Question 1

Solve the problem.
-Find the dimensions of a rectangular enclosure with perimeter $34 \mathrm { ft }$ and area $60 \mathrm { ft } ^ { 2 }$.

Accepted Answer

A)  $12 \mathrm { ft }$ by $22 \mathrm { ft }$ 
B)  $10 \mathrm { ft }$ by $6 \mathrm { ft }$ 
C)  $12 \mathrm { ft }$ by $5 \mathrm { ft }$ 
D)  $10 \mathrm { ft }$ by $24 \mathrm { ft }$ 
A)  $12 \mathrm { ft }$ by $22 \mathrm { ft }$ 
B)  $10 \mathrm { ft }$ by $6 \mathrm { ft }$ 
C)  $12 \mathrm { ft }$ by $5 \mathrm { ft }$ 
D)  $10 \mathrm { ft }$ by $24 \mathrm { ft }$

Question 2

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective
function.
-objective function $= 7 x + 3 y ;$ minimum

Accepted Answer

A)  36 
B)  0 
C)  24 
D)  16 
A)  36 
B)  0 
C)  24 
D)  16

Question 3

Provide an appropriate response.
-If the graphs of a system of two equations are a circle and a parabola, what are the
possible numbers of solutions (with real coordinates) of this system?

Accepted Answer

The answer of Provide an appropriate response.
-If the graphs of...

Question 4

Find the partial fraction decomposition for the rational expression.
-$\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 }$

Accepted Answer

A)  $1 + \frac { - 6 } { x + 3 } + \frac { 9 } { ( x + 3 ) ^ { 2 } }$ 
B)  $1 + \frac { 6 } { x + 3 } + \frac { - 9 } { ( x + 31 ) ^ { 2 } }$ 
C)  $\frac { 6 } { x + 3 } + \frac { - 6 } { ( x + 3 ) ^ { 2 } }$ 
D)  $\frac { - 6 } { x + 3 } + \frac { 9 } { ( x + 3 ) ^ { 2 } }$ 
A)  $1 + \frac { - 6 } { x + 3 } + \frac { 9 } { ( x + 3 ) ^ { 2 } }$ 
B)  $1 + \frac { 6 } { x + 3 } + \frac { - 9 } { ( x + 31 ) ^ { 2 } }$ 
C)  $\frac { 6 } { x + 3 } + \frac { - 6 } { ( x + 3 ) ^ { 2 } }$ 
D)  $\frac { - 6 } { x + 3 } + \frac { 9 } { ( x + 3 ) ^ { 2 } }$

Question 5

Find the values of the variables for which the statement is true, if possible.
-$$\left[ \begin{array} { l l } 
0 & 0 \
a & b
\end{array} \right] = \left[ \begin{array} { r r } 
0 & q \
4 & - 2
\end{array} \right]$$

Accepted Answer

A)  $\mathrm { a } = 0 ; \mathrm { b } = 0 ; \mathrm { q } = 0$ 
B)  $\mathrm { a } = - 2 ; \mathrm { b } = 4 ; \mathrm { q } = 0$ 
C)  $a = - 4 ; b = 2 ; q = 0$ 
D)  $a = 4 ; b = - 2 ; q = 0$ 
A)  $\mathrm { a } = 0 ; \mathrm { b } = 0 ; \mathrm { q } = 0$ 
B)  $\mathrm { a } = - 2 ; \mathrm { b } = 4 ; \mathrm { q } = 0$ 
C)  $a = - 4 ; b = 2 ; q = 0$ 
D)  $a = 4 ; b = - 2 ; q = 0$

Question 6

A nonlinear system is given, along with the graphs of both equations in the system. Determine if the points of
intersection specified on the graph are solutions of the system by substituting directly into both equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 52 \
2 y + 3 x = 0
\end{array}$$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 7

Perform the operation or operations when possible.
-$\left[\begin{array}{r}
2 x+7 y \
7 k-2 z \
-3 w+5 v \
6 m-9 n
\end{array}\right]-\left[\begin{array}{r}
-5 x-4 y \
-3 k-5 z \
-8 w+3 v \
2 m-3 n
\end{array}\right]$

