Question 1

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 3 x ^ { 2 } - 3 x - 2 } { x ^ { 3 } - x }$

Accepted Answer

A)  $\frac { 2 } { x } + \frac { 2 } { x + 1 } - \frac { 1 } { x + 1 }$ 
B)  $\frac { 2 } { x } + \frac { 2 } { x + 1 } - \frac { 1 } { x - 1 }$ 
C)  $\frac { 2 } { x } - \frac { 2 } { x + 1 } - \frac { 1 } { x - 1 }$ 
D)  $\frac { 2 } { x } + \frac { 2 } { x + 1 } + \frac { 1 } { x - 1 }$ 
E)  $\frac { 2 } { x } + \frac { 2 } { x - 1 } - \frac { 1 } { x - 1 }$ 
A)  $\frac { 2 } { x } + \frac { 2 } { x + 1 } - \frac { 1 } { x + 1 }$ 
B)  $\frac { 2 } { x } + \frac { 2 } { x + 1 } - \frac { 1 } { x - 1 }$ 
C)  $\frac { 2 } { x } - \frac { 2 } { x + 1 } - \frac { 1 } { x - 1 }$ 
D)  $\frac { 2 } { x } + \frac { 2 } { x + 1 } + \frac { 1 } { x - 1 }$ 
E)  $\frac { 2 } { x } + \frac { 2 } { x - 1 } - \frac { 1 } { x - 1 }$

Question 2

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. ​
Objective function:
​
Z = 5x + 6y
​
Constraints:
​
X ≥ 0
Y ≥ 0
X + y ≥ 8
3x + 5y ≥ 30
​

Accepted Answer

A)    No minimum 
B)    Minimum at (10, 0): 50 
C)    Minimum at (8, 0): 49 
D)    Minimum at (5, 3): 43 
E)    Minimum at (0, 8): 48 
A)    No minimum 
B)    Minimum at (10, 0): 50 
C)    Minimum at (8, 0): 49 
D)    Minimum at (5, 3): 43 
E)    Minimum at (0, 8): 48

Question 3

Use any method to solve the system of linear equations, find (x,y).  $\left\{ \begin{aligned}
- x + 3 y & = 15 \
2 x + 3 y & = 6
\end{aligned} \right.$

Accepted Answer

A)  (3, 4) 
B)  (4, -3) 
C)  (-3, -4) 
D)  (-3, 4) 
E)  (4, -3). 
A)  (3, 4) 
B)  (4, -3) 
C)  (-3, -4) 
D)  (-3, 4) 
E)  (4, -3).

Question 4

The linear programming problem has an unusual characteristic.Select a graph of the solution region for the problem and describe the unusual characteristic.Find the maximum value of the objective function (if possible) and where it occurs. ​
Z = 3x + 4y
​
Constraints:
​
X ≥ 0
Y ≥ 0
X + y ≤1
3x + y ≤ 6
​

Accepted Answer

A) ​   The constraint 3x + y ≤ 6 is extraneous. Maximum at (1, 1): 7 
B) ​   The constraint 3x + y ≤ 6 is extraneous. Maximum at (1, 0): 3 
C) ​   The constraint 3x + y ≤ 6 is extraneous. Maximum at (0, 1): 4 
D) ​   The constraint 3x + y ≤ 6 is extraneous. Maximum at (0, 0): 0 
E) ​   The constraint 3x + y ≤ 6 is extraneous. No maximum. 
A) ​   The constraint 3x + y ≤ 6 is extraneous. Maximum at (1, 1): 7 
B) ​   The constraint 3x + y ≤ 6 is extraneous. Maximum at (1, 0): 3 
C) ​   The constraint 3x + y ≤ 6 is extraneous. Maximum at (0, 1): 4 
D) ​   The constraint 3x + y ≤ 6 is extraneous. Maximum at (0, 0): 0 
E) ​   The constraint 3x + y ≤ 6 is extraneous. No maximum.

