Question 1

Solve the system by the method of substitution.  $\left\{ \begin{array} { l } 
y = x ^ { 3 } - 6 x ^ { 2 } + 4 \
y = x ^ { 2 } - 10 x + 4
\end{array} \right.$

Accepted Answer

A) (2, -12), (1, -5) 
B) (5, -21), (2, -12), (0, 4) 
C) (5, -21), (-1, 15) 
D) No real solution 
E) (5, -21), (-2, 28), (1, -5) 
A) (2, -12), (1, -5) 
B) (5, -21), (2, -12), (0, 4) 
C) (5, -21), (-1, 15) 
D) No real solution 
E) (5, -21), (-2, 28), (1, -5)

Question 2

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically.  $\left\{ \begin{array} { l } 
x + 2 y = 6 \
x - 2 y = 2
\end{array} \right.$

Accepted Answer

A)  (1, 4) 
B)  (4, 1) 
C) (- 4, -1) 
D) ( 4, -1) 
E)  (1, -4) 
A)  (1, 4) 
B)  (4, 1) 
C) (- 4, -1) 
D) ( 4, -1) 
E)  (1, -4)

Question 3

A small corporation borrowed $771,000 to expand its clothing line.Some of the money was borrowed at 8%, some at 9%, and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%? ​

Accepted Answer

A) $252,000 at 8%$456,000 at 9%$63,000 at 10% 
B) $252,000 at 9%$456,000 at 8%$63,000 at 10% 
C) $252,000 at 8%$63,000 at 9%$63,000 at 9% 
D) $252,000 at 8%$63,000 at 9%$63,000 at 10% 
E) $252,000 at 8%$63,000 at 9%$456,000 at 10% 
A) $252,000 at 8%$456,000 at 9%$63,000 at 10% 
B) $252,000 at 9%$456,000 at 8%$63,000 at 10% 
C) $252,000 at 8%$63,000 at 9%$63,000 at 9% 
D) $252,000 at 8%$63,000 at 9%$63,000 at 10% 
E) $252,000 at 8%$63,000 at 9%$456,000 at 10%

Question 4

Find the maximum value of the objective function and where it occurs, subject to the constraints: ​
Objective function:
​
Z = 7x + y
​
Constraints:
​
X ≥ 0
Y ≥ 0
3x + y ≤ 15
4x + 3y ≤ 30
​

Accepted Answer

A) Maximum at (0, 0): 0 
B) Maximum at (5, 0): 35 
C) Maximum at (0, 6): 46 
D) Maximum at (6, 3): 45 
E) Maximum at (3, 0): 21 
A) Maximum at (0, 0): 0 
B) Maximum at (5, 0): 35 
C) Maximum at (0, 6): 46 
D) Maximum at (6, 3): 45 
E) Maximum at (3, 0): 21

Question 5

Select the correct graph of the inequality.  $( x + 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } < 9$

Accepted Answer

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

Question 6

Use any method to solve the system of linear equations, find (x,y).  $\left\{ \begin{array} { l } 
x - 3 y = 25 \
4 x + 3 y = 25
\end{array} \right.$

Accepted Answer

A)  (-10, -5) 
B) (10, -5) 
C)  (3, -5) 
D)  (-5, 10) 
E)  (-5, -10) 
A)  (-10, -5) 
B) (10, -5) 
C)  (3, -5) 
D)  (-5, 10) 
E)  (-5, -10)

Question 7

According to automobile association of a country, on March 27, 2009, the national average price per gallon of regular unleaded (86-octane) gasoline was $2.02, and the price of premium unleaded (91-octane) gasoline was $2.26.The cost of the blend of mid-grade unleaded gasoline (90-octane).Select a graph of the region determined by the constraints. ​
Constraints:
​
X ≥ 0
Y ≥ 0
X + y = 1
86x + 91y = 90
​

Accepted Answer

A)    
B) ​   
C)    
D)    
E) ​   
A)    
B) ​   
C)    
D)    
E) ​

Question 8

Solve the system graphically.  $\left\{ \begin{array} { l } 
x - y = 0 \
5 x - 2 y = 9
\end{array} \right.$

Accepted Answer

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

Question 9

The predicted cost C (in thousands of dollars) for a company to remove p% of a chemical from its waste water is given by the model  $C = \frac { 124 p } { 90,000 - p ^ { 2 } } , 0 \leq p < 100$ .  
Write the partial fraction decomposition for the rational function.Verify your result by using the table feature of a graphing utility to create a table comparing the original function with the partial fractions.

