Question 1

Find the partial fraction decomposition for the rational expression.
$\frac { - 5 x ^ { 2 } - 9 x + 11 } { ( x + 4 ) ^ { 2 } ( 3 x + 1 ) }$

Accepted Answer

A)  $\frac { 1 } { 3 x + 1 } + \frac { 2 } { ( x + 4 ) ^ { 2 } } + \frac { - 3 } { x + 4 }$ 
B)  $\frac { 1 } { 3 x + 1 } + \frac { - 2 } { x + 4 } + \frac { 3 } { ( x + 4 ) ^ { 2 } }$ 
C)  $\frac { 1 } { 3 x + 1 } + \frac { 3 } { ( x + 4 ) ^ { 2 } } + \frac { 2 } { x + 4 }$ 
D)  $\frac { 1 } { 3 x + 1 } + \frac { - 3 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 } { x + 4 }$ 
A)  $\frac { 1 } { 3 x + 1 } + \frac { 2 } { ( x + 4 ) ^ { 2 } } + \frac { - 3 } { x + 4 }$ 
B)  $\frac { 1 } { 3 x + 1 } + \frac { - 2 } { x + 4 } + \frac { 3 } { ( x + 4 ) ^ { 2 } }$ 
C)  $\frac { 1 } { 3 x + 1 } + \frac { 3 } { ( x + 4 ) ^ { 2 } } + \frac { 2 } { x + 4 }$ 
D)  $\frac { 1 } { 3 x + 1 } + \frac { - 3 } { ( x + 4 ) ^ { 2 } } + \frac { - 2 } { x + 4 }$ B

Question 2

Graph the solution set of the system of inequalities.
-$\begin{array}{l}
y \geq-x^{2} \
y \leq x+1 \
y \geq-5 \
x \geq-4
\end{array}$

Accepted Answer

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

Question 3

Provide an appropriate response.
-For a certain system of two linear equations, the values of the determinants used in Cramer's rule are $D = 26$, $D _ { x } = 23$, and $D _ { y } = - 13$. What is the solution set of the system?

Accepted Answer

A)  $\left\{ \left( \frac { 26 } { 23 } , - 2 \right) \right\}$ 
B)  $\left\{ \left( \frac { 23 } { 26 } , - \frac { 1 } { 2 } \right) \right\}$ 
C)  $\{ ( 23 , - 13 ) \}$ 
D)  $\left\{ \left( - \frac { 1 } { 2 } , \frac { 23 } { 26 } \right) \right\}$ 
A)  $\left\{ \left( \frac { 26 } { 23 } , - 2 \right) \right\}$ 
B)  $\left\{ \left( \frac { 23 } { 26 } , - \frac { 1 } { 2 } \right) \right\}$ 
C)  $\{ ( 23 , - 13 ) \}$ 
D)  $\left\{ \left( - \frac { 1 } { 2 } , \frac { 23 } { 26 } \right) \right\}$ B

Question 4

Find the indicated matrix.
-Let $C = \left[ \begin{array} { r } 6 \ - 2 \ 12 \end{array} \right]$. Find $\frac { 1 } { 2 } C$

Accepted Answer

A) 
$\left[ \begin{array} { r } 3 \ - 1 \ 6 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r } 3 \ - 2 \ 12 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r } 6 \ - 1 \ 12 \end{array} \right]$ 
D) 
$\left[ \begin{array} { l } 12 \ - 4 \ 24 \end{array} \right]$ 
A) 
$\left[ \begin{array} { r } 3 \ - 1 \ 6 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r } 3 \ - 2 \ 12 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r } 6 \ - 1 \ 12 \end{array} \right]$ 
D) 
$\left[ \begin{array} { l } 12 \ - 4 \ 24 \end{array} \right]$

Question 5

Find the value of the determinant.
$$\left| \begin{array} { r r r } 
5 & 4 & 3 \
0 & 4 & 1 \
- 5 & 0 & 4
\end{array} \right|$$

Accepted Answer

A)   -120 
B)  120 
C)  160 
D)  0 
A)   -120 
B)  120 
C)  160 
D)  0

Question 6

If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l } 
3 x + 2 y + z = 4 \
2 x - 3 y - z = 5 \
5 x + 12 y + 5 z = 2
\end{array}$$