Question 5

Solve the system of linear equations. $$\left\{ \begin{array} { l l } 
- x + 2 y - 5 z & = - 24 \
2 x + 5 z & = 25 \
4 x + 4 y + 3 z & = 21
\end{array} \right.$$

Accepted Answer

A)   $( - 5,5,2 )$ 
B)   $( - 2,3,5 )$ 
C)   $( 5,2 , - 5 )$ 
D)   $( 5 , - 2,3 )$ 
E)   $( 5 , - 2,0 )$ 
A)   $( - 5,5,2 )$ 
B)   $( - 2,3,5 )$ 
C)   $( 5,2 , - 5 )$ 
D)   $( 5 , - 2,3 )$ 
E)   $( 5 , - 2,0 )$

Question 6

One eight-ounce glass of apple juice and one eight-ounce glass of orange juice contain a total of 176.4 milligrams of vitamin C.Twoeight-ounce glasses of apple juice and three eight-ounce glasses of orange juice contain a total of 432.7 milligrams of vitamin C.How much vitamin C is in an eight-ounce glass of each type of juice? ​

Accepted Answer

A) ​Apple juice: 96.5 mg; Orange juice: 96.5 mg 
B) Apple juice: 96.5 mg; Orange juice: 79.9 mg 
C) ​Apple juice: 79.9 mg; Orange juice: 79.9 mg 
D) ​Apple juice: 79.9 mg; Orange juice: 96.5 mg 
E) ​Apple juice: 176.4 mg; Orange juice: 79.9 mg 
A) ​Apple juice: 96.5 mg; Orange juice: 96.5 mg 
B) Apple juice: 96.5 mg; Orange juice: 79.9 mg 
C) ​Apple juice: 79.9 mg; Orange juice: 79.9 mg 
D) ​Apple juice: 79.9 mg; Orange juice: 96.5 mg 
E) ​Apple juice: 176.4 mg; Orange juice: 79.9 mg

Question 7

Fourty liters of a 40% acid solution is obtained by mixing a 28% solution with a 50% solution.Write a system of equations in which one equation represents the amount of final mixture required and the other represents the percent of acid in the final mixture.Let x and y represent the amounts of the 28% and 50% solutions, respectively.

Accepted Answer

A)   $\left\{ \begin{array} { l } 
x + y = 40 \
0.28 x + 0.5 y = 40
\end{array} \right.$ 
B)   $\left\{ \begin{array} { l } 
0.28 x + 0.5 y = 40 \
x + y = 16
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
x + y = 40 \
0.28 x + 0.5 y = 16
\end{array} \right.$. 
D)   $\left\{ \begin{array} { l } 
x + y = 40 \
0.28 x + 0.5 y = 16
\end{array} \right.$ 
E)   $\left\{ \begin{array} { l } 
0.28 x + 0.5 y = 40 \
x + y = 16
\end{array} \right.$. 
A)   $\left\{ \begin{array} { l } 
x + y = 40 \
0.28 x + 0.5 y = 40
\end{array} \right.$ 
B)   $\left\{ \begin{array} { l } 
0.28 x + 0.5 y = 40 \
x + y = 16
\end{array} \right.$ 
C)  $\left\{ \begin{array} { l } 
x + y = 40 \
0.28 x + 0.5 y = 16
\end{array} \right.$. 
D)   $\left\{ \begin{array} { l } 
x + y = 40 \
0.28 x + 0.5 y = 16
\end{array} \right.$ 
E)   $\left\{ \begin{array} { l } 
0.28 x + 0.5 y = 40 \
x + y = 16
\end{array} \right.$.

Question 8

Select the ordered pair that is a solution of the system of equations.  $\left\{ \begin{array} { c } 
2 x ^ { 2 } + y = - 11 \
- x - y = 12
\end{array} \right.$

Accepted Answer

A) (1, 13) 
B) (13, -1) 
C) (-1, -13) 
D) (1, -13) 
E) (13, 1) 
A) (1, 13) 
B) (13, -1) 
C) (-1, -13) 
D) (1, -13) 
E) (13, 1)

Question 9

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. ​
Objective function:
​
Z = 9x + 8y
​
Constraints:
​
X ≥ 0
Y ≥ 0
2x + 2y ≥ 10
X + 2y ≥ 6
​

Accepted Answer

A) ​   Minimum at (0, 5): 40 
B) ​   Minimum at (0, 5): 41 
C) ​   Minimum at (4, 1): 44 
D) ​   Minimum at (6, 0): 54 
E) ​   No minimum 
A) ​   Minimum at (0, 5): 40 
B) ​   Minimum at (0, 5): 41 
C) ​   Minimum at (4, 1): 44 
D) ​   Minimum at (6, 0): 54 
E) ​   No minimum

