Question 1

Complete the table of solutions for the equation $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$ . 
$\begin{array}{|l|l|}
  \hline \text { x } & \text { y }   \
\hline  5 &\
\hline 
\end{array}$

Accepted Answer

The answer of Complete the table of solutions for the...

Question 2

Find two points on the graph of $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 16 } = 1$ by letting x=5 and finding the corresponding values of y .

Accepted Answer

The answer of Find two points on the graph of...

Question 3

The most number of points a hyperbola can intersect a circle is _________ points.

Accepted Answer

A)  one 
B)  two 
C)  three 
D)  four 
A)  one 
B)  two 
C)  three 
D)  four

Question 4

Graph the hyperbola. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Accepted Answer

The answer of Graph the hyperbola. \(\log _ { 4...

Question 5

Solve the system of equations for real values of x and y . $\left\{ \begin{array} { l } 
2 y ^ { 2 } = x y \
x ^ { 2 } + x y - 6 = 0
\end{array} \right.$

Accepted Answer

The answer of Solve the system of equations for real...

Question 6

The position of a sonic boom caused by the faster-than-sound aircraft is the hyperbola $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$ in the coordinate system shown. How wide is the hyperbola 2 units from its vertex?
 $1 + \log _ { 4 } 9 x - \log _ { 4 } y$

Accepted Answer

The answer of The position of a sonic boom caused...

Question 7

Describe the ellipse which is the graph of the equation $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$ .

Accepted Answer

A)  vertical; vertices: $( 0,3 ) , ( 0 , - 3 )$ 
B)  horizontal; vertices: $( 16,0 ) , ( - 16,0 )$ 
C)  vertical; vertices: $( 0,9 ) , ( 0,9 )$ 
D)  horizontal; vertices: $( 4,0 ) , ( - 4,0 )$ 
A)  vertical; vertices: $( 0,3 ) , ( 0 , - 3 )$ 
B)  horizontal; vertices: $( 16,0 ) , ( - 16,0 )$ 
C)  vertical; vertices: $( 0,9 ) , ( 0,9 )$ 
D)  horizontal; vertices: $( 4,0 ) , ( - 4,0 )$

Question 8

The two-branch curve graphed below is a __________.

Accepted Answer

The answer of The two-branch curve graphed below is a...

Question 9

Graph the equation. $\log _ { 7 } \frac { x y } { 7 }$

Accepted Answer

The answer of Graph the equation. \(\log _ { 7...

Question 10

What is the equation of the hyperbola?
 $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Accepted Answer

The answer of What is the equation of the hyperbola?
...

Question 11

The arch of an underpass is a part of an ellipse. Find the equation of the ellipse.

Accepted Answer

The answer of The arch of an underpass is a...

Question 12

A __________ is a line that intersects a circle at one point.

Accepted Answer

The answer of A __________ is a line that intersects...

Question 13

The rectangular pasture shown below is to be fenced in along a riverbank. If 260 feet of fencing is to enclose an area of 8162 square feet, find the dimensions of the pasture.   __________ ft

Accepted Answer

The answer of The rectangular pasture shown below is to...

Question 14

Graph the hyperbola. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Accepted Answer

The answer of Graph the hyperbola. \(\log _ { 4...

Question 15

A __________ is the set of all points in a plane for which the difference of the distances from two fixed points is a constant.

Accepted Answer

A hyperbola is the set of all

Question 16

Write $x ^ { 2 } - 2 x - y ^ { 2 } + 6 y = 24$ in standard form.

Accepted Answer

A)  $\frac { ( x - 1 ) ^ { 2 } } { 16 } - \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 1 ) ^ { 2 } } { 16 } - \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 24 } - \frac { ( y + 3 ) ^ { 2 } } { 24 } = 1$ 
D)  $\frac { ( x - 1 ) ^ { 2 } } { 24 } - \frac { ( y - 3 ) ^ { 2 } } { 24 } = 1$ 
A)  $\frac { ( x - 1 ) ^ { 2 } } { 16 } - \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 1 ) ^ { 2 } } { 16 } - \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 24 } - \frac { ( y + 3 ) ^ { 2 } } { 24 } = 1$ 
D)  $\frac { ( x - 1 ) ^ { 2 } } { 24 } - \frac { ( y - 3 ) ^ { 2 } } { 24 } = 1$

Question 17

Solve: $\left\{ \begin{aligned}
x ^ { 2 } + y ^ { 2 } & = 182 \
y & = x ^ { 2 }
\end{aligned} \right.$

Accepted Answer

A)  $\{ ( \sqrt { 13 } , 13 ) , ( - \sqrt { 13 } , 13 ) \}$ 
B)  $\{ ( \sqrt { 13 } , 13 ) \}$ 
C)  $\{ ( 169,13 ) \}$ 
D)  no solution 
A)  $\{ ( \sqrt { 13 } , 13 ) , ( - \sqrt { 13 } , 13 ) \}$ 
B)  $\{ ( \sqrt { 13 } , 13 ) \}$ 
C)  $\{ ( 169,13 ) \}$ 
D)  no solution

Question 18

The area of a rectangle is 75 square centimeters and its perimeter is 40 centimeters. Find the dimensions of the rectangle.

Accepted Answer

A)  13 cm by 2 cm 
B)  24 cm by 5 cm 
C)  16 cm by 3 cm 
D)  15 cm by 5 cm 
A)  13 cm by 2 cm 
B)  24 cm by 5 cm 
C)  16 cm by 3 cm 
D)  15 cm by 5 cm

Question 19

Solve the system $\left\{ \begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 12 \
x ^ { 2 } + y ^ { 2 } = 10
\end{array} \right.$ over the complex numbers.