Accepted Answer

A)  $\frac { 1 } { 300 - p } - \frac { 1 } { 300 + p }$ 
B)  $\frac { 124 } { 300 - p } - \frac { 124 } { 300 + p }$ 
C)  $\frac { 62 } { 300 - p } - \frac { 62 } { ( 300 - p ) ^ { 2 } }$ 
D)  $\frac { 62 } { 300 - p } - \frac { 62 } { 300 + p }$ 
E)  $\frac { 62 } { 300 - p } + \frac { 62 } { 300 + p }$ 
A)  $\frac { 1 } { 300 - p } - \frac { 1 } { 300 + p }$ 
B)  $\frac { 124 } { 300 - p } - \frac { 124 } { 300 + p }$ 
C)  $\frac { 62 } { 300 - p } - \frac { 62 } { ( 300 - p ) ^ { 2 } }$ 
D)  $\frac { 62 } { 300 - p } - \frac { 62 } { 300 + p }$ 
E)  $\frac { 62 } { 300 - p } + \frac { 62 } { 300 + p }$

Question 10

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 = 8x + 7y
​
Constraints:
​
X ≥ 0
Y ≥ 0
2x + 2y ≥ 10
X + 2y ≥ 6
​

Accepted Answer

A) ​   Maximum at (0, 5): 35 
B) ​   Maximum at (5, 0): 36 
C) ​   Maximum at (6, 0): 48 
D) ​   Maximum at (4, 1): 39 
E) ​   No maximum 
A) ​   Maximum at (0, 5): 35 
B) ​   Maximum at (5, 0): 36 
C) ​   Maximum at (6, 0): 48 
D) ​   Maximum at (4, 1): 39 
E) ​   No maximum

Question 11

Select the correct graph of the inequality.  $y \geq - 4 - \ln ( x + 5 )$

Accepted Answer

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

Question 12

Sketch the graph of the inequality. $( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 }$ < 4

Accepted Answer

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

Question 13

Find the consumer surplus and producer surplus.  
Demand $p = 70 - 0.5 x$  
Supply $p = 0.125 x$

Accepted Answer

A) Consumer surplus: $3136Producer surplus: $784 
B) Consumer surplus: $3286Producer surplus: $784 
C) Consumer surplus: $3236Producer surplus: $784 
D) Consumer surplus: $3186Producer surplus: $784 
E) Consumer surplus: $3336Producer surplus: $784 
A) Consumer surplus: $3136Producer surplus: $784 
B) Consumer surplus: $3286Producer surplus: $784 
C) Consumer surplus: $3236Producer surplus: $784 
D) Consumer surplus: $3186Producer surplus: $784 
E) Consumer surplus: $3336Producer surplus: $784

Question 14

A manufacturer produces two models of elliptical cross-training exercise machines. The times for assembling, finishing, and packaging model X are 3 hours, 3 hours, and 0.8 hour, respectively.The times for model Y are 4 hours, 2.5 hours, and 0.4 hour.The total times available for assembling, finishing, and packaging are 6000 hours, 4200 hours, and 950 hours, respectively.The profits per unit are $200 for model X and $275 for model Y.What is the optimal production level for each model? What is the optimal profit?

