Question 1

Write the partial fraction decomposition of the rational expression.Check your result algebraically.  26
$$\overline { x ^ { 2 } + 3 x - 40 }$$

Accepted Answer

A)  $\frac { 1 } { x - 5 } + \frac { 1 } { x + 8 }$ 
B)  $\frac { 1 } { x - 5 } - \frac { 1 } { x + 8 }$ 
C)  $\frac { 2 } { x - 5 } - \frac { 2 } { x + 8 }$ 
D)  $\frac { 2 } { x + 5 } - \frac { 2 } { x - 8 }$ 
E)  $\frac { 2 } { x - 5 } + \frac { 2 } { x + 8 }$ 
A)  $\frac { 1 } { x - 5 } + \frac { 1 } { x + 8 }$ 
B)  $\frac { 1 } { x - 5 } - \frac { 1 } { x + 8 }$ 
C)  $\frac { 2 } { x - 5 } - \frac { 2 } { x + 8 }$ 
D)  $\frac { 2 } { x + 5 } - \frac { 2 } { x - 8 }$ 
E)  $\frac { 2 } { x - 5 } + \frac { 2 } { x + 8 }$

Question 2

A residential building contractor borrowed $29,000 to complete a new home.Some of the money was borrowed at 4%, some at 6%, and some at 7%.How much was borrowed at each rate if the annual interest owed was $1,580 and the amount borrowed at 6% is two times more than the amount borrowed at 7%?

Accepted Answer

A) $11,000 at 4%; $12,000 at 6%; $6,000 at 7% 
B) $9,000 at 4%; $14,000 at 6%; $6,000 at 7% 
C) $9,000 at 4%; $13,000 at 6%; $7,000 at 7% 
D) $10,000 at 4%; $10,000 at 6%; $8,000 at 7% 
E) $10,000 at 4%; $14,000 at 6%; $7,000 at 7% 
A) $11,000 at 4%; $12,000 at 6%; $6,000 at 7% 
B) $9,000 at 4%; $14,000 at 6%; $6,000 at 7% 
C) $9,000 at 4%; $13,000 at 6%; $7,000 at 7% 
D) $10,000 at 4%; $10,000 at 6%; $8,000 at 7% 
E) $10,000 at 4%; $14,000 at 6%; $7,000 at 7%

Question 3

Solve the system of linear equations and check any solution algebraically.  $\left\{ \begin{array} { l } 
2 x + 2 z = 14 \
5 x + 3 y = 16 \
3 y - 4 z = 16
\end{array} \right.$

Accepted Answer

A)   $( - 28 , - 52 , - 35 )$ 
B)   $( 28 , - 52 , - 35 )$ 
C)   $( - 28,52,35 )$ 
D)   $( 28 , - 52,35 )$ 
E)   $( 28,52,35 )$ 
A)   $( - 28 , - 52 , - 35 )$ 
B)   $( 28 , - 52 , - 35 )$ 
C)   $( - 28,52,35 )$ 
D)   $( 28 , - 52,35 )$ 
E)   $( 28,52,35 )$

Question 4

Solve the system by the method of substitution.   $\left\{ \begin{array} { l } 
\frac { 1 } { 10 } x + \frac { 3 } { 10 } y = 1 \
- \frac { 1 } { 5 } x + \frac { 2 } { 5 } y = 1
\end{array} \right.$

Accepted Answer

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

Question 5

Find the dimensions of the rectangle meeting the specified condition. ​
The perimeter is 36 meters and the length is 4 meters greater than the width.
​

Accepted Answer

A) 13 m × 7 m 
B) 13 m × 9 m 
C) 11 m × 7 m 
D) 15 m × 11 m 
E) 11 m × 11 m 
A) 13 m × 7 m 
B) 13 m × 9 m 
C) 11 m × 7 m 
D) 15 m × 11 m 
E) 11 m × 11 m

Question 6

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 1 } { x ^ { 2 } + 6 x }$

Accepted Answer

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

Question 7

Write the partial fraction decomposition of the rational expression.Check your result algebraically.  $\frac { x + 1 } { x ^ { 2 } - 2 x - 8 }$