Accepted Answer

A) 
$\left[\begin{array}{r}
7 x+3 y \
10 k-7 z \
5 w+8 v \
4 m-12 n
\end{array}\right]$ 
B) 
$\left[\begin{array}{r}
-3 x+3 y \
4 k-7 z \
-11 w+8 v \
8 m-12 n
\end{array}\right]$ 
C) 
$\left[\begin{array}{r}
-3 x+11 y \
4 k+3 z \
-11 w+2 v \
8 m-6 n
\end{array}\right]$ 
D) 
$\left[\begin{array}{c}
7 x+11 y \
10 k+3 z \
5 w+2 v \
4 m-6 n
\end{array}\right]$ 
A) 
$\left[\begin{array}{r}
7 x+3 y \
10 k-7 z \
5 w+8 v \
4 m-12 n
\end{array}\right]$ 
B) 
$\left[\begin{array}{r}
-3 x+3 y \
4 k-7 z \
-11 w+8 v \
8 m-12 n
\end{array}\right]$ 
C) 
$\left[\begin{array}{r}
-3 x+11 y \
4 k+3 z \
-11 w+2 v \
8 m-6 n
\end{array}\right]$ 
D) 
$\left[\begin{array}{c}
7 x+11 y \
10 k+3 z \
5 w+2 v \
4 m-6 n
\end{array}\right]$

Question 8

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form.
-

Accepted Answer

A)  $x + y \geq 2$
$2 x + y \leq 5$ 
B)  $x - y \geq 2$
$2 x + y \leq 5$ 
C)  $x + y \leq 2$
$2 x + y \geq 5$ 
D)  $x - y \leq 2$
$2 x + y \geq 5$ 
A)  $x + y \geq 2$
$2 x + y \leq 5$ 
B)  $x - y \geq 2$
$2 x + y \leq 5$ 
C)  $x + y \leq 2$
$2 x + y \geq 5$ 
D)  $x - y \leq 2$
$2 x + y \geq 5$

Question 9

Solve the problem.
-A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 100 black, 110
White and 90 red wires. How many of each type of cable were made?

Accepted Answer

A)  10 A; 30 B; 20 C 
B) 10A; 103 B; 20 C 
C)  20 A; 30 B; 10 C 
D) 10A; 30 B; 93 C 
A)  10 A; 30 B; 20 C 
B) 10A; 103 B; 20 C 
C)  20 A; 30 B; 10 C 
D) 10A; 30 B; 93 C

Question 10

Find the matrix product when possible.
-$\left[ \begin{array} { l l l } - 2 & 2 & 6 \end{array} \right] \left[ \begin{array} { r } 5 \ 0 \ - 3 \end{array} \right]$

Accepted Answer

A) 
$\left[ \begin{array} { r } - 10 \ 0 \ - 18 \end{array} \right]$ 
B) 
[54] 
C) 
$\left[ \begin{array} { l l l } - 10 & 0 & - 18 \end{array} \right]$ 
D) 
$[ - 28 ]$ 
A) 
$\left[ \begin{array} { r } - 10 \ 0 \ - 18 \end{array} \right]$ 
B) 
[54] 
C) 
$\left[ \begin{array} { l l l } - 10 & 0 & - 18 \end{array} \right]$ 
D) 
$[ - 28 ]$

Question 11

Find the partial fraction decomposition for the rational expression.
-$$\frac { 4 x ^ { 2 } + 2 x + 42 } { \left( x ^ { 2 } - 49 \right) ( x - 1 ) }$$

