Question 1

Determine whether the graph of the equation is a circle or an ellipse.
-$$\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 144 } = 1$$

Accepted Answer

A)  Ellipse 
B)  Circle 
A)  Ellipse 
B)  Circle

Question 2

Suppose an animal feed to be mixed from soybean meal and oats must contain at least 100 lb of protein, 20 lb of fat, and 12 lb of mineral ash. Each 100-lb sack of soybean meal costs $20 and contains 50 lb of protein, 10 lb of Fat, and 8 lb of mineral ash. Each 100-lb sack of alfalfa costs $11 and contains 30 lb of protein, 8 lb of fat, and 3 lb Of mineral ash. How many sacks of each should be used to satisfy the minimum requirements at minimum cost?
Fractional sacks are allowed.

Accepted Answer

A)  2 sacks of soybeans and 0 sacks of alfalfa 
B)  $\frac { 18 } { 17 }$ sacks of soybeans and $\frac { 20 } { 17 }$ sacks of alfalfa 
C)  $\frac { 2 } { 3 }$ sack of soybeans and $\frac { 20 } { 9 }$ sacks of alfalfa 
D)  0 sacks of soybeans and 4 sacks of alfalfa 
A)  2 sacks of soybeans and 0 sacks of alfalfa 
B)  $\frac { 18 } { 17 }$ sacks of soybeans and $\frac { 20 } { 17 }$ sacks of alfalfa 
C)  $\frac { 2 } { 3 }$ sack of soybeans and $\frac { 20 } { 9 }$ sacks of alfalfa 
D)  0 sacks of soybeans and 4 sacks of alfalfa

Question 3

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
-Find the values of $x$ and $y$ that give the maximum possible value of $g = 8 x + 12 y$ subject to the following constraints:
$$\left\{ \begin{array} { l } 
40 x + 80 y \leq 560 \
6 x + 8 y \leq 72 \
x \geq 0 , y \geq 0
\end{array} \right.$$

Accepted Answer

A)  $x = 8 , y = 3$ 
B)  $x = 14 , y = 0$ 
C)  $x = 12 , y = 0$ 
D)  $x = 0 , y = 9$ 
A)  $x = 8 , y = 3$ 
B)  $x = 14 , y = 0$ 
C)  $x = 12 , y = 0$ 
D)  $x = 0 , y = 9$

Question 4

Graph.
-$y ^ { 2 } - x ^ { 2 } - 4 y + 6 x - 41 = 0$

Accepted Answer

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

Question 5

Write the binomial expansion of the expression.
-$$( - 3 m - 3 n ) ^ { 4 }$$

Accepted Answer

A)  $81 m ^ { 4 } + 5184 m ^ { 3 } n + 2916 m ^ { 2 } n ^ { 2 } + 324 m n ^ { 3 } + 81 n ^ { 4 }$ 
B)  $81 m ^ { 4 } + 324 m ^ { 3 } n - 486 m ^ { 2 } n ^ { 2 } + 324 m n ^ { 3 } - 81 n ^ { 4 }$ 
C)  $81 m ^ { 4 } + 324 m ^ { 3 } n + 486 m ^ { 2 } n ^ { 2 } + 324 m n ^ { 3 } + 81 n ^ { 4 }$ 
D)  $81 m ^ { 4 } + 5184 m ^ { 3 } n - 2916 m ^ { 2 } n ^ { 2 } + 324 m n ^ { 3 } - 81 n ^ { 4 }$ 
A)  $81 m ^ { 4 } + 5184 m ^ { 3 } n + 2916 m ^ { 2 } n ^ { 2 } + 324 m n ^ { 3 } + 81 n ^ { 4 }$ 
B)  $81 m ^ { 4 } + 324 m ^ { 3 } n - 486 m ^ { 2 } n ^ { 2 } + 324 m n ^ { 3 } - 81 n ^ { 4 }$ 
C)  $81 m ^ { 4 } + 324 m ^ { 3 } n + 486 m ^ { 2 } n ^ { 2 } + 324 m n ^ { 3 } + 81 n ^ { 4 }$ 
D)  $81 m ^ { 4 } + 5184 m ^ { 3 } n - 2916 m ^ { 2 } n ^ { 2 } + 324 m n ^ { 3 } - 81 n ^ { 4 }$

Question 6

Write the equation in the form $y = c x ^ { b }$ where b is a constant.
-$$y = 3 \sqrt { x }$$

Accepted Answer

A)  $y = x ^ { 1 / 3 }$ 
B)  $y = x ^ { 3 / 2 }$ 
C)  $y = 3 x ^ { 1 / 2 }$ 
D)  $y = 3 \ln x$ 
A)  $y = x ^ { 1 / 3 }$ 
B)  $y = x ^ { 3 / 2 }$ 
C)  $y = 3 x ^ { 1 / 2 }$ 
D)  $y = 3 \ln x$

