Question 1

Write a set of inequalities to describe the region. ​
Rectangle: vertices at $$( 1,5 ) , ( 9,5 ) , ( 9,9 ) , ( 1,9 )$$ ​

Accepted Answer

A)  $$\left\{ \begin{array} { l } 
x \geq 1 \
x \leq 9 \
y \geq 5 \
y \leq 9
\end{array} \right.$$ 
B)  $$\left\{ \begin{array} { l } 
x \geq 4 \
x \leq 5 \
y \geq 9 \
y \leq 5
\end{array} \right.$$ 
C)  $$\left\{ \begin{array} { l } 
x \geq 3 \
x \leq 5 \
y \geq 9 \
y \leq 5
\end{array} \right.$$ 
D)  $$\left\{ \begin{array} { l } 
x \geq 2 \
x \leq 5 \
y \geq 9 \
y \leq 5
\end{array} \right.$$ 
E)  $$\left\{ \begin{array} { l } 
x \geq 5 \
x \leq 5 \
y \geq 9 \
y \leq 9
\end{array} \right.$$ 
A)  $$\left\{ \begin{array} { l } 
x \geq 1 \
x \leq 9 \
y \geq 5 \
y \leq 9
\end{array} \right.$$ 
B)  $$\left\{ \begin{array} { l } 
x \geq 4 \
x \leq 5 \
y \geq 9 \
y \leq 5
\end{array} \right.$$ 
C)  $$\left\{ \begin{array} { l } 
x \geq 3 \
x \leq 5 \
y \geq 9 \
y \leq 5
\end{array} \right.$$ 
D)  $$\left\{ \begin{array} { l } 
x \geq 2 \
x \leq 5 \
y \geq 9 \
y \leq 5
\end{array} \right.$$ 
E)  $$\left\{ \begin{array} { l } 
x \geq 5 \
x \leq 5 \
y \geq 9 \
y \leq 9
\end{array} \right.$$

Question 2

Determine which one of the ordered pairs below is a solution of the system of linear inequalities.​ $$\left\{ \begin{array} { c } 
x > - 3 \
y > - 1 \
y \leq 4 - \frac { 2 x } { 3 }
\end{array} \right.$$ ​

Accepted Answer

A) (-2,2) 
B) (3,-3) 
C) (-5,-9) 
D) (4,-7) 
E) (9,8) 
A) (-2,2) 
B) (3,-3) 
C) (-5,-9) 
D) (4,-7) 
E) (9,8)

Question 3

Find the consumer surplus and producer surplus. ​
Demand $p = 100 - 0.03 x$ ​
Supply $p = 35 + 0.1 x$ ​

Accepted Answer

A) Consumer surplus: $3,750 Producer surplus: $12,800 
B) Consumer surplus: $3,750 Producer surplus: $12,500 
C) Consumer surplus: $3,750 Producer surplus: $12,600 
D) Consumer surplus: $3,750 Producer surplus: $12,900 
E) Consumer surplus: $3,750 Producer surplus: $12,700 
A) Consumer surplus: $3,750 Producer surplus: $12,800 
B) Consumer surplus: $3,750 Producer surplus: $12,500 
C) Consumer surplus: $3,750 Producer surplus: $12,600 
D) Consumer surplus: $3,750 Producer surplus: $12,900 
E) Consumer surplus: $3,750 Producer surplus: $12,700

Question 4

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 5

Select the correct graph of the inequality.​ $$y > 7 x - 6$$ ​

Accepted Answer

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

Question 6

Select an inequality for the shaded region shown in the figure.​   ​

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } < 25$ 
B)  $x ^ { 2 } + y ^ { 2 } < 4$ 
C)  $x ^ { 2 } + y ^ { 2 } < 9$ 
D)  $x ^ { 2 } + y ^ { 2 } < 1$ 
E)  $x ^ { 2 } + y ^ { 2 } < 16$ 
A)  $x ^ { 2 } + y ^ { 2 } < 25$ 
B)  $x ^ { 2 } + y ^ { 2 } < 4$ 
C)  $x ^ { 2 } + y ^ { 2 } < 9$ 
D)  $x ^ { 2 } + y ^ { 2 } < 1$ 
E)  $x ^ { 2 } + y ^ { 2 } < 16$

Question 7

A small company that manufactures two models of exercise machines has an order for 17 units of the standard model and 18 units of the deluxe model.The company has trucks of two different sizes that can haul the products,as shown in the table. $$\begin{array} { | l | l | l | } 
\hline \text { Truck } & \text { Standard } & \text { Deluxe } \
\hline \text { Large } & 6 & 3 \
\hline \text { Medium } & 4 & 6 \
\hline
\end{array}$$
Find and graph a system of inequalities describing the numbers of trucks of each size that are needed to deliver the order.