Accepted Answer

A)  $\frac { 1 } { 6 } \left( \frac { 2 } { x - 4 } - \frac { 4 } { x + 2 } \right)$ 
B)  $\frac { 1 } { 2 } \left( \frac { 5 } { x - 4 } - \frac { 1 } { x + 2 } \right)$ 
C)  $\frac { 1 } { 6 } \left( \frac { 5 } { x - 4 } - \frac { 1 } { x + 2 } \right)$ 
D)  $\frac { 1 } { 4 } \left( \frac { 5 } { x - 4 } - \frac { 1 } { x + 2 } \right)$ 
E)  $\frac { 1 } { 6 } \left( \frac { 5 } { x - 4 } + \frac { 1 } { x + 2 } \right)$ 
A)  $\frac { 1 } { 6 } \left( \frac { 2 } { x - 4 } - \frac { 4 } { x + 2 } \right)$ 
B)  $\frac { 1 } { 2 } \left( \frac { 5 } { x - 4 } - \frac { 1 } { x + 2 } \right)$ 
C)  $\frac { 1 } { 6 } \left( \frac { 5 } { x - 4 } - \frac { 1 } { x + 2 } \right)$ 
D)  $\frac { 1 } { 4 } \left( \frac { 5 } { x - 4 } - \frac { 1 } { x + 2 } \right)$ 
E)  $\frac { 1 } { 6 } \left( \frac { 5 } { x - 4 } + \frac { 1 } { x + 2 } \right)$

Question 8

Select the region determined by the constraints.Then find the maximum value of the objective function (if possible) and where it occurs, subject to the indicated constraints.  
Objective function:
 $z = 7 x + \frac { 1 } { 8 } y$  
Constraints:  $$\begin{aligned}
x & \geq 0 \
y & \geq 0 \
\frac { 1 } { 2 } x + y & \leq 8 \
x + \frac { 1 } { 2 } y & \geq 4
\end{aligned}$$

Accepted Answer

A)    Maximum at (4, 0): 28.00 
B)    Maximum at (8, 0): 2.00 
C)    Maximum at (16, 0): 112.00 
D)    No maximum 
E)    Maximum at (0, 8): 1.00 
A)    Maximum at (4, 0): 28.00 
B)    Maximum at (8, 0): 2.00 
C)    Maximum at (16, 0): 112.00 
D)    No maximum 
E)    Maximum at (0, 8): 1.00

Question 9

Seven hundred gallons of 91-octane gasoline is obtained by mixing 87-octane gasoline with 94-octane gasoline.Write a system of equations in which one equation represents the amount of final mixture required and the other represents the amounts of 87- and 94-octane gasolines in the final mixture.Let x and y represent the numbers of gallons of 87-octane and 94-octane gasolines, respectively.

Accepted Answer

A)   $\left\{ \begin{array} { c } 
x + y = 85 \
87 x + 94 y = 63,700
\end{array} \right.$ 
B)   $\left\{ \begin{array} { c } 
87 x + 94 y = 700 \
x + y = 85
\end{array} \right.$ 
C)   $\left\{ \begin{array} { l } 
x + y = 63,700 \
87 x + 94 y = 85
\end{array} \right.$ 
D)   $\left\{ \begin{array} { c } 
87 x + 94 y = 700 \
x + y = 63,700
\end{array} \right.$ 
E)   $\left\{ \begin{array} { c } 
x + y = 700 \
87 x + 94 y = 63,700
\end{array} \right.$ 
A)   $\left\{ \begin{array} { c } 
x + y = 85 \
87 x + 94 y = 63,700
\end{array} \right.$ 
B)   $\left\{ \begin{array} { c } 
87 x + 94 y = 700 \
x + y = 85
\end{array} \right.$ 
C)   $\left\{ \begin{array} { l } 
x + y = 63,700 \
87 x + 94 y = 85
\end{array} \right.$ 
D)   $\left\{ \begin{array} { c } 
87 x + 94 y = 700 \
x + y = 63,700
\end{array} \right.$ 
E)   $\left\{ \begin{array} { c } 
x + y = 700 \
87 x + 94 y = 63,700
\end{array} \right.$