Question 7

Graph the inequality.
-$2 x+4 y \geq-8$

Accepted Answer

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

Question 8

Graph the solution set of the system of inequalities.
-$$\left\{ \begin{array} { l } 
y > x ^ { 2 } - 4 \
2 y - x < 0
\end{array} \right.$$

Accepted Answer

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

Question 9

Write the inequalities that describe the constraints on production.
-The Pen-Ink Company manufactures two ballpoint pens: silver and gold. The silver requires 7 minutes in a grinder and 12 minutes in a bonder. The gold requires 7 minutes in a grinder and 9 minutes in a bonder. The
Grinder can be run no more than 610 minutes per day and the bonder no more than 230 minutes per day. Let x Represent the silver pens and let y represent the gold pens.

Accepted Answer

A)  $0 \leq 19 x + 16 y \leq 840 , x \geq 0 , y \geq 0$ 
B)  $7 x + 7 y \leq 610,12 x + 9 y \leq 230 , x \geq 0 , y \geq 0$ 
C)  $x + y \leq 610 , x + y \leq 230 , x + y \leq 840 , x \geq 0 , y \geq 0$ 
D)  $7 x + 12 y \leq 610,7 x + 9 y \leq 230 , x \geq 0 , y \geq 0$ 
A)  $0 \leq 19 x + 16 y \leq 840 , x \geq 0 , y \geq 0$ 
B)  $7 x + 7 y \leq 610,12 x + 9 y \leq 230 , x \geq 0 , y \geq 0$ 
C)  $x + y \leq 610 , x + y \leq 230 , x + y \leq 840 , x \geq 0 , y \geq 0$ 
D)  $7 x + 12 y \leq 610,7 x + 9 y \leq 230 , x \geq 0 , y \geq 0$

Question 10

Beaufort Canal has a semi-elliptical cross section with a width W = 67 feet and a depth D = 13 feet (see figure). The keel on Sasha's yacht rides 5 feet below the water line at the keel's deepest point. If the yacht travels parallel
To the canal, and assuming the canal is completely full of water, how close can Sasha bring the yacht's centerline
To the edge of the canal without running aground? (The keel is the very bottom of a boat hull and runs directly
Below the boat's centerline from front to back.)

Accepted Answer

A)  4 ft 
B)  5 ft 
C)  12 ft 
D)  21 ft 
A)  4 ft 
B)  5 ft 
C)  12 ft 
D)  21 ft

Question 11

Write the indicated term of the binomial expansion.
-$( 2 x + 8 ) ^ { 3 } ; \quad$ 3rd term

Accepted Answer

A)  $384 x$ 
B)  $768 x$ 
C)  64 
D)  $96 \mathrm { x } ^ { 2 }$ 
A)  $384 x$ 
B)  $768 x$ 
C)  64 
D)  $96 \mathrm { x } ^ { 2 }$

Question 12

Write the equation in the form $y = f ( x )$ f(x) by solving for y.
-$11 y - 5 x ^ { 3 } = 20$

Accepted Answer

A)  $y = \frac { 4 + x ^ { 3 } } { 11 }$ 
B)  $y = \frac { 20 - 5 x ^ { 3 } } { 11 }$ 
C)  $y = \frac { 20 + 5 x ^ { 3 } } { 11 }$ 
D)  $y = 4 + x ^ { 3 }$ 
A)  $y = \frac { 4 + x ^ { 3 } } { 11 }$ 
B)  $y = \frac { 20 - 5 x ^ { 3 } } { 11 }$ 
C)  $y = \frac { 20 + 5 x ^ { 3 } } { 11 }$ 
D)  $y = 4 + x ^ { 3 }$

Question 13

Find the center and radius of the circle with the given equation.
-$$x ^ { 2 } + y ^ { 2 } = 9$$

Accepted Answer

A)  $( 3,3 ) ; r = 9$ 
B)  $( 0,0 ) ; r = 9$ 
C)  $( 3,3 ) ; r = 3$ 
D)  $( 0,0 ) ; r = 3$ 
A)  $( 3,3 ) ; r = 9$ 
B)  $( 0,0 ) ; r = 9$ 
C)  $( 3,3 ) ; r = 3$ 
D)  $( 0,0 ) ; r = 3$

Question 14

An airline with two types of airplans, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers . for a certain trip, airplane P1 costs $10,00 to operate and can accommodate 20 first class, 50 tourist class, 110 economy class passengers. Airplane P2 costs $8500 to operate and can accommodate 18 first class, 30 rourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