Accepted Answer

A)  $$\left\{ \begin{array} { c } 
6 x + 4 y \geq 17 \
3 x + 6 y \geq 18 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​  
​ 
B)  $$\left\{ \begin{array} { c } 
6 x + 4 y \geq 16 \
3 x + 6 y \geq 18 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​
​   
C)  $$\left\{ \begin{array} { c } 
6 x + 4 y \geq 18 \
3 x + 6 y \geq 18 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​   
D)  $$\left\{ \begin{array} { c } 
6 x + 4 y \geq 14 \
3 x + 6 y \geq 18 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​  
​ 
E) ​ $$\left\{ \begin{array} { c } 
6 x + 4 y \geq 20 \
3 x + 6 y \geq 18 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​   
A)  $$\left\{ \begin{array} { c } 
6 x + 4 y \geq 17 \
3 x + 6 y \geq 18 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​  
​ 
B)  $$\left\{ \begin{array} { c } 
6 x + 4 y \geq 16 \
3 x + 6 y \geq 18 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​
​   
C)  $$\left\{ \begin{array} { c } 
6 x + 4 y \geq 18 \
3 x + 6 y \geq 18 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​   
D)  $$\left\{ \begin{array} { c } 
6 x + 4 y \geq 14 \
3 x + 6 y \geq 18 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​  
​ 
E) ​ $$\left\{ \begin{array} { c } 
6 x + 4 y \geq 20 \
3 x + 6 y \geq 18 \
x \geq 0 \
y \geq 0
\end{array} \right.$$ ​

Question 8

Select the correct graph of the inequality.​ $$10 x ^ { 2 } - y - 11 > 0$$ ​

Accepted Answer

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

Question 9

A warehouse supervisor is told to ship at least 50 packages of gravel that weigh 55 pounds each and at least 40 bags of stone that weigh 70 pounds each.The maximum weight capacity of the truck to be used is 9,500 pounds.Find and graph a system of inequalities describing the numbers of bags of stone and gravel that can be shipped.
​

Accepted Answer

A)  $$\left\{ \begin{array} { c } 
55 x + 70 y \leq 9,500 \
x \geq 50 \
y \geq 40
\end{array} \right.$$ ​   
B) ​ $$\left\{ \begin{array} { c } 
55 x + 70 y \leq 7,000 \
x \geq 50 \
y \geq 40
\end{array} \right.$$   
C)  $$\left\{ \begin{array} { c } 
55 x + 70 y \leq 8,000 \
x \geq 50 \
y \geq 40
\end{array} \right.$$ ​   
D) ​ $$\left\{ \begin{array} { c } 
55 x + 70 y \leq 10,000 \
x \geq 50 \
y \geq 40
\end{array} \right.$$   
E)  $$\left\{ \begin{array} { c } 
55 x + 70 y \leq 8,500 \
x \geq 50 \
y \geq 40
\end{array} \right.$$ ​  
​ 
A)  $$\left\{ \begin{array} { c } 
55 x + 70 y \leq 9,500 \
x \geq 50 \
y \geq 40
\end{array} \right.$$ ​   
B) ​ $$\left\{ \begin{array} { c } 
55 x + 70 y \leq 7,000 \
x \geq 50 \
y \geq 40
\end{array} \right.$$   
C)  $$\left\{ \begin{array} { c } 
55 x + 70 y \leq 8,000 \
x \geq 50 \
y \geq 40
\end{array} \right.$$ ​   
D) ​ $$\left\{ \begin{array} { c } 
55 x + 70 y \leq 10,000 \
x \geq 50 \
y \geq 40
\end{array} \right.$$   
E)  $$\left\{ \begin{array} { c } 
55 x + 70 y \leq 8,500 \
x \geq 50 \
y \geq 40
\end{array} \right.$$ ​  
​

Question 10

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

Accepted Answer

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

Exam 45: Systems of Inequalities

Write a set of inequalities to describe the region. ​ Rectangle: vertices at (1,5),(9,5),(9,9),(1,9)( 1,5 ) , ( 9,5 ) , ( 9,9 ) , ( 1,9 )(1,5),(9,5),(9,9),(1,9) ​

Determine which one of the ordered pairs below is a solution of the system of linear inequalities.​ {x>−3y>−1y≤4−2x3\left\{ \begin{array} { c } x > - 3 \\y > - 1 \\y \leq 4 - \frac { 2 x } { 3 }\end{array} \right.⎩⎨⎧​x>−3y>−1y≤4−32x​​ ​

Find the consumer surplus and producer surplus. ​ Demand p=100−0.03xp = 100 - 0.03 xp=100−0.03x ​ Supply p=35+0.1xp = 35 + 0.1 xp=35+0.1x ​

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 ​

Select the correct graph of the inequality.​ y>7x−6y > 7 x - 6y>7x−6 ​

Select an inequality for the shaded region shown in the figure.​ ​

Select the correct graph of the inequality.​ 10x2−y−11>010 x ^ { 2 } - y - 11 > 010x2−y−11>0 ​

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 ​

Rectangular Coordinates

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Introduction to Conics Parabolas

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Polar Equations of Conics

Graphs of Polar Equations

Filters

Write a set of inequalities to describe the region. Rectangle: vertices at $( 1,5 ) , ( 9,5 ) , ( 9,9 ) , ( 1,9 )$

Determine which one of the ordered pairs below is a solution of the system of linear inequalities. $\left\{ \begin{array} { c } x > - 3 \\y > - 1 \\y \leq 4 - \frac { 2 x } { 3 }\end{array} \right.$

Find the consumer surplus and producer surplus. Demand $p = 100 - 0.03 x$ Supply $p = 35 + 0.1 x$

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

Select the correct graph of the inequality. $y > 7 x - 6$

Select an inequality for the shaded region shown in the figure.

Select the correct graph of the inequality. $10 x ^ { 2 } - y - 11 > 0$

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