Question 10

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints.(You should graph the feasible solutions on the grid below before you attempt to find the minimum and maximum values.) Objective function:
Z = 6x - 7y
Constraints: $$\left\{ \begin{array} { l } 
x \geq 0 \
y \geq 0 \
5 x + 4 y \leq 20 \
3 x + 2 y \leq 6
\end{array} \right.$$

Accepted Answer

A) maximum = 24 at (4, 0) 
B) The maximum is unbounded. 
C) maximum = 35 at (0, 5) 
D) maximum = 12 at (2, 0) 
E) There is no maximum. The feasable solution set is empty. 
A) maximum = 24 at (4, 0) 
B) The maximum is unbounded. 
C) maximum = 35 at (0, 5) 
D) maximum = 12 at (2, 0) 
E) There is no maximum. The feasable solution set is empty.

Question 11

Solve the system of linear equations by the method of elimination.Use the graph to check your solution.  $\left\{ \begin{array} { c } 
x + y = 0 \
9 x + 8 y = 1
\end{array} \right.$

Accepted Answer

A)  (1, -1)    
B)  (0, 1)   
C)  (-1, 1)    
D)  (1, 1)    
E)  (-1, -1)    
A)  (1, -1)    
B)  (0, 1)   
C)  (-1, 1)    
D)  (1, 1)    
E)  (-1, -1)

Question 12

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 + 2y
​
Constraints:
​
X ≥ 0
Y ≥ 0
X ≤ 10
X + y ≤ 8
​

Accepted Answer

A) ​   The constraint x ≤ 10 is extraneous. Minimum at (0, 8): 16 
B)    The constraint x ≤ 10 is extraneous. Minimum at (8, 0): -8 
C)    The constraint x ≤ 10 is extraneous. No minimum. 
D)    The constraint x ≤ 10 is extraneous. Minimum at (8, 8): 8 
E)    The constraint x ≤ 10 is extraneous. Minimum at (0, 0): 0 
A) ​   The constraint x ≤ 10 is extraneous. Minimum at (0, 8): 16 
B)    The constraint x ≤ 10 is extraneous. Minimum at (8, 0): -8 
C)    The constraint x ≤ 10 is extraneous. No minimum. 
D)    The constraint x ≤ 10 is extraneous. Minimum at (8, 8): 8 
E)    The constraint x ≤ 10 is extraneous. Minimum at (0, 0): 0

Question 13

Select a set of inequalities to describe the region.

Accepted Answer

A)  $\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 9
\end{array} \right.$ 
B)  $\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 1
\end{array} \right.$ 
C)  $\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 4
\end{array} \right.$ 
D)  $\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 25
\end{array} \right.$ 
E)  $\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 16
\end{array} \right.$ 
A)  $\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 9
\end{array} \right.$ 
B)  $\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 1
\end{array} \right.$ 
C)  $\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 4
\end{array} \right.$ 
D)  $\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 25
\end{array} \right.$ 
E)  $\left\{ \begin{array} { c } 
x \geq 0 \
y \geq 0 \
x ^ { 2 } + y ^ { 2 } < 16
\end{array} \right.$

Question 14

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points $( - 4 , - 1 ) , ( - 6 , - 3 ) , ( - 2 , - 3 )$ .