Accepted Answer

A)  $\{ ( x , 5 x - 9 , - 13 x + 22 ) \}$ 
B)  $\{ ( x , - 5 x + 9 , - 13 x + 22 ) \}$ 
C)  $\{ ( x , - 5 x - 9 , - 13 x + 22 ) \}$ 
D)  $\{ ( x , 5 x + 9 , - 13 x + 22 ) \}$ 
A)  $\{ ( x , 5 x - 9 , - 13 x + 22 ) \}$ 
B)  $\{ ( x , - 5 x + 9 , - 13 x + 22 ) \}$ 
C)  $\{ ( x , - 5 x - 9 , - 13 x + 22 ) \}$ 
D)  $\{ ( x , 5 x + 9 , - 13 x + 22 ) \}$

Question 7

The perimeter of a rectangle is 44 cm. The length is 12 cm longer than the width. What are the length and width of the rectangle?

Accepted Answer

A)  Length: 22 cm; width: 10 cm 
B)  Length: 17 cm; width: 5 cm 
C)  Length: 23 cm; width: 11 cm 
D)  Length: 12 cm; width: 5 cm 
A)  Length: 22 cm; width: 10 cm 
B)  Length: 17 cm; width: 5 cm 
C)  Length: 23 cm; width: 11 cm 
D)  Length: 12 cm; width: 5 cm

Question 8

The sum of the squares of the digits of a positive two-digit number is 85, and the tens digit is 1 less than the units digit. Find the number.

Accepted Answer

A)  67 
B)  56 
C)  65 
D)  76 
A)  67 
B)  56 
C)  65 
D)  76

Question 9

Evaluate the determinant.
$\left| \begin{array} { l l l l } 
2 & 9 & 3 & 6 \
8 & 9 & 4 & 4 \
2 & 4 & 6 & 5 \
2 & 7 & 7 & 2
\end{array} \right|$

Accepted Answer

A)   -21 
B)  1280 
C)   -12 
D)   -36 
A)   -21 
B)  1280 
C)   -12 
D)   -36

Question 10

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the
solution with y arbitrary.
$\begin{array} { c } 
7 x - 5 y = - 21 \
- 4 x + 3 y = 12
\end{array}$

Accepted Answer

A)  $\{ ( - 3,1 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( - 3,0 ) \}$ 
D)  $\{ ( - 4,1 ) \}$ 
A)  $\{ ( - 3,1 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( - 3,0 ) \}$ 
D)  $\{ ( - 4,1 ) \}$

Question 11

Graph the solution set of the system of inequalities.
-$\begin{array}{l}
y \geq\left(\frac{1}{3}\right)^{x} \
y \leq 8
\end{array}$

Accepted Answer

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

Question 12

Solve the problem using matrices.
-In a study of heat transfer in a grid of wires, the temperature at an exterior node is maintained at a constant value (in °F) as shown in the figure. When the grid is in thermal equilibrium, the temperature at an interior
Node is the average of the temperatures at the four adjacent nodes. For instance $\mathrm { T } _ { 1 } = \frac { 0 + 0 + 300 + \mathrm { T } _ { 2 } } { 4 }$, or $4 \mathrm {~T} _ { 1 } - \mathrm { T } _ { 2 } = 300$. Find the temperatures $\mathrm { T } _ { 1 } , \mathrm {~T} _ { 2 }$, and $\mathrm { T } _ { 3 }$ when the grid is in thermal equilibrium.