Accepted Answer

A) 6000 units of model X
950 units of model Y
Optimal profit: $1,461,250 
B) 950 units of model X
6000 units of model Y
Optimal profit: $1,840,000 
C) 400 units of model X
1200 units of model Y
Optimal profit: $410,000 
D) 950 units of model X
4200 units of model Y
Optimal profit: $1,345,000 
E) 4200 units of model X
950 units of model Y
Optimal profit: $1,101,250 
A) 6000 units of model X
950 units of model Y
Optimal profit: $1,461,250 
B) 950 units of model X
6000 units of model Y
Optimal profit: $1,840,000 
C) 400 units of model X
1200 units of model Y
Optimal profit: $410,000 
D) 950 units of model X
4200 units of model Y
Optimal profit: $1,345,000 
E) 4200 units of model X
950 units of model Y
Optimal profit: $1,101,250

Question 15

Solve the system of linear equations and check any solution algebraically.  $\left\{ \begin{array} { l } 
6 y + 4 z = - 24 \
3 x + 3 y = 21 \
2 x - 3 z = 22
\end{array} \right.$

Accepted Answer

A)  $( - 4,0 , - 11 )$ 
B)   $( - 11,0 , - 4 )$ 
C)   $( 11,0 , - 4 )$ 
D)   $( - 4,0,11 )$ 
E)   $( 11 , - 4,0 )$ 
A)  $( - 4,0 , - 11 )$ 
B)   $( - 11,0 , - 4 )$ 
C)   $( 11,0 , - 4 )$ 
D)   $( - 4,0,11 )$ 
E)   $( 11 , - 4,0 )$

Question 16

Find values of x, y, and $\lambda$ that satisfy the system.These systems arise in certain optimization problems in calculus, and $\lambda$is called a Lagrange multiplier. 
 $$\left\{ \begin{array} { l } 
2 + 2 y + 2 \lambda = 0 \
2 x + 1 + \lambda = 0 \
2 x + y - 96 = 0
\end{array} \right.$$

Accepted Answer

A)  x = 24, y = -49, $\lambda$ = 24 
B)  x = -49, y = 48, $\lambda$ = -49 
C)  x = 24, y = 48, $\lambda$ = -49 
D) x = 24, y = -49, $\lambda$ = -49 
E)  x = 24, y = 48, $\lambda$ = 48 
A)  x = 24, y = -49, $\lambda$ = 24 
B)  x = -49, y = 48, $\lambda$ = -49 
C)  x = 24, y = 48, $\lambda$ = -49 
D) x = 24, y = -49, $\lambda$ = -49 
E)  x = 24, y = 48, $\lambda$ = 48

Question 17

Solve the system by the method of substitution.  $\left\{ \begin{aligned}
6 x + 5 y & = - 6 \
- x - \frac { 5 } { 6 } y & = - 3
\end{aligned} \right.$

Accepted Answer

A) No solution 
B) (6, 3) 
C) (-5, -3) 
D) (5, 4) 
E) (-5, -4) 
A) No solution 
B) (6, 3) 
C) (-5, -3) 
D) (5, 4) 
E) (-5, -4)

Question 18

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x + 5 } { x \left( x ^ { 2 } + 6 \right) ^ { 2 } }$

Accepted Answer

A)  $\frac { A } { x } + \frac { B x + C } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
B)  $\frac { A x + B } { x ^ { 2 } + 6 } + \frac { C x + D } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
C)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 6 } + \frac { D x + E } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
D)  $\frac { A x + B } { x } + \frac { C x + D } { x ^ { 2 } + 6 } + \frac { E x + F } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
E)  $\frac { A } { x } + \frac { B } { x ^ { 2 } + 6 } + \frac { C } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
A)  $\frac { A } { x } + \frac { B x + C } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
B)  $\frac { A x + B } { x ^ { 2 } + 6 } + \frac { C x + D } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
C)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 6 } + \frac { D x + E } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
D)  $\frac { A x + B } { x } + \frac { C x + D } { x ^ { 2 } + 6 } + \frac { E x + F } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ 
E)  $\frac { A } { x } + \frac { B } { x ^ { 2 } + 6 } + \frac { C } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$

Question 19

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.  $\frac { x - 3 } { x ^ { 2 } + 7 x + 12 }$

Accepted Answer

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

Question 20

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. ​
Z = x + y
​
Constraints:
​
X ≥ 0
Y ≥ 0
X + y ≤ 1
3x + y ≤ 6
​