Question 10

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. ​
Objective function:
​
Z = 2x + 8y
​
Constraints:
​
X ≥ 0
Y ≥ 0
2x + y ≤ 12​   ​

Accepted Answer

A) Maximum at (6, 0): 24 
B) Maximum at (12, 0): 97 
C) Maximum at (0, 6): 25 
D) Maximum at (0, 12): 96 
E) Maximum at (0, 0): 0 
A) Maximum at (6, 0): 24 
B) Maximum at (12, 0): 97 
C) Maximum at (0, 6): 25 
D) Maximum at (0, 12): 96 
E) Maximum at (0, 0): 0

Question 11

Solve the system graphically.  $\left\{ \begin{aligned}
6 x + 8 y & = 48 \
x - 8 y & = - 20
\end{aligned} \right.$

Accepted Answer

A) (6, 3) 
B) (-4, -3) 
C) (4, 3) 
D) (6, 6) 
E) (-6, -6) 
A) (6, 3) 
B) (-4, -3) 
C) (4, 3) 
D) (6, 6) 
E) (-6, -6)

Question 12

Write the partial fraction decomposition of the rational expression.Check your result algebraically.  $\frac { 1 } { x ^ { 2 } - 16 }$

Accepted Answer

A)  $\frac { 1 } { 8 } \left( \frac { A } { x - 4 } - \frac { B } { x + 4 } \right)$ 
B)  $\frac { 8 } { x - 4 } - \frac { 8 } { x + 4 }$ 
C)  $\frac { 1 } { 8 } \left( \frac { 8 } { x - 4 } - \frac { 8 } { x + 4 } \right)$ 
D)  $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } - \frac { 1 } { x + 4 } \right)$ 
E)  $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } + \frac { 1 } { x + 4 } \right)$ 
A)  $\frac { 1 } { 8 } \left( \frac { A } { x - 4 } - \frac { B } { x + 4 } \right)$ 
B)  $\frac { 8 } { x - 4 } - \frac { 8 } { x + 4 }$ 
C)  $\frac { 1 } { 8 } \left( \frac { 8 } { x - 4 } - \frac { 8 } { x + 4 } \right)$ 
D)  $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } - \frac { 1 } { x + 4 } \right)$ 
E)  $\frac { 1 } { 8 } \left( \frac { 1 } { x - 4 } + \frac { 1 } { x + 4 } \right)$

Question 13

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically.  $\left\{ \begin{array} { l } 
2 x + 7 y = \frac { 112 } { 9 } \
7 x + 8 y = \frac { 62 } { 9 }
\end{array} \right.$

Accepted Answer

A)  $\left( \frac { - 14 } { 9 } , \frac { 20 } { 9 } \right)$ 
B)   $\left( \frac { 20 } { 9 } , \frac { - 14 } { 9 } \right)$ 
C)   $\left( \frac { 20 } { 9 } , \frac { 14 } { 9 } \right)$ 
D)   $\left( \frac { 14 } { 9 } , \frac { 20 } { 9 } \right)$ 
E)   $\left( \frac { 14 } { 9 } , \frac { - 20 } { 9 } \right)$ 
A)  $\left( \frac { - 14 } { 9 } , \frac { 20 } { 9 } \right)$ 
B)   $\left( \frac { 20 } { 9 } , \frac { - 14 } { 9 } \right)$ 
C)   $\left( \frac { 20 } { 9 } , \frac { 14 } { 9 } \right)$ 
D)   $\left( \frac { 14 } { 9 } , \frac { 20 } { 9 } \right)$ 
E)   $\left( \frac { 14 } { 9 } , \frac { - 20 } { 9 } \right)$

Question 14

Select the ordered pair that is a solution of the system of equations.  $\left\{ \begin{array} { l } 
2 x - y = 3 \
8 x + y = - 18
\end{array} \right.$