Accepted Answer

A)   $x ^ { 2 } + y ^ { 2 } + 8 x + 6 y + 29 = 0$ 
B)   $x ^ { 2 } + y ^ { 2 } + 4 x + 3 y - 4 = 0$ 
C)   $x ^ { 2 } + y ^ { 2 } + 8 x + 6 y - 4 = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 4 x + 3 y + 21 = 0$ 
E)   $x ^ { 2 } + y ^ { 2 } + 8 x + 6 y + 21 = 0$ 
A)   $x ^ { 2 } + y ^ { 2 } + 8 x + 6 y + 29 = 0$ 
B)   $x ^ { 2 } + y ^ { 2 } + 4 x + 3 y - 4 = 0$ 
C)   $x ^ { 2 } + y ^ { 2 } + 8 x + 6 y - 4 = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 4 x + 3 y + 21 = 0$ 
E)   $x ^ { 2 } + y ^ { 2 } + 8 x + 6 y + 21 = 0$

Question 15

If a system of three linear equations is inconsistent, then its graph has one points common to all three equations.

Accepted Answer

A) True 
 B)False

Question 16

Solve the system by the method of substitution.   $\left\{ \begin{array} { l } 
1.3 x + 0.6 y = 5.7 \
0.9 x - 0.2 y = 2.1
\end{array} \right.$

Accepted Answer

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

Question 17

Write the partial fraction decomposition of the rational expression.Check your result algebraically.  $\frac { 5 } { x ^ { 2 } + 5 x }$

Accepted Answer

A)  $\frac { A } { x } + \frac { B } { x - 5 }$ 
B)  $\frac { 1 } { x } - \frac { 1 } { x + 5 }$ 
C)  $\frac { 1 } { x } + \frac { 1 } { x + 5 }$ 
D)  $\frac { A } { x } - \frac { B } { x - 5 }$ 
E)  $\frac { 1 } { x } - \frac { 1 } { x - 5 }$ 
A)  $\frac { A } { x } + \frac { B } { x - 5 }$ 
B)  $\frac { 1 } { x } - \frac { 1 } { x + 5 }$ 
C)  $\frac { 1 } { x } + \frac { 1 } { x + 5 }$ 
D)  $\frac { A } { x } - \frac { B } { x - 5 }$ 
E)  $\frac { 1 } { x } - \frac { 1 } { x - 5 }$

Question 18

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. ​
Objective function:
​
​
Z = 5x + 8y
​
Constraints:
​
X ≥ 0
Y ≥ 0
X + 3y ≤ 15
4x + y ≤ 16
​​   ​

Accepted Answer

A) Maximum at (3, 4): 47 
B) Maximum at (4, 0): 20 
C) Maximum at (5, 0): 44 
D) Maximum at (0, 5): 40 
E) Maximum at (0, 0): 0 
A) Maximum at (3, 4): 47 
B) Maximum at (4, 0): 20 
C) Maximum at (5, 0): 44 
D) Maximum at (0, 5): 40 
E) Maximum at (0, 0): 0

Question 19

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:
 $z = 7 x + \frac { 1 } { 4 } y$  
Constraints:  $\begin{aligned}
x & \geq 0 \
y & \geq 0 \
\frac { 1 } { 2 } x + y & \leq 8 \
x + \frac { 1 } { 2 } y & \geq 4
\end{aligned}$

Accepted Answer

A)     Minimum at (8, 0): 3.00 
B)    No minimum 
C)     Minimum at (4, 0): 28.00 
D)     Minimum at (16, 0): 112.00 
E)     Minimum at (0, 8): 2.00 
A)     Minimum at (8, 0): 3.00 
B)    No minimum 
C)     Minimum at (4, 0): 28.00 
D)     Minimum at (16, 0): 112.00 
E)     Minimum at (0, 8): 2.00

Question 20

Solve the system of linear equations by the method of elimination, find (x,y).  $\left\{ \begin{array} { c } 
- 5 x + 2 y = - 38 \
3 x - y = 23
\end{array} \right.$

Accepted Answer

A) No solution 
B)   $( 8,1 )$ 
C)   $( 8 , - 1 )$ 
D)   $\left( \frac { 3 } { 38 } , \frac { 2 } { 23 } \right)$ 
E)   $\left( - 5 , \frac { 2 } { 23 } \right)$ 
A) No solution 
B)   $( 8,1 )$ 
C)   $( 8 , - 1 )$ 
D)   $\left( \frac { 3 } { 38 } , \frac { 2 } { 23 } \right)$ 
E)   $\left( - 5 , \frac { 2 } { 23 } \right)$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. 26 $\overline { x ^ { 2 } + 3 x - 40 }$

A residential building contractor borrowed $29,000 to complete a new home.Some of the money was borrowed at 4%, some at 6%, and some at 7%.How much was borrowed at each rate if the annual interest owed was $1,580 and the amount borrowed at 6% is two times more than the amount borrowed at 7%?