Accepted Answer

A) ​   The constraint 3x + y ≤ 6 is extraneous. Minimum at (1, 1): 9 
B) ​   The constraint 3x + y ≤ 6 is extraneous. No minimum. 
C) ​   The constraint 3x + y ≤ 6 is extraneous. Minimum at (1, 0): 4 
D)    The constraint 3x + y ≤ 6 is extraneous. Minimum at (0, 0): 0 
E) ​   The constraint 3x + y ≤ 6 is extraneous. Minimum at (0, 1): 5 
A) ​   The constraint 3x + y ≤ 6 is extraneous. Minimum at (1, 1): 9 
B) ​   The constraint 3x + y ≤ 6 is extraneous. No minimum. 
C) ​   The constraint 3x + y ≤ 6 is extraneous. Minimum at (1, 0): 4 
D)    The constraint 3x + y ≤ 6 is extraneous. Minimum at (0, 0): 0 
E) ​   The constraint 3x + y ≤ 6 is extraneous. Minimum at (0, 1): 5

Solve the system by the method of substitution. $\left\{ \begin{array} { l } y = x ^ { 3 } - 6 x ^ { 2 } + 4 \\y = x ^ { 2 } - 10 x + 4\end{array} \right.$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } x + 2 y = 6 \\x - 2 y = 2\end{array} \right.$

A small corporation borrowed $771,000 to expand its clothing line.Some of the money was borrowed at 8%, some at 9%, and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%?

Find the maximum value of the objective function and where it occurs, subject to the constraints: Objective function: Z = 7x + y Constraints: X ≥ 0 Y ≥ 0 3x + y ≤ 15 4x + 3y ≤ 30

Select the correct graph of the inequality. $( x + 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } < 9$

Use any method to solve the system of linear equations, find (x,y). $\left\{ \begin{array} { l } x - 3 y = 25 \\4 x + 3 y = 25\end{array} \right.$

Solve the system graphically. $\left\{ \begin{array} { l } x - y = 0 \\5 x - 2 y = 9\end{array} \right.$

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 = 8x + 7y Constraints: X ≥ 0 Y ≥ 0 2x + 2y ≥ 10 X + 2y ≥ 6

Select the correct graph of the inequality. $y \geq - 4 - \ln ( x + 5 )$

Sketch the graph of the inequality. $( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 }$ < 4 $Sketch the graph of the inequality. ( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 } < 4$

Find the consumer surplus and producer surplus. Demand $p = 70 - 0.5 x$ Supply $p = 0.125 x$

Solve the system of linear equations and check any solution algebraically. $\left\{ \begin{array} { l } 6 y + 4 z = - 24 \\3 x + 3 y = 21 \\2 x - 3 z = 22\end{array} \right.$

Find values of x, y, and $\lambda$ that satisfy the system.These systems arise in certain optimization problems in calculus, and $\lambda$ is called a Lagrange multiplier. $\left\{ \begin{array} { l } 2 + 2 y + 2 \lambda = 0 \\2 x + 1 + \lambda = 0 \\2 x + y - 96 = 0\end{array} \right.$

Solve the system by the method of substitution. $\left\{ \begin{aligned}6 x + 5 y & = - 6 \\- x - \frac { 5 } { 6 } y & = - 3\end{aligned} \right.$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x + 5 } { x \left( x ^ { 2 } + 6 \right) ^ { 2 } }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x - 3 } { x ^ { 2 } + 7 x + 12 }$

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

Solve the system by the method of substitution. {y=x3−6x2+4y=x2−10x+4\left\{ \begin{array} { l } y = x ^ { 3 } - 6 x ^ { 2 } + 4 \\y = x ^ { 2 } - 10 x + 4\end{array} \right.{y=x3−6x2+4y=x2−10x+4​

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. {x+2y=6x−2y=2\left\{ \begin{array} { l } x + 2 y = 6 \\x - 2 y = 2\end{array} \right.{x+2y=6x−2y=2​

A small corporation borrowed $771,000 to expand its clothing line.Some of the money was borrowed at 8%, some at 9%, and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%? ​

Find the maximum value of the objective function and where it occurs, subject to the constraints: ​ Objective function: ​ Z = 7x + y ​ Constraints: ​ X ≥ 0 Y ≥ 0 3x + y ≤ 15 4x + 3y ≤ 30 ​