Accepted Answer

A) (-6, $- \frac { 3 } { 2 }$ ) 
B) (3, 6) 
C) ( $- \frac { 3 } { 2 }$ , -6) 
D) ( $\frac { 3 } { 2 }$ , 6) 
E) (-3, -6) 
A) (-6, $- \frac { 3 } { 2 }$ ) 
B) (3, 6) 
C) ( $- \frac { 3 } { 2 }$ , -6) 
D) ( $\frac { 3 } { 2 }$ , 6) 
E) (-3, -6)

Question 15

The linear programming problem has an unusual characteristic.Select a graph of the solution region for the problem and describe the unusual characteristic.Find the minimum value of the objective function (if possible) and where it occurs. ​
Objective function:
​
Z = x + y
​
Constraints:
​
X ≥ 0
Y ≥ 0
-x + y ≤ 1
-x + 5y ≤ 7
​

Accepted Answer

A)    Minimum at (0, 1): 1 
B)    Minimum at (1.5, 0.5): 2 
C)    Minimum at (0.5, 1.5): 2 
D) ​   Minimum at (0, 0): 0 
E)    No minimum. 
A)    Minimum at (0, 1): 1 
B)    Minimum at (1.5, 0.5): 2 
C)    Minimum at (0.5, 1.5): 2 
D) ​   Minimum at (0, 0): 0 
E)    No minimum.

Question 16

Solve the system, if possible.   $\left\{ \begin{array} { l } 
x + y = - 9 \
y + z = - 15 \
2 x - z = 7
\end{array} \right.$

Accepted Answer

A) x = -9, y = 12, z = 5 
B) x = 1, y = -10, z = -5 
C) x = -1, y = 10, z = 5 
D) x = -9, y = 1, z = 5 
E) no solution; inconsistent system 
A) x = -9, y = 12, z = 5 
B) x = 1, y = -10, z = -5 
C) x = -1, y = 10, z = 5 
D) x = -9, y = 1, z = 5 
E) no solution; inconsistent system

Question 17

Write the partial fraction decomposition of the rational expression.Check your result algebraically.  $\frac { 8 } { x ^ { 2 } + 2 x - 3 }$

Accepted Answer

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

Question 18

Write the form of the partial fraction decomposition of the rational expression $\frac { 6 x - 1 } { x \left( x ^ { 2 } - 16 \right) }$

Accepted Answer

A)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x ^ { 2 } - 16 }$ 
B)  $\frac { A } { 6 x } + \frac { B x + C } { 6 ( x + 4 ) } + \frac { C x + D } { 6 ( x - 4 ) }$ 
C)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x - 16 }$ 
D)  $\frac { A } { x } + \frac { B } { x + 4 } + \frac { C } { x - 4 }$ 
E)  $\frac { A } { x } - \frac { B } { ( x + 16 ) ( x - 16 ) }$ 
A)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x ^ { 2 } - 16 }$ 
B)  $\frac { A } { 6 x } + \frac { B x + C } { 6 ( x + 4 ) } + \frac { C x + D } { 6 ( x - 4 ) }$ 
C)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x - 16 }$ 
D)  $\frac { A } { x } + \frac { B } { x + 4 } + \frac { C } { x - 4 }$ 
E)  $\frac { A } { x } - \frac { B } { ( x + 16 ) ( x - 16 ) }$

Question 19

Solve the system of linear equations and check any solution algebraically. $\left\{ \begin{array} { c c } 
x + y + z & = 16 \
2 x - y + z & = 18 \
3 x - z & = 19
\end{array} \right.$

Accepted Answer

A)   $( 8 , - 3 , - 5 )$ 
B)   $( - 8 , - 3,5 )$ 
C)   $( 8,3,5 )$ 
D)    $( - 8 , - 3 , - 5 )$ 
E)   $( 8 , - 3,5 )$ 
A)   $( 8 , - 3 , - 5 )$ 
B)   $( - 8 , - 3,5 )$ 
C)   $( 8,3,5 )$ 
D)    $( - 8 , - 3 , - 5 )$ 
E)   $( 8 , - 3,5 )$

Question 20

Determine whether the ordered triple is a solution of the system of equations.  $$\left\{ \begin{aligned}
4 x + y - z & = 0 \
- 8 x - 6 y + z & = - \frac { 7 } { 4 } \
3 x - y & = - \frac { 9 } { 4 }
\end{aligned} \right.$$   $$\left( \frac { - 1 } { 2 } , \frac { 3 } { 4 } , \frac { - 5 } { 4 } \right)$$