Accepted Answer

A)  $\frac { 5 } { x ^ { 2 } - 49 } + \frac { - 1 } { x - 1 }$ 
B)  $\frac { 2 } { x - 7 } + \frac { 3 } { x + 7 } + \frac { 1 } { x - 1 }$ 
C)  $\frac { 5 } { x - 7 } + \frac { 3 } { x + 7 } + \frac { - 2 } { x - 1 }$ 
D)  $\frac { 3 } { x - 7 } + \frac { 2 } { x + 7 } + \frac { - 1 } { x - 1 }$ 
A)  $\frac { 5 } { x ^ { 2 } - 49 } + \frac { - 1 } { x - 1 }$ 
B)  $\frac { 2 } { x - 7 } + \frac { 3 } { x + 7 } + \frac { 1 } { x - 1 }$ 
C)  $\frac { 5 } { x - 7 } + \frac { 3 } { x + 7 } + \frac { - 2 } { x - 1 }$ 
D)  $\frac { 3 } { x - 7 } + \frac { 2 } { x + 7 } + \frac { - 1 } { x - 1 }$

Question 12

Provide an appropriate response.
-Fill in the blank to complete the statement. In order for a matrix to have a determinant, it must be ــــــــــــ matrix.

Accepted Answer

A)  a minor 
B)  a square 
C)  a rectangular 
D)  an augmented 
A)  a minor 
B)  a square 
C)  a rectangular 
D)  an augmented

Question 13

Find the partial fraction decomposition for the rational expression.
-$\frac { - 31 x - 77 } { 2 x ^ { 2 } + 14 x + 20 }$

Accepted Answer

A)  $\frac { - 5 } { 2 x + 4 } + \frac { - 13 } { x + 5 }$ 
B)  $\frac { - 5 } { x + 4 } + \frac { - 13 } { 2 x + 5 }$ 
C)  $\frac { 5 } { 2 x + 4 } + \frac { 13 } { x + 5 }$ 
D)  $\frac { - 5 } { 2 x - 4 } + \frac { - 13 } { x - 5 }$ 
A)  $\frac { - 5 } { 2 x + 4 } + \frac { - 13 } { x + 5 }$ 
B)  $\frac { - 5 } { x + 4 } + \frac { - 13 } { 2 x + 5 }$ 
C)  $\frac { 5 } { 2 x + 4 } + \frac { 13 } { x + 5 }$ 
D)  $\frac { - 5 } { 2 x - 4 } + \frac { - 13 } { x - 5 }$

Question 14

Find the partial fraction decomposition for the rational expression.
-$$\frac { 26 x ^ { 2 } - 88 x + 76 } { ( x - 2 ) ( 2 x - 3 ) ^ { 2 } }$$

Accepted Answer

A)  $\frac { 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { - 4 } { x - 2 }$ 
B)  $\frac { - 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { 4 } { x - 2 }$ 
C)  $\frac { 5 } { 2 x - 3 } + \frac { - 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 4 } { x - 2 }$ 
D)  $\frac { - 4 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { 5 } { x - 2 }$ 
A)  $\frac { 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { - 4 } { x - 2 }$ 
B)  $\frac { - 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { 4 } { x - 2 }$ 
C)  $\frac { 5 } { 2 x - 3 } + \frac { - 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 4 } { x - 2 }$ 
D)  $\frac { - 4 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { 5 } { x - 2 }$

Question 15

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form.
-

Accepted Answer

A)  $- x + 3 y  - 4$
$2 x + y  - 4$
$2 x + y < - 2$ 
D)  $x - 3 y < - 4$
$2 x + y < - 2$ 
A)  $- x + 3 y  - 4$
$2 x + y  - 4$
$2 x + y < - 2$ 
D)  $x - 3 y < - 4$
$2 x + y < - 2$

Question 16

Solve the problem.
-A grain dealer sold to one customer 10 bushels of wheat, 8 of corn, and 5 of rye for $67.80; to another, 8 of wheat, 5 of corn, and 10 of rye for $67.90; and to a third, 5 of wheat, 10 of corn, and 8
Of rye for $69.00. What was the price per bushel for corn?