Accepted Answer

A)  14 P1 plans and 7 P2 plans 
B)  9 P1 plans and 12 P2 plans 
C)  5 P1 plans and 22 P2 plans 
D)  9 P1 plans and 13 P2 plans 
A)  14 P1 plans and 7 P2 plans 
B)  9 P1 plans and 12 P2 plans 
C)  5 P1 plans and 22 P2 plans 
D)  9 P1 plans and 13 P2 plans

Question 15

Find the center and radius of the circle with the given equation.
-$( x - 1.7 ) ^ { 2 } + ( y + 4.7 ) ^ { 2 } = 7$

Accepted Answer

A)  $( 4.7 , - 1.7 ) ; r = \sqrt { 7 }$ 
B)  $( 4.7 , - 1.7 ) ; \mathrm { r } = 7$ 
C)  $( 1.7 , - 4.7 ) ; r = 7$ 
D)  $( 1.7 , - 4.7 ) ; r = \sqrt { 7 }$ 
A)  $( 4.7 , - 1.7 ) ; r = \sqrt { 7 }$ 
B)  $( 4.7 , - 1.7 ) ; \mathrm { r } = 7$ 
C)  $( 1.7 , - 4.7 ) ; r = 7$ 
D)  $( 1.7 , - 4.7 ) ; r = \sqrt { 7 }$

Question 16

Write the function without radicals by using fractional exponents.
-$$y = \sqrt [ 4 ] { ( x - 3 ) ^ { 3 } }$$

Accepted Answer

A)  $y = x ^ { 4 / 3 } - 3$ 
B)  $y = x ^ { 3 / 4 } - 3$ 
C)  $y = ( x - 3 ) ^ { 3 / 4 }$ 
D)  $y = ( x - 3 ) ^ { 4 / 3 }$ 
A)  $y = x ^ { 4 / 3 } - 3$ 
B)  $y = x ^ { 3 / 4 } - 3$ 
C)  $y = ( x - 3 ) ^ { 3 / 4 }$ 
D)  $y = ( x - 3 ) ^ { 4 / 3 }$

Question 17

Graph.
-$y=-\sqrt{x^{2}+2}$

Accepted Answer

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

Question 18

Graph the region that satisfies the constraints.
-A contractor builds two models of homes, the Raskolnikov and the Karamazov. The Raskolnikov requires 180 worker-days of labor and $300,000 in capital, while the Karamazov requires 270 worker-days of labor and
$200,000 in capital. The contractor has a total of 5400 worker-days and $6,000,000 in capital available per
Month. Let x represent the number of Raskolnikov models and y represent the number of Karmazov models.

Accepted Answer

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

Question 19

Draw the graph of the equation.
-$$y ^ { 2 } = - 5 x$$

Accepted Answer

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

Question 20

Draw the graph of the equation.
-$y=x^{2}-2 x-5$

Accepted Answer

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

Determine whether the graph of the equation is a circle or an ellipse. - $\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 144 } = 1$

Graph. - $y ^ { 2 } - x ^ { 2 } - 4 y + 6 x - 41 = 0$ $Graph. - y ^ { 2 } - x ^ { 2 } - 4 y + 6 x - 41 = 0$

Write the binomial expansion of the expression. - $( - 3 m - 3 n ) ^ { 4 }$

Write the equation in the form $y = c x ^ { b }$ where b is a constant. - $y = 3 \sqrt { x }$

Graph the inequality. - $2 x+4 y \geq-8$ $Graph the inequality. - 2 x+4 y \geq-8$

Graph the solution set of the system of inequalities. - $\left\{ \begin{array} { l } y > x ^ { 2 } - 4 \\2 y - x < 0\end{array} \right.$ $Graph the solution set of the system of inequalities. - \left\{ \begin{array} { l } y > x ^ { 2 } - 4 \\ 2 y - x < 0 \end{array} \right.$

Write the indicated term of the binomial expansion. - $( 2 x + 8 ) ^ { 3 } ; \quad$ 3rd term

Write the equation in the form $y = f ( x )$ f(x) by solving for y. - $11 y - 5 x ^ { 3 } = 20$

Find the center and radius of the circle with the given equation. - $x ^ { 2 } + y ^ { 2 } = 9$

Find the center and radius of the circle with the given equation. - $( x - 1.7 ) ^ { 2 } + ( y + 4.7 ) ^ { 2 } = 7$

Write the function without radicals by using fractional exponents. - $y = \sqrt [ 4 ] { ( x - 3 ) ^ { 3 } }$