Accepted Answer

A) True 
 B)False

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 3 x ^ { 2 } - 3 x - 2 } { x ^ { 3 } - x }$

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: Z = 5x + 6y Constraints: X ≥ 0 Y ≥ 0 X + y ≥ 8 3x + 5y ≥ 30

Use any method to solve the system of linear equations, find (x,y). $\left\{ \begin{aligned}- x + 3 y & = 15 \\2 x + 3 y & = 6\end{aligned} \right.$

Solve the system of linear equations. $\left\{ \begin{array} { l l } - x + 2 y - 5 z & = - 24 \\2 x + 5 z & = 25 \\4 x + 4 y + 3 z & = 21\end{array} \right.$

Select the ordered pair that is a solution of the system of equations. $\left\{ \begin{array} { c } 2 x ^ { 2 } + y = - 11 \\- x - y = 12\end{array} \right.$

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: Z = 9x + 8y Constraints: X ≥ 0 Y ≥ 0 2x + 2y ≥ 10 X + 2y ≥ 6

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. Objective function: Z = 2x + 8y Constraints: X ≥ 0 Y ≥ 0 2x + y ≤ 12

Solve the system graphically. $\left\{ \begin{aligned}6 x + 8 y & = 48 \\x - 8 y & = - 20\end{aligned} \right.$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 1 } { x ^ { 2 } - 16 }$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } 2 x + 7 y = \frac { 112 } { 9 } \\7 x + 8 y = \frac { 62 } { 9 }\end{array} \right.$

Select the ordered pair that is a solution of the system of equations. $\left\{ \begin{array} { l } 2 x - y = 3 \\8 x + y = - 18\end{array} \right.$

Solve the system, if possible. $\left\{ \begin{array} { l } x + y = - 9 \\y + z = - 15 \\2 x - z = 7\end{array} \right.$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 8 } { x ^ { 2 } + 2 x - 3 }$

Write the form of the partial fraction decomposition of the rational expression $\frac { 6 x - 1 } { x \left( x ^ { 2 } - 16 \right) }$

Solve the system of linear equations and check any solution algebraically. $\left\{ \begin{array} { c c } x + y + z & = 16 \\2 x - y + z & = 18 \\3 x - z & = 19\end{array} \right.$

Determine whether the ordered triple is a solution of the system of equations. $\left\{ \begin{aligned}4 x + y - z & = 0 \\- 8 x - 6 y + z & = - \frac { 7 } { 4 } \\3 x - y & = - \frac { 9 } { 4 }\end{aligned} \right.$ $\left( \frac { - 1 } { 2 } , \frac { 3 } { 4 } , \frac { - 5 } { 4 } \right)$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 7: Systems Of Equations and Inequalities

Write the partial fraction decomposition of the rational expression.Check your result algebraically. 3x2−3x−2x3−x\frac { 3 x ^ { 2 } - 3 x - 2 } { x ^ { 3 } - x }x3−x3x2−3x−2​

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. ​ Objective function: ​ Z = 5x + 6y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X + y ≥ 8 3x + 5y ≥ 30 ​

Use any method to solve the system of linear equations, find (x,y). {−x+3y=152x+3y=6\left\{ \begin{aligned}- x + 3 y & = 15 \\2 x + 3 y & = 6\end{aligned} \right.{−x+3y2x+3y​=15=6​

Solve the system of linear equations. {−x+2y−5z=−242x+5z=254x+4y+3z=21\left\{ \begin{array} { l l } - x + 2 y - 5 z & = - 24 \\2 x + 5 z & = 25 \\4 x + 4 y + 3 z & = 21\end{array} \right.⎩⎨⎧​−x+2y−5z2x+5z4x+4y+3z​=−24=25=21​

Select the ordered pair that is a solution of the system of equations. {2x2+y=−11−x−y=12\left\{ \begin{array} { c } 2 x ^ { 2 } + y = - 11 \\- x - y = 12\end{array} \right.{2x2+y=−11−x−y=12​

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. ​ Objective function: ​ Z = 9x + 8y ​ Constraints: ​ X ≥ 0 Y ≥ 0 2x + 2y ≥ 10 X + 2y ≥ 6 ​