Accepted Answer

A)  $\mathrm { T } _ { 1 } = \frac { 769 } { 7 } \circ \mathrm { F } , \mathrm { T } _ { 2 } = \frac { 976 } { 7 } \circ \mathrm { F } , \mathrm { T } _ { 3 } = \frac { 475 } { 7 } \circ \mathrm { F }$ 
B)  $\mathrm { T } _ { 1 } = 97 ^ { \circ } \mathrm { F } , \mathrm { T } _ { 2 } = 88 ^ { \circ } \mathrm { F } , \mathrm { T } _ { 3 } = \frac { 745 } { 14 } ^ { \circ } \mathrm { F }$ 
C)  $\mathrm { T } _ { 1 } = 194 ^ { \circ } \mathrm { F } , \mathrm { T } _ { 2 } = 88 ^ { \circ } \mathrm { F } , \mathrm { T } _ { 3 } = \frac { 745 } { 7 } { } ^ { \circ } \mathrm { F }$ 
D)  $\mathrm { T } _ { 1 } = \frac { 669 } { 7 } { } ^ { \circ } \mathrm { F } , \mathrm { T } _ { 2 } = \frac { 576 } { 7 } { } ^ { \circ } \mathrm { F } , \mathrm { T } _ { 3 } = \frac { 870 } { 7 } { } ^ { \circ } \mathrm { F }$ 
A)  $\mathrm { T } _ { 1 } = \frac { 769 } { 7 } \circ \mathrm { F } , \mathrm { T } _ { 2 } = \frac { 976 } { 7 } \circ \mathrm { F } , \mathrm { T } _ { 3 } = \frac { 475 } { 7 } \circ \mathrm { F }$ 
B)  $\mathrm { T } _ { 1 } = 97 ^ { \circ } \mathrm { F } , \mathrm { T } _ { 2 } = 88 ^ { \circ } \mathrm { F } , \mathrm { T } _ { 3 } = \frac { 745 } { 14 } ^ { \circ } \mathrm { F }$ 
C)  $\mathrm { T } _ { 1 } = 194 ^ { \circ } \mathrm { F } , \mathrm { T } _ { 2 } = 88 ^ { \circ } \mathrm { F } , \mathrm { T } _ { 3 } = \frac { 745 } { 7 } { } ^ { \circ } \mathrm { F }$ 
D)  $\mathrm { T } _ { 1 } = \frac { 669 } { 7 } { } ^ { \circ } \mathrm { F } , \mathrm { T } _ { 2 } = \frac { 576 } { 7 } { } ^ { \circ } \mathrm { F } , \mathrm { T } _ { 3 } = \frac { 870 } { 7 } { } ^ { \circ } \mathrm { F }$

Question 13

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { c } 
x ^ { 2 } - x y + y ^ { 2 } = 3 \
2 x ^ { 2 } + x y + 2 y ^ { 2 } = 12
\end{array}$

Accepted Answer

A)   {(2,1),(1,2)} 
B)   {(2,0),(-2,0),(1,0),(-1,0)} 
C)   {(1,0),(-1,0)} 
D)   {(2,1),(-2,-1),(1,2),(-1,-2)} 
A)   {(2,1),(1,2)} 
B)   {(2,0),(-2,0),(1,0),(-1,0)} 
C)   {(1,0),(-1,0)} 
D)   {(2,1),(-2,-1),(1,2),(-1,-2)}

Question 14

Matt bought 3 pounds of oranges and 2 pounds of apples and paid $\$ 3.94$, before tax. Andy bought 4 pounds of oranges and 3 pounds of apples and paid $\$ 5.53$, before tax. Use this information to set up a matrix equation of the form $\mathrm { AX } = \mathrm { B }$, which can be solved to determine the price per pound for oranges and apples. Solve this matrix equation to find the price per pound of apples.
Use the fact that for $\mathrm { A } = \left[ \begin{array} { l l } 3 & 2 \ 4 & 3 \end{array} \right] , \mathrm { A } ^ { - 1 } = \left[ \begin{array} { r r } 3 & - 2 \ - 4 & 3 \end{array} \right]$.

Accepted Answer

A)  $0.83 per pound 
B)  $0.74 per pound 
C)  $0.80 per pound 
D)  $0.87 per pound 
A)  $0.83 per pound 
B)  $0.74 per pound 
C)  $0.80 per pound 
D)  $0.87 per pound

Question 15

Solve the system to find $W _ { 1 } \text { and } W _ { 2 }$
-Linear systems occur in the design of roof trusses for new homes and buildings. The simplest type of roof truss is a triangle. The truss shown in the figure is used to frame roofs of small buildings. If a 123-pound force is applied at the peak of the truss, then the forces or weights $W _ { 1 }$ and $W _ { 2 }$ exerted parallel to each rafter of the truss are determined by the following linear system of equations.

$$\begin{array} { l } 
W _ { 1 } + \sqrt { 2 } W _ { 2 } = 246 \
\sqrt { 3 } W _ { 1 } - \sqrt { 2 } W _ { 2 } = 0
\end{array}$$