Graph. - $y=-\sqrt{x^{2}+2}$ $Graph. - y=-\sqrt{x^{2}+2}$

Draw the graph of the equation. - $y ^ { 2 } = - 5 x$ $Draw the graph of the equation. - y ^ { 2 } = - 5 x$

Draw the graph of the equation. - $y=x^{2}-2 x-5$ $Draw the graph of the equation. - y=x^{2}-2 x-5$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Filters

Exam 8: Special Topics in Algebra

Determine whether the graph of the equation is a circle or an ellipse. - x2225+y2144=1\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 144 } = 1225x2​+144y2​=1

Graph. - y2−x2−4y+6x−41=0y ^ { 2 } - x ^ { 2 } - 4 y + 6 x - 41 = 0y2−x2−4y+6x−41=0

Write the binomial expansion of the expression. - (−3m−3n)4( - 3 m - 3 n ) ^ { 4 }(−3m−3n)4

Write the equation in the form y=cxby = c x ^ { b }y=cxb where b is a constant. - y=3xy = 3 \sqrt { x }y=3x​

Graph the inequality. - 2x+4y≥−82 x+4 y \geq-82x+4y≥−8

Graph the solution set of the system of inequalities. - {y>x2−42y−x<0\left\{ \begin{array} { l } y > x ^ { 2 } - 4 \\2 y - x < 0\end{array} \right.{y>x2−42y−x<0​

Write the indicated term of the binomial expansion. - (2x+8)3;( 2 x + 8 ) ^ { 3 } ; \quad(2x+8)3; 3rd term

Write the equation in the form y=f(x)y = f ( x )y=f(x) f(x) by solving for y. - 11y−5x3=2011 y - 5 x ^ { 3 } = 2011y−5x3=20

Find the center and radius of the circle with the given equation. - x2+y2=9x ^ { 2 } + y ^ { 2 } = 9x2+y2=9

Find the center and radius of the circle with the given equation. - (x−1.7)2+(y+4.7)2=7( x - 1.7 ) ^ { 2 } + ( y + 4.7 ) ^ { 2 } = 7(x−1.7)2+(y+4.7)2=7

Write the function without radicals by using fractional exponents. - y=(x−3)34y = \sqrt [ 4 ] { ( x - 3 ) ^ { 3 } }y=4(x−3)3​

Graph. - y=−x2+2y=-\sqrt{x^{2}+2}y=−x2+2​

Draw the graph of the equation. - y2=−5xy ^ { 2 } = - 5 xy2=−5x

Draw the graph of the equation. - y=x2−2x−5y=x^{2}-2 x-5y=x2−2x−5

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Filters

Determine whether the graph of the equation is a circle or an ellipse. - $\frac { x ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 144 } = 1$

Graph. - $y ^ { 2 } - x ^ { 2 } - 4 y + 6 x - 41 = 0$ $Graph. - y ^ { 2 } - x ^ { 2 } - 4 y + 6 x - 41 = 0$

Write the binomial expansion of the expression. - $( - 3 m - 3 n ) ^ { 4 }$

Write the equation in the form $y = c x ^ { b }$ where b is a constant. - $y = 3 \sqrt { x }$

Graph the inequality. - $2 x+4 y \geq-8$ $Graph the inequality. - 2 x+4 y \geq-8$

Graph the solution set of the system of inequalities. - $\left\{ \begin{array} { l } y > x ^ { 2 } - 4 \\2 y - x < 0\end{array} \right.$ $Graph the solution set of the system of inequalities. - \left\{ \begin{array} { l } y > x ^ { 2 } - 4 \\ 2 y - x < 0 \end{array} \right.$

Write the indicated term of the binomial expansion. - $( 2 x + 8 ) ^ { 3 } ; \quad$ 3rd term

Write the equation in the form $y = f ( x )$ f(x) by solving for y. - $11 y - 5 x ^ { 3 } = 20$

Find the center and radius of the circle with the given equation. - $x ^ { 2 } + y ^ { 2 } = 9$

Find the center and radius of the circle with the given equation. - $( x - 1.7 ) ^ { 2 } + ( y + 4.7 ) ^ { 2 } = 7$

Write the function without radicals by using fractional exponents. - $y = \sqrt [ 4 ] { ( x - 3 ) ^ { 3 } }$

Graph. - $y=-\sqrt{x^{2}+2}$ $Graph. - y=-\sqrt{x^{2}+2}$

Draw the graph of the equation. - $y ^ { 2 } = - 5 x$ $Draw the graph of the equation. - y ^ { 2 } = - 5 x$

Draw the graph of the equation. - $y=x^{2}-2 x-5$ $Draw the graph of the equation. - y=x^{2}-2 x-5$