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. ​ Objective function: ​ Z = 2x + 8y ​ Constraints: ​ X ≥ 0 Y ≥ 0 2x + y ≤ 12​ ​

Solve the system graphically. {6x+8y=48x−8y=−20\left\{ \begin{aligned}6 x + 8 y & = 48 \\x - 8 y & = - 20\end{aligned} \right.{6x+8yx−8y​=48=−20​

Write the partial fraction decomposition of the rational expression.Check your result algebraically. 1x2−16\frac { 1 } { x ^ { 2 } - 16 }x2−161​

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. {2x+7y=11297x+8y=629\left\{ \begin{array} { l } 2 x + 7 y = \frac { 112 } { 9 } \\7 x + 8 y = \frac { 62 } { 9 }\end{array} \right.{2x+7y=9112​7x+8y=962​​

Select the ordered pair that is a solution of the system of equations. {2x−y=38x+y=−18\left\{ \begin{array} { l } 2 x - y = 3 \\8 x + y = - 18\end{array} \right.{2x−y=38x+y=−18​

Solve the system, if possible. {x+y=−9y+z=−152x−z=7\left\{ \begin{array} { l } x + y = - 9 \\y + z = - 15 \\2 x - z = 7\end{array} \right.⎩⎨⎧​x+y=−9y+z=−152x−z=7​

Write the partial fraction decomposition of the rational expression.Check your result algebraically. 8x2+2x−3\frac { 8 } { x ^ { 2 } + 2 x - 3 }x2+2x−38​

Write the form of the partial fraction decomposition of the rational expression 6x−1x(x2−16)\frac { 6 x - 1 } { x \left( x ^ { 2 } - 16 \right) }x(x2−16)6x−1​

Solve the system of linear equations and check any solution algebraically. {x+y+z=162x−y+z=183x−z=19\left\{ \begin{array} { c c } x + y + z & = 16 \\2 x - y + z & = 18 \\3 x - z & = 19\end{array} \right.⎩⎨⎧​x+y+z2x−y+z3x−z​=16=18=19​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 3 x ^ { 2 } - 3 x - 2 } { x ^ { 3 } - x }$

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: Z = 5x + 6y Constraints: X ≥ 0 Y ≥ 0 X + y ≥ 8 3x + 5y ≥ 30

Use any method to solve the system of linear equations, find (x,y). $\left\{ \begin{aligned}- x + 3 y & = 15 \\2 x + 3 y & = 6\end{aligned} \right.$

Solve the system of linear equations. $\left\{ \begin{array} { l l } - x + 2 y - 5 z & = - 24 \\2 x + 5 z & = 25 \\4 x + 4 y + 3 z & = 21\end{array} \right.$

Select the ordered pair that is a solution of the system of equations. $\left\{ \begin{array} { c } 2 x ^ { 2 } + y = - 11 \\- x - y = 12\end{array} \right.$

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: Z = 9x + 8y Constraints: X ≥ 0 Y ≥ 0 2x + 2y ≥ 10 X + 2y ≥ 6

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. Objective function: Z = 2x + 8y Constraints: X ≥ 0 Y ≥ 0 2x + y ≤ 12

Solve the system graphically. $\left\{ \begin{aligned}6 x + 8 y & = 48 \\x - 8 y & = - 20\end{aligned} \right.$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 1 } { x ^ { 2 } - 16 }$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } 2 x + 7 y = \frac { 112 } { 9 } \\7 x + 8 y = \frac { 62 } { 9 }\end{array} \right.$

Select the ordered pair that is a solution of the system of equations. $\left\{ \begin{array} { l } 2 x - y = 3 \\8 x + y = - 18\end{array} \right.$

Solve the system, if possible. $\left\{ \begin{array} { l } x + y = - 9 \\y + z = - 15 \\2 x - z = 7\end{array} \right.$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 8 } { x ^ { 2 } + 2 x - 3 }$

Write the form of the partial fraction decomposition of the rational expression $\frac { 6 x - 1 } { x \left( x ^ { 2 } - 16 \right) }$

Solve the system of linear equations and check any solution algebraically. $\left\{ \begin{array} { c c } x + y + z & = 16 \\2 x - y + z & = 18 \\3 x - z & = 19\end{array} \right.$