Accepted Answer

A)  $\mathrm { W } _ { 1 } = 110.28 \mathrm { lb } ; \mathrm { W } _ { 2 } = 90.04 \mathrm { lb }$ 
B)  $\mathrm { W } _ { 1 } = 90.04 \mathrm { lb } ; \mathrm { W } _ { 2 } = 110.28 \mathrm { lb }$ 
C)  $\mathrm { W } _ { 1 } = 123 \mathrm { lb } ; \mathrm { W } _ { 2 } = 150.64 \mathrm { lb }$ 
D)  $W _ { 1 } = 45.02 \mathrm { lb } ; W _ { 2 } = 55.14 \mathrm { lb }$ 
A)  $\mathrm { W } _ { 1 } = 110.28 \mathrm { lb } ; \mathrm { W } _ { 2 } = 90.04 \mathrm { lb }$ 
B)  $\mathrm { W } _ { 1 } = 90.04 \mathrm { lb } ; \mathrm { W } _ { 2 } = 110.28 \mathrm { lb }$ 
C)  $\mathrm { W } _ { 1 } = 123 \mathrm { lb } ; \mathrm { W } _ { 2 } = 150.64 \mathrm { lb }$ 
D)  $W _ { 1 } = 45.02 \mathrm { lb } ; W _ { 2 } = 55.14 \mathrm { lb }$

Question 16

Use a graphing calculator to Express solutions with approximations to the nearest thousandth.
-$$0.4 x + \sqrt { 2 } y = 1$$
$\sqrt { 5 } x + 0.8 y = 1$

Accepted Answer

A)  $\{ ( 0.216,0.646 ) \}$ 
B)  $\{ ( 0.097,0.980 ) \}$ 
C)  $\{ ( 0.176,0.757 ) \}$ 
D)  $\varnothing$ 
A)  $\{ ( 0.216,0.646 ) \}$ 
B)  $\{ ( 0.097,0.980 ) \}$ 
C)  $\{ ( 0.176,0.757 ) \}$ 
D)  $\varnothing$

Question 17

Find the matrix product when possible.
-$$\left[ \begin{array} { r r r } 
8 & - 7 & - 7 \
- 6 & 5 & - 2
\end{array} \right] \left[ \begin{array} { r r r } 
- 3 & 7 & - 1 \
8 & - 9 & 9 \
4 & 1 & - 5
\end{array} \right]$$

Accepted Answer

A) 
$\left[\begin{array}{rrr}
8 & -7 & -7 \
-6 & 5 & -2 \
-3 & 7 & -1 \
8 & -9 & 9 \
4 & 1 & -5
\end{array}\right]$ 
B) 
$\left[\begin{array}{rrr}
-24 & -49 & 7 \
-48 & -45 & -18 \
-24 & 5 & 10
\end{array}\right]$ 
C) 
$$\left[ \begin{array} { r r } 
- 108 & 50 \
112 & - 89 \
- 36 & 61
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { r r r } 
- 108 & 112 & - 36 \
50 & - 89 & 61
\end{array} \right]$$ 
A) 
$\left[\begin{array}{rrr}
8 & -7 & -7 \
-6 & 5 & -2 \
-3 & 7 & -1 \
8 & -9 & 9 \
4 & 1 & -5
\end{array}\right]$ 
B) 
$\left[\begin{array}{rrr}
-24 & -49 & 7 \
-48 & -45 & -18 \
-24 & 5 & 10
\end{array}\right]$ 
C) 
$$\left[ \begin{array} { r r } 
- 108 & 50 \
112 & - 89 \
- 36 & 61
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { r r r } 
- 108 & 112 & - 36 \
50 & - 89 & 61
\end{array} \right]$$

Question 18

The following table shows the per capita cumquat consumption, in pounds, in the Virgin Islands in three different years. Find a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ that fits this data. Using this function, what would you predict the per capita cumquat consumption to be in year 14 ?