Accepted Answer

A)  $3.30 
B)  $3.10 
C)  $2.80 
D)  $3.00 
A)  $3.30 
B)  $3.10 
C)  $2.80 
D)  $3.00

Question 17

Provide an appropriate response.
-For a certain system of three linear equations, the solution set is $\{ 6,1 , - 7 \}$, and $D = - 17$. Find the values of $\mathrm { D } _ { \mathrm { X } } , \mathrm { D } _ { \mathrm { y } }$, and $\mathrm { D } _ { \mathrm { Z } }$.

Accepted Answer

A)  $\mathrm { D } _ { \mathrm { x } } = 6 ; \mathrm { D } _ { \mathrm { y } } = 1 ; \mathrm { D } _ { \mathrm { z } } = - 7$ 
B)  $\mathrm { D } _ { \mathrm { X } } = - 17 ; \mathrm { D } _ { \mathrm { y } } = - 102 ; \mathrm { D } _ { \mathrm { z } } = 119$ 
C)  $\mathrm { D } _ { \mathrm { x } } = - 102 ; \mathrm { D } _ { \mathrm { y } } = - 17 ; \mathrm { D } _ { \mathrm { Z } } = 119$ 
D)  $\mathrm { D } _ { \mathrm { X } } = - \frac { 17 } { 6 } ; \mathrm { D } _ { \mathrm { y } } = - 17 ; \mathrm { D } _ { \mathrm { Z } } = \frac { 17 } { 7 }$ 
A)  $\mathrm { D } _ { \mathrm { x } } = 6 ; \mathrm { D } _ { \mathrm { y } } = 1 ; \mathrm { D } _ { \mathrm { z } } = - 7$ 
B)  $\mathrm { D } _ { \mathrm { X } } = - 17 ; \mathrm { D } _ { \mathrm { y } } = - 102 ; \mathrm { D } _ { \mathrm { z } } = 119$ 
C)  $\mathrm { D } _ { \mathrm { x } } = - 102 ; \mathrm { D } _ { \mathrm { y } } = - 17 ; \mathrm { D } _ { \mathrm { Z } } = 119$ 
D)  $\mathrm { D } _ { \mathrm { X } } = - \frac { 17 } { 6 } ; \mathrm { D } _ { \mathrm { y } } = - 17 ; \mathrm { D } _ { \mathrm { Z } } = \frac { 17 } { 7 }$

Question 18

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the
solution with y arbitrary.
-$$\begin{array} { l } 
3 x + 3 y = 9 \
2 x + 2 y = 6
\end{array}$$

Accepted Answer

A)  $\{ ( - 3 , - 6 ) \}$ 
B)  $\{ ( 6 , - 3 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( - 3,6 ) \}$ 
A)  $\{ ( - 3 , - 6 ) \}$ 
B)  $\{ ( 6 , - 3 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( - 3,6 ) \}$

Question 19

Provide an appropriate response.
-You are graphing $2 x ^ { 2 } + 3 y ^ { 2 } > 5$. You have drawn the graph of $2 x ^ { 2 } + 3 y ^ { 2 } = 5$. What single point will allow you to determine the correct region?

Accepted Answer

A)  $( 3,5 )$ 
B)  The origin 
C)  $( 2,3 )$ 
D)  $( 2,5 )$ 
A)  $( 3,5 )$ 
B)  The origin 
C)  $( 2,3 )$ 
D)  $( 2,5 )$

Question 20

Solve the system.
-$$\begin{array} { r } 
5 x - 4 y - 2 z + 1 = 0 \
15 x - 4 y + 4 z - 4 = 0 \
8 y + 2 z - 3 = 0
\end{array}$$

Accepted Answer

A)  $\left\{ \left( - \frac { 1 } { 5 } , \frac { 1 } { 4 } , - \frac { 1 } { 2 } \right) \right\}$ 
B)  $\left\{ \left( - \frac { 1 } { 5 } , - \frac { 1 } { 4 } , \frac { 1 } { 2 } \right) \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \left( \frac { 1 } { 5 } , \frac { 1 } { 4 } , \frac { 1 } { 2 } \right) \right\}$ 
A)  $\left\{ \left( - \frac { 1 } { 5 } , \frac { 1 } { 4 } , - \frac { 1 } { 2 } \right) \right\}$ 
B)  $\left\{ \left( - \frac { 1 } { 5 } , - \frac { 1 } { 4 } , \frac { 1 } { 2 } \right) \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ \left( \frac { 1 } { 5 } , \frac { 1 } { 4 } , \frac { 1 } { 2 } \right) \right\}$

Solve the problem. -Find the dimensions of a rectangular enclosure with perimeter $34 \mathrm { ft }$ and area $60 \mathrm { ft } ^ { 2 }$ .

