y > 2412x+6y>24

Find the x- and y-intercepts of the ellipse x281+y2144=1\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 144 } = 181x2​+144y2​=1

Solve the system by the addition method. 2+2=18 2y-x=12

Solve the system of nonlinear equations by the addition method. +=12 -=2

Write the distance formula.

Write an equation that represents the graph of the circle.

How would the solution set for x216−y29≤1\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } \leq 116x2​−9y2​≤1 change for the strict inequality x216−y29<1?\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } < 1 ?16x2​−9y2​<1?

Use the equation of the ellipse to identify the center (h, k). (x+2)236+(y+4)24=1\frac { ( x + 2 ) ^ { 2 } } { 36 } + \frac { ( y + 4 ) ^ { 2 } } { 4 } = 136(x+2)2​+4(y+4)2​=1

Write an equation of a circle centered at (−23,13)\left( - \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)(−32​,31​) with a radius of 353 \sqrt { 5 }35​ .

Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right. y=(x+1)2−7y = ( x + 1 ) ^ { 2 } - 7y=(x+1)2−7

Solve the system by the substitution method. y=7-14x y=7x

Solve the system of nonlinear equations by the addition method. 7y=-x+7 +49=49

Solve the system by the substitution method. x+=12 y+x=6

Find the x- and y-intercepts of the ellipse x225+y29=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 125x2​+9y2​=1 = 1 and graph the ellipse.

Find the center of a circle if a diameter of the circle has endpoints (-5, -4) and (-11, -2).

Graph the solution set to the system of inequalities. +\geq25 +\geq16

Find all values of k so that the distance from (-10, 6) to (-7, k) is 5 units.

Solve the system of nonlinear equations by the addition method. 9x2+8xy=649 x ^ { 2 } + 8 x y = 649x2+8xy=64 x2−xy=9x ^ { 2 } - x y = 9x2−xy=9

Determine if the three points define the vertices of a right triangle. (-1, -2), (-5, 6), (7, 2)

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Graph the solution set. $12 x + 6 y > 24$

Find the x- and y-intercepts of the ellipse $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 144 } = 1$

How would the solution set for $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } \leq 1$ change for the strict inequality $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } < 1 ?$

Use the equation of the ellipse to identify the center (h, k). $\frac { ( x + 2 ) ^ { 2 } } { 36 } + \frac { ( y + 4 ) ^ { 2 } } { 4 } = 1$

Write an equation of a circle centered at $\left( - \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)$ with a radius of $3 \sqrt { 5 }$ .

Use the equation of the parabola first to determine whether the axis of symmetry is vertical or horizontal. Then determine if the parabola opens upward, downward, left, or right. $y = ( x + 1 ) ^ { 2 } - 7$

Find the x- and y-intercepts of the ellipse $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$ = 1 and graph the ellipse.

Solve the system of nonlinear equations by the addition method. $9 x ^ { 2 } + 8 x y = 64$ $x ^ { 2 } - x y = 9$