Select the correct graph of the inequality. (x+3)2+(y−2)2<9( x + 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } < 9(x+3)2+(y−2)2<9

Use any method to solve the system of linear equations, find (x,y). {x−3y=254x+3y=25\left\{ \begin{array} { l } x - 3 y = 25 \\4 x + 3 y = 25\end{array} \right.{x−3y=254x+3y=25​

Solve the system graphically. {x−y=05x−2y=9\left\{ \begin{array} { l } x - y = 0 \\5 x - 2 y = 9\end{array} \right.{x−y=05x−2y=9​

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 = 8x + 7y ​ Constraints: ​ X ≥ 0 Y ≥ 0 2x + 2y ≥ 10 X + 2y ≥ 6 ​

Select the correct graph of the inequality. y≥−4−ln⁡(x+5)y \geq - 4 - \ln ( x + 5 )y≥−4−ln(x+5)

Sketch the graph of the inequality. (x−3)2+(y+1)2( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 }(x−3)2+(y+1)2 < 4

Find the consumer surplus and producer surplus. Demand p=70−0.5xp = 70 - 0.5 xp=70−0.5x Supply p=0.125xp = 0.125 xp=0.125x

Solve the system of linear equations and check any solution algebraically. {6y+4z=−243x+3y=212x−3z=22\left\{ \begin{array} { l } 6 y + 4 z = - 24 \\3 x + 3 y = 21 \\2 x - 3 z = 22\end{array} \right.⎩⎨⎧​6y+4z=−243x+3y=212x−3z=22​

Solve the system by the method of substitution. {6x+5y=−6−x−56y=−3\left\{ \begin{aligned}6 x + 5 y & = - 6 \\- x - \frac { 5 } { 6 } y & = - 3\end{aligned} \right.⎩⎨⎧​6x+5y−x−65​y​=−6=−3​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. x+5x(x2+6)2\frac { x + 5 } { x \left( x ^ { 2 } + 6 \right) ^ { 2 } }x(x2+6)2x+5​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. x−3x2+7x+12\frac { x - 3 } { x ^ { 2 } + 7 x + 12 }x2+7x+12x−3​

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

Solve the system by the method of substitution. $\left\{ \begin{array} { l } y = x ^ { 3 } - 6 x ^ { 2 } + 4 \\y = x ^ { 2 } - 10 x + 4\end{array} \right.$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } x + 2 y = 6 \\x - 2 y = 2\end{array} \right.$

A small corporation borrowed $771,000 to expand its clothing line.Some of the money was borrowed at 8%, some at 9%, and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%?

Find the maximum value of the objective function and where it occurs, subject to the constraints: Objective function: Z = 7x + y Constraints: X ≥ 0 Y ≥ 0 3x + y ≤ 15 4x + 3y ≤ 30

Select the correct graph of the inequality. $( x + 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } < 9$

Use any method to solve the system of linear equations, find (x,y). $\left\{ \begin{array} { l } x - 3 y = 25 \\4 x + 3 y = 25\end{array} \right.$

Solve the system graphically. $\left\{ \begin{array} { l } x - y = 0 \\5 x - 2 y = 9\end{array} \right.$

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 = 8x + 7y Constraints: X ≥ 0 Y ≥ 0 2x + 2y ≥ 10 X + 2y ≥ 6

Select the correct graph of the inequality. $y \geq - 4 - \ln ( x + 5 )$

Sketch the graph of the inequality. $( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 }$ < 4 $Sketch the graph of the inequality. ( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 } < 4$

Find the consumer surplus and producer surplus. Demand $p = 70 - 0.5 x$ Supply $p = 0.125 x$

Solve the system of linear equations and check any solution algebraically. $\left\{ \begin{array} { l } 6 y + 4 z = - 24 \\3 x + 3 y = 21 \\2 x - 3 z = 22\end{array} \right.$

Solve the system by the method of substitution. $\left\{ \begin{aligned}6 x + 5 y & = - 6 \\- x - \frac { 5 } { 6 } y & = - 3\end{aligned} \right.$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x + 5 } { x \left( x ^ { 2 } + 6 \right) ^ { 2 } }$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x - 3 } { x ^ { 2 } + 7 x + 12 }$