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective function. -objective function $= 7 x + 3 y ;$ minimum

Provide an appropriate response. -If the graphs of a system of two equations are a circle and a parabola, what are the possible numbers of solutions (with real coordinates) of this system?

Find the partial fraction decomposition for the rational expression. - $\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 }$

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l l } 0 & 0 \\a & b\end{array} \right] = \left[ \begin{array} { r r } 0 & q \\4 & - 2\end{array} \right]$

Perform the operation or operations when possible. - $\left[\begin{array}{r}2 x+7 y \\7 k-2 z \\-3 w+5 v \\6 m-9 n\end{array}\right]-\left[\begin{array}{r}-5 x-4 y \\-3 k-5 z \\-8 w+3 v \\2 m-3 n\end{array}\right]$

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Solve the problem. -A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 100 black, 110 White and 90 red wires. How many of each type of cable were made?

Find the matrix product when possible. - $\left[ \begin{array} { l l l } - 2 & 2 & 6 \end{array} \right] \left[ \begin{array} { r } 5 \\ 0 \\ - 3 \end{array} \right]$

Find the partial fraction decomposition for the rational expression. - $\frac { 4 x ^ { 2 } + 2 x + 42 } { \left( x ^ { 2 } - 49 \right) ( x - 1 ) }$

Provide an appropriate response. -Fill in the blank to complete the statement. In order for a matrix to have a determinant, it must be ــــــــــــ matrix.

Find the partial fraction decomposition for the rational expression. - $\frac { - 31 x - 77 } { 2 x ^ { 2 } + 14 x + 20 }$

Find the partial fraction decomposition for the rational expression. - $\frac { 26 x ^ { 2 } - 88 x + 76 } { ( x - 2 ) ( 2 x - 3 ) ^ { 2 } }$

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Solve the problem. -A grain dealer sold to one customer 10 bushels of wheat, 8 of corn, and 5 of rye for $67.80; to another, 8 of wheat, 5 of corn, and 10 of rye for $67.90; and to a third, 5 of wheat, 10 of corn, and 8 Of rye for $69.00. What was the price per bushel for corn?

Provide an appropriate response. -For a certain system of three linear equations, the solution set is $\{ 6,1 , - 7 \}$ , and $D = - 17$ . Find the values of $\mathrm { D } _ { \mathrm { X } } , \mathrm { D } _ { \mathrm { y } }$ , and $\mathrm { D } _ { \mathrm { Z } }$ .

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - 3x+3y=9 2x+2y=6

Provide an appropriate response. -You are graphing $2 x ^ { 2 } + 3 y ^ { 2 } > 5$ . You have drawn the graph of $2 x ^ { 2 } + 3 y ^ { 2 } = 5$ . What single point will allow you to determine the correct region?

Solve the system. - 5x-4y-2z+1=0 15x-4y+4z-4=0 8y+2z-3=0

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 9: Systems and Matrices

Solve the problem. -Find the dimensions of a rectangular enclosure with perimeter 34ft34 \mathrm { ft }34ft and area 60ft260 \mathrm { ft } ^ { 2 }60ft2 .

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective function. -objective function =7x+3y;= 7 x + 3 y ;=7x+3y; minimum

Provide an appropriate response. -If the graphs of a system of two equations are a circle and a parabola, what are the possible numbers of solutions (with real coordinates) of this system?