Solve the system of linear equations and check any solution algebraically. $\left\{ \begin{array} { l } 2 x + 2 z = 14 \\5 x + 3 y = 16 \\3 y - 4 z = 16\end{array} \right.$

Solve the system by the method of substitution. $\left\{ \begin{array} { l } \frac { 1 } { 10 } x + \frac { 3 } { 10 } y = 1 \\- \frac { 1 } { 5 } x + \frac { 2 } { 5 } y = 1\end{array} \right.$

Find the dimensions of the rectangle meeting the specified condition. The perimeter is 36 meters and the length is 4 meters greater than the width.

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 1 } { x ^ { 2 } + 6 x }$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { x + 1 } { x ^ { 2 } - 2 x - 8 }$

Select the region determined by the constraints.Then find the maximum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: $z = 7 x + \frac { 1 } { 8 } y$ Constraints: x \geq0 y \geq0 x+y \leq8 x+y \geq4

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. $\left\{ \begin{array} { c } x + y = 0 \\9 x + 8 y = 1\end{array} \right.$

Select a set of inequalities to describe the region.

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points $( - 4 , - 1 ) , ( - 6 , - 3 ) , ( - 2 , - 3 )$ .

If a system of three linear equations is inconsistent, then its graph has one points common to all three equations.

Solve the system by the method of substitution. $\left\{ \begin{array} { l } 1.3 x + 0.6 y = 5.7 \\0.9 x - 0.2 y = 2.1\end{array} \right.$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 5 } { x ^ { 2 } + 5 x }$

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. Objective function: Z = 5x + 8y Constraints: X ≥ 0 Y ≥ 0 X + 3y ≤ 15 4x + y ≤ 16

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: $z = 7 x + \frac { 1 } { 4 } y$ Constraints: x \geq0 y \geq0 x+y \leq8 x+y \geq4

Solve the system of linear equations by the method of elimination, find (x,y). $\left\{ \begin{array} { c } - 5 x + 2 y = - 38 \\3 x - y = 23\end{array} \right.$

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. 26 x2+3x−40‾\overline { x ^ { 2 } + 3 x - 40 }x2+3x−40​

A residential building contractor borrowed $29,000 to complete a new home.Some of the money was borrowed at 4%, some at 6%, and some at 7%.How much was borrowed at each rate if the annual interest owed was $1,580 and the amount borrowed at 6% is two times more than the amount borrowed at 7%?

Solve the system of linear equations and check any solution algebraically. {2x+2z=145x+3y=163y−4z=16\left\{ \begin{array} { l } 2 x + 2 z = 14 \\5 x + 3 y = 16 \\3 y - 4 z = 16\end{array} \right.⎩⎨⎧​2x+2z=145x+3y=163y−4z=16​

Solve the system by the method of substitution. {110x+310y=1−15x+25y=1\left\{ \begin{array} { l } \frac { 1 } { 10 } x + \frac { 3 } { 10 } y = 1 \\- \frac { 1 } { 5 } x + \frac { 2 } { 5 } y = 1\end{array} \right.{101​x+103​y=1−51​x+52​y=1​

Find the dimensions of the rectangle meeting the specified condition. ​ The perimeter is 36 meters and the length is 4 meters greater than the width. ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. 1x2+6x\frac { 1 } { x ^ { 2 } + 6 x }x2+6x1​

Write the partial fraction decomposition of the rational expression.Check your result algebraically. x+1x2−2x−8\frac { x + 1 } { x ^ { 2 } - 2 x - 8 }x2−2x−8x+1​

Select the region determined by the constraints.Then find the maximum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: z=7x+18yz = 7 x + \frac { 1 } { 8 } yz=7x+81​y Constraints: x \geq0 y \geq0 x+y \leq8 x+y \geq4

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. {x+y=09x+8y=1\left\{ \begin{array} { c } x + y = 0 \\9 x + 8 y = 1\end{array} \right.{x+y=09x+8y=1​

Select a set of inequalities to describe the region.