Accepted Answer

A)  80.1 lb 
B)  82.8 lb 
C)  83.9 lb 
D)  82.4 lb 
A)  80.1 lb 
B)  82.8 lb 
C)  83.9 lb 
D)  82.4 lb

Question 19

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
$\begin{array} { l } 
2 x + 8 y + 8 z = 24 \
x + 4 y + 4 z = - 4 \
x + y + z = - 6
\end{array}$

Accepted Answer

A)  Cramer's rule does not apply since $D = 0 ; \varnothing$ 
B)  Cramer's rule does not apply since D}=0 ;{(2z - 1, z+2, z)} 
C)   {(-1,5,-6)} 
D)   {(-6,-1,5)} 
A)  Cramer's rule does not apply since $D = 0 ; \varnothing$ 
B)  Cramer's rule does not apply since D}=0 ;{(2z - 1, z+2, z)} 
C)   {(-1,5,-6)} 
D)   {(-6,-1,5)}

Question 20

Momma's ice cream shop sells three types of ice cream: soft-serve, chunky, and nonfat. Location I sells 30 gal of soft-serve, 80 gal of chunky, and 30 gal of nonfat ice cream each day. Location II sells 35 gal of soft-serve and
Location III sells 60 gal of soft-serve each day. Daily sales of chunky ice cream are 90 gal at Location II and 120
Gal at Location III. At Location II, 19 gal of nonfat are sold each day, and 40 gal of nonfat are sold each day at Location
III. Write a $3 \times 3$ matrix that shows the sales figures for the three locations, with the rows representing the three locations. The incomes per gallon for soft-serve, chunky, and nonfat ice cream are $\$ 4 , \$ 5$, and $\$ 4$, respectively. Write a $3 \times 1$ matrix displaying the incomes. Find a matrix product that gives the daily income at each of the three locations.

Accepted Answer

A) 
$\left[ \begin{array} { l } 640 \ 666 \ 1000 \end{array} \right]$ 
B) 
$\left[ \begin{array} { l } 4 \ 5 \ 4 \end{array} \right]$ 
C) 
$\left[ \begin{array} { l } 500 \ 1450 \ 356 \end{array} \right]$ 
D) 
$\left[ \begin{array} { l } 690 \ 616 \ 1000 \end{array} \right]$ 
A) 
$\left[ \begin{array} { l } 640 \ 666 \ 1000 \end{array} \right]$ 
B) 
$\left[ \begin{array} { l } 4 \ 5 \ 4 \end{array} \right]$ 
C) 
$\left[ \begin{array} { l } 500 \ 1450 \ 356 \end{array} \right]$ 
D) 
$\left[ \begin{array} { l } 690 \ 616 \ 1000 \end{array} \right]$

Find the partial fraction decomposition for the rational expression. $\frac { - 5 x ^ { 2 } - 9 x + 11 } { ( x + 4 ) ^ { 2 } ( 3 x + 1 ) }$

Graph the solution set of the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\geq-4 $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq-x^{2} \\ y \leq x+1 \\ y \geq-5 \\ x \geq-4 \end{array}$

Provide an appropriate response. -For a certain system of two linear equations, the values of the determinants used in Cramer's rule are $D = 26$ , $D _ { x } = 23$ , and $D _ { y } = - 13$ . What is the solution set of the system?

Find the indicated matrix. -Let $C = \left[ \begin{array} { r } 6 \\ - 2 \\ 12 \end{array} \right]$ . Find $\frac { 1 } { 2 } C$

Find the value of the determinant. $\left| \begin{array} { r r r } 5 & 4 & 3 \\0 & 4 & 1 \\- 5 & 0 & 4\end{array} \right|$

If the system has infinitely many solutions, write the solution set with x arbitrary. - 3x+2y+z=4 2x-3y-z=5 5x+12y+5z=2

The perimeter of a rectangle is 44 cm. The length is 12 cm longer than the width. What are the length and width of the rectangle?

The sum of the squares of the digits of a positive two-digit number is 85, and the tens digit is 1 less than the units digit. Find the number.