Find the partial fraction decomposition for the rational expression. - x2x2+6x+9\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 }x2+6x+9x2​

Find the values of the variables for which the statement is true, if possible. - [00ab]=[0q4−2]\left[ \begin{array} { l l } 0 & 0 \\a & b\end{array} \right] = \left[ \begin{array} { r r } 0 & q \\4 & - 2\end{array} \right][0a​0b​]=[04​q−2​]

A nonlinear system is given, along with the graphs of both equations in the system. Determine if the points of intersection specified on the graph are solutions of the system by substituting directly into both equations. - +=52 2y+3x=0

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Solve the problem. -A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 100 black, 110 White and 90 red wires. How many of each type of cable were made?

Find the matrix product when possible. - [−226][50−3]\left[ \begin{array} { l l l } - 2 & 2 & 6 \end{array} \right] \left[ \begin{array} { r } 5 \\ 0 \\ - 3 \end{array} \right][−2​2​6​]​50−3​​

Find the partial fraction decomposition for the rational expression. - 4x2+2x+42(x2−49)(x−1)\frac { 4 x ^ { 2 } + 2 x + 42 } { \left( x ^ { 2 } - 49 \right) ( x - 1 ) }(x2−49)(x−1)4x2+2x+42​

Provide an appropriate response. -Fill in the blank to complete the statement. In order for a matrix to have a determinant, it must be ــــــــــــ matrix.

Find the partial fraction decomposition for the rational expression. - −31x−772x2+14x+20\frac { - 31 x - 77 } { 2 x ^ { 2 } + 14 x + 20 }2x2+14x+20−31x−77​

Find the partial fraction decomposition for the rational expression. - 26x2−88x+76(x−2)(2x−3)2\frac { 26 x ^ { 2 } - 88 x + 76 } { ( x - 2 ) ( 2 x - 3 ) ^ { 2 } }(x−2)(2x−3)226x2−88x+76​

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Solve the problem. -A grain dealer sold to one customer 10 bushels of wheat, 8 of corn, and 5 of rye for $67.80; to another, 8 of wheat, 5 of corn, and 10 of rye for $67.90; and to a third, 5 of wheat, 10 of corn, and 8 Of rye for $69.00. What was the price per bushel for corn?

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - 3x+3y=9 2x+2y=6

Provide an appropriate response. -You are graphing 2x2+3y2>52 x ^ { 2 } + 3 y ^ { 2 } > 52x2+3y2>5 . You have drawn the graph of 2x2+3y2=52 x ^ { 2 } + 3 y ^ { 2 } = 52x2+3y2=5 . What single point will allow you to determine the correct region?

Solve the system. - 5x-4y-2z+1=0 15x-4y+4z-4=0 8y+2z-3=0

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Solve the problem. -Find the dimensions of a rectangular enclosure with perimeter $34 \mathrm { ft }$ and area $60 \mathrm { ft } ^ { 2 }$ .

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective function. -objective function $= 7 x + 3 y ;$ minimum

Find the partial fraction decomposition for the rational expression. - $\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 }$

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l l } 0 & 0 \\a & b\end{array} \right] = \left[ \begin{array} { r r } 0 & q \\4 & - 2\end{array} \right]$

Find the matrix product when possible. - $\left[ \begin{array} { l l l } - 2 & 2 & 6 \end{array} \right] \left[ \begin{array} { r } 5 \\ 0 \\ - 3 \end{array} \right]$

Find the partial fraction decomposition for the rational expression. - $\frac { 4 x ^ { 2 } + 2 x + 42 } { \left( x ^ { 2 } - 49 \right) ( x - 1 ) }$

Find the partial fraction decomposition for the rational expression. - $\frac { - 31 x - 77 } { 2 x ^ { 2 } + 14 x + 20 }$

Find the partial fraction decomposition for the rational expression. - $\frac { 26 x ^ { 2 } - 88 x + 76 } { ( x - 2 ) ( 2 x - 3 ) ^ { 2 } }$

Provide an appropriate response. -You are graphing $2 x ^ { 2 } + 3 y ^ { 2 } > 5$ . You have drawn the graph of $2 x ^ { 2 } + 3 y ^ { 2 } = 5$ . What single point will allow you to determine the correct region?