Find the equation of the circle x2+y2+Dx+Ey+F=0x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0x2+y2+Dx+Ey+F=0 that passes through the points (−4,−1),(−6,−3),(−2,−3)( - 4 , - 1 ) , ( - 6 , - 3 ) , ( - 2 , - 3 )(−4,−1),(−6,−3),(−2,−3) .

If a system of three linear equations is inconsistent, then its graph has one points common to all three equations.

Solve the system by the method of substitution. {1.3x+0.6y=5.70.9x−0.2y=2.1\left\{ \begin{array} { l } 1.3 x + 0.6 y = 5.7 \\0.9 x - 0.2 y = 2.1\end{array} \right.{1.3x+0.6y=5.70.9x−0.2y=2.1​

Write the partial fraction decomposition of the rational expression.Check your result algebraically. 5x2+5x\frac { 5 } { x ^ { 2 } + 5 x }x2+5x5​

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. ​ Objective function: ​ ​ Z = 5x + 8y ​ Constraints: ​ X ≥ 0 Y ≥ 0 X + 3y ≤ 15 4x + y ≤ 16 ​​ ​

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=7x+14yz = 7 x + \frac { 1 } { 4 } yz=7x+41​y Constraints: x \geq0 y \geq0 x+y \leq8 x+y \geq4

Solve the system of linear equations by the method of elimination, find (x,y). {−5x+2y=−383x−y=23\left\{ \begin{array} { c } - 5 x + 2 y = - 38 \\3 x - y = 23\end{array} \right.{−5x+2y=−383x−y=23​

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. 26 $\overline { x ^ { 2 } + 3 x - 40 }$

Solve the system of linear equations and check any solution algebraically. $\left\{ \begin{array} { l } 2 x + 2 z = 14 \\5 x + 3 y = 16 \\3 y - 4 z = 16\end{array} \right.$

Solve the system by the method of substitution. $\left\{ \begin{array} { l } \frac { 1 } { 10 } x + \frac { 3 } { 10 } y = 1 \\- \frac { 1 } { 5 } x + \frac { 2 } { 5 } y = 1\end{array} \right.$

Find the dimensions of the rectangle meeting the specified condition. The perimeter is 36 meters and the length is 4 meters greater than the width.

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 1 } { x ^ { 2 } + 6 x }$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { x + 1 } { x ^ { 2 } - 2 x - 8 }$

Select the region determined by the constraints.Then find the maximum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. Objective function: $z = 7 x + \frac { 1 } { 8 } y$ Constraints: x \geq0 y \geq0 x+y \leq8 x+y \geq4

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. $\left\{ \begin{array} { c } x + y = 0 \\9 x + 8 y = 1\end{array} \right.$

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points $( - 4 , - 1 ) , ( - 6 , - 3 ) , ( - 2 , - 3 )$ .

Solve the system by the method of substitution. $\left\{ \begin{array} { l } 1.3 x + 0.6 y = 5.7 \\0.9 x - 0.2 y = 2.1\end{array} \right.$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 5 } { x ^ { 2 } + 5 x }$

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. Objective function: Z = 5x + 8y Constraints: X ≥ 0 Y ≥ 0 X + 3y ≤ 15 4x + y ≤ 16

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: $z = 7 x + \frac { 1 } { 4 } y$ Constraints: x \geq0 y \geq0 x+y \leq8 x+y \geq4

Solve the system of linear equations by the method of elimination, find (x,y). $\left\{ \begin{array} { c } - 5 x + 2 y = - 38 \\3 x - y = 23\end{array} \right.$