Evaluate the determinant. $\left| \begin{array} { l l l l } 2 & 9 & 3 & 6 \\8 & 9 & 4 & 4 \\2 & 4 & 6 & 5 \\2 & 7 & 7 & 2\end{array} \right|$

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. 7x-5y=-21 -4x+3y=12

Graph the solution set of the system of inequalities. - y\geq y\leq8 $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq\left(\frac{1}{3}\right)^{x} \\ y \leq 8 \end{array}$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. -xy+=3 2+xy+2=12

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - $0.4 x + \sqrt { 2 } y = 1$ $\sqrt { 5 } x + 0.8 y = 1$

Find the matrix product when possible. - $\left[ \begin{array} { r r r } 8 & - 7 & - 7 \\- 6 & 5 & - 2\end{array} \right] \left[ \begin{array} { r r r } - 3 & 7 & - 1 \\8 & - 9 & 9 \\4 & 1 & - 5\end{array} \right]$

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. 2x+8y+8z=24 x+4y+4z=-4 x+y+z=-6

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 6: Systems and Matrices

Find the partial fraction decomposition for the rational expression. −5x2−9x+11(x+4)2(3x+1)\frac { - 5 x ^ { 2 } - 9 x + 11 } { ( x + 4 ) ^ { 2 } ( 3 x + 1 ) }(x+4)2(3x+1)−5x2−9x+11​

Graph the solution set of the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\geq-4

Provide an appropriate response. -For a certain system of two linear equations, the values of the determinants used in Cramer's rule are D=26D = 26D=26 , Dx=23D _ { x } = 23Dx​=23 , and Dy=−13D _ { y } = - 13Dy​=−13 . What is the solution set of the system?

Find the indicated matrix. -Let C=[6−212]C = \left[ \begin{array} { r } 6 \\ - 2 \\ 12 \end{array} \right]C=​6−212​​ . Find 12C\frac { 1 } { 2 } C21​C

Find the value of the determinant. ∣543041−504∣\left| \begin{array} { r r r } 5 & 4 & 3 \\0 & 4 & 1 \\- 5 & 0 & 4\end{array} \right|​50−5​440​314​​

If the system has infinitely many solutions, write the solution set with x arbitrary. - 3x+2y+z=4 2x-3y-z=5 5x+12y+5z=2

The perimeter of a rectangle is 44 cm. The length is 12 cm longer than the width. What are the length and width of the rectangle?

The sum of the squares of the digits of a positive two-digit number is 85, and the tens digit is 1 less than the units digit. Find the number.

Evaluate the determinant. ∣2936894424652772∣\left| \begin{array} { l l l l } 2 & 9 & 3 & 6 \\8 & 9 & 4 & 4 \\2 & 4 & 6 & 5 \\2 & 7 & 7 & 2\end{array} \right|​2822​9947​3467​6452​​

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. 7x-5y=-21 -4x+3y=12

Graph the solution set of the system of inequalities. - y\geq y\leq8

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. -xy+=3 2+xy+2=12

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - 0.4x+2y=10.4 x + \sqrt { 2 } y = 10.4x+2​y=1 5x+0.8y=1\sqrt { 5 } x + 0.8 y = 15​x+0.8y=1

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. 2x+8y+8z=24 x+4y+4z=-4 x+y+z=-6

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Arithmetic Sequence: Common Difference and First n Terms

Filters

Find the partial fraction decomposition for the rational expression. $\frac { - 5 x ^ { 2 } - 9 x + 11 } { ( x + 4 ) ^ { 2 } ( 3 x + 1 ) }$

Graph the solution set of the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\geq-4 $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq-x^{2} \\ y \leq x+1 \\ y \geq-5 \\ x \geq-4 \end{array}$

Provide an appropriate response. -For a certain system of two linear equations, the values of the determinants used in Cramer's rule are $D = 26$ , $D _ { x } = 23$ , and $D _ { y } = - 13$ . What is the solution set of the system?

Find the indicated matrix. -Let $C = \left[ \begin{array} { r } 6 \\ - 2 \\ 12 \end{array} \right]$ . Find $\frac { 1 } { 2 } C$

Find the value of the determinant. $\left| \begin{array} { r r r } 5 & 4 & 3 \\0 & 4 & 1 \\- 5 & 0 & 4\end{array} \right|$

Evaluate the determinant. $\left| \begin{array} { l l l l } 2 & 9 & 3 & 6 \\8 & 9 & 4 & 4 \\2 & 4 & 6 & 5 \\2 & 7 & 7 & 2\end{array} \right|$

Graph the solution set of the system of inequalities. - y\geq y\leq8 $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq\left(\frac{1}{3}\right)^{x} \\ y \leq 8 \end{array}$

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - $0.4 x + \sqrt { 2 } y = 1$ $\sqrt { 5 } x + 0.8 y = 1$