Accepted Answer

The answer of Solve the system \(\left\{ \begin{array} { l...

Question 20

Graph the equation. $\log _ { 7 } \frac { x y } { 7 }$

Accepted Answer

The answer of Graph the equation. \(\log _ { 7...

Complete the table of solutions for the equation $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$ . x y 5

Find two points on the graph of $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 16 } = 1$ by letting x=5 and finding the corresponding values of y .

The most number of points a hyperbola can intersect a circle is _________ points.

Graph the hyperbola. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Solve the system of equations for real values of x and y . $\left\{ \begin{array} { l } 2 y ^ { 2 } = x y \\x ^ { 2 } + x y - 6 = 0\end{array} \right.$

The position of a sonic boom caused by the faster-than-sound aircraft is the hyperbola $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$ in the coordinate system shown. How wide is the hyperbola 2 units from its vertex? $1 + \log _ { 4 } 9 x - \log _ { 4 } y$

Describe the ellipse which is the graph of the equation $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$ .

The two-branch curve graphed below is a __________.

Graph the equation. $\log _ { 7 } \frac { x y } { 7 }$

What is the equation of the hyperbola? $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

The arch of an underpass is a part of an ellipse. Find the equation of the ellipse.

A __________ is a line that intersects a circle at one point.

The rectangular pasture shown below is to be fenced in along a riverbank. If 260 feet of fencing is to enclose an area of 8162 square feet, find the dimensions of the pasture. __________ ft

Graph the hyperbola. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

A __________ is the set of all points in a plane for which the difference of the distances from two fixed points is a constant.

Write $x ^ { 2 } - 2 x - y ^ { 2 } + 6 y = 24$ in standard form.

Solve: $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 182 \\y & = x ^ { 2 }\end{aligned} \right.$

The area of a rectangle is 75 square centimeters and its perimeter is 40 centimeters. Find the dimensions of the rectangle.

Solve the system $\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 12 \\x ^ { 2 } + y ^ { 2 } = 10\end{array} \right.$ over the complex numbers.

Graph the equation. $\log _ { 7 } \frac { x y } { 7 }$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Miscellaneous Topics

Filters

Exam 10: Conic Sections; More Graphing

Complete the table of solutions for the equation x29−y216=1\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 19x2​−16y2​=1 . x y 5

Find two points on the graph of x2400+y216=1\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 16 } = 1400x2​+16y2​=1 by letting x=5 and finding the corresponding values of y .

The most number of points a hyperbola can intersect a circle is _________ points.

Graph the hyperbola. log⁡44x9y\log _ { 4 } \frac { 4 x ^ { 9 } } { y }log4​y4x9​

Solve the system of equations for real values of x and y . {2y2=xyx2+xy−6=0\left\{ \begin{array} { l } 2 y ^ { 2 } = x y \\x ^ { 2 } + x y - 6 = 0\end{array} \right.{2y2=xyx2+xy−6=0​

Describe the ellipse which is the graph of the equation x216+y29=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 116x2​+9y2​=1 .

The two-branch curve graphed below is a __________.

Graph the equation. log⁡7xy7\log _ { 7 } \frac { x y } { 7 }log7​7xy​

What is the equation of the hyperbola? log⁡44x9y\log _ { 4 } \frac { 4 x ^ { 9 } } { y }log4​y4x9​

The arch of an underpass is a part of an ellipse. Find the equation of the ellipse.

A __________ is a line that intersects a circle at one point.

The rectangular pasture shown below is to be fenced in along a riverbank. If 260 feet of fencing is to enclose an area of 8162 square feet, find the dimensions of the pasture. __________ ft

Graph the hyperbola. log⁡44x9y\log _ { 4 } \frac { 4 x ^ { 9 } } { y }log4​y4x9​

A __________ is the set of all points in a plane for which the difference of the distances from two fixed points is a constant.

Write x2−2x−y2+6y=24x ^ { 2 } - 2 x - y ^ { 2 } + 6 y = 24x2−2x−y2+6y=24 in standard form.

Solve: {x2+y2=182y=x2\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 182 \\y & = x ^ { 2 }\end{aligned} \right.{x2+y2y​=182=x2​

The area of a rectangle is 75 square centimeters and its perimeter is 40 centimeters. Find the dimensions of the rectangle.

Solve the system {x2−y2=12x2+y2=10\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 12 \\x ^ { 2 } + y ^ { 2 } = 10\end{array} \right.{x2−y2=12x2+y2=10​ over the complex numbers.

Graph the equation. log⁡7xy7\log _ { 7 } \frac { x y } { 7 }log7​7xy​

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Exponents, Polynomials, and Polynomial Functions

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Miscellaneous Topics

Filters

Complete the table of solutions for the equation $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$ . x y 5

Find two points on the graph of $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 16 } = 1$ by letting x=5 and finding the corresponding values of y .

Graph the hyperbola. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Solve the system of equations for real values of x and y . $\left\{ \begin{array} { l } 2 y ^ { 2 } = x y \\x ^ { 2 } + x y - 6 = 0\end{array} \right.$

Describe the ellipse which is the graph of the equation $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$ .

Graph the equation. $\log _ { 7 } \frac { x y } { 7 }$

What is the equation of the hyperbola? $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Graph the hyperbola. $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$

Write $x ^ { 2 } - 2 x - y ^ { 2 } + 6 y = 24$ in standard form.

Solve: $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 182 \\y & = x ^ { 2 }\end{aligned} \right.$

Solve the system $\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 12 \\x ^ { 2 } + y ^ { 2 } = 10\end{array} \right.$ over the complex numbers.

Graph the equation. $\log _ { 7 } \frac { x y } { 7 }$