Question 1

Solve the problem. Round your answer, as needed.
-A machine can fill 4352 cartons of milk in 0.5 hour. How many cartons of milk can it fill per hour?

Accepted Answer

A)  2176 cartons 
B)  7253 cartons 
C)  4353 cartons 
D)  8704 cartons 
A)  2176 cartons 
B)  7253 cartons 
C)  4353 cartons 
D)  8704 cartons

Question 2

Add or subtract as indicated. Write the answer in lowest terms.
-$\frac{2}{r}+\frac{3}{r+6}$

Accepted Answer

A)  $\frac{-12 r-5}{r(r+6)}$ 
B)  $\frac{-12 r-5}{r(-6-r)}$ 
C)  $\frac{5 r+12}{r(r+6)}$ 
D)  $\frac{5 r+12}{r(-6-r)}$ 
A)  $\frac{-12 r-5}{r(r+6)}$ 
B)  $\frac{-12 r-5}{r(-6-r)}$ 
C)  $\frac{5 r+12}{r(r+6)}$ 
D)  $\frac{5 r+12}{r(-6-r)}$

Question 3

Assume that the expressions given are denominators of fractions. Find the least common denominator.
-$x^{2}+4 x-12,5 x+30$

Accepted Answer

A)  $5(x+2)(x+6)$ 
B)  $5(x-2)(x+6)$ 
C)  $5(x+2)(x-6)$ 
D)  $5(x-2)(x-6)$ 
A)  $5(x+2)(x+6)$ 
B)  $5(x-2)(x+6)$ 
C)  $5(x+2)(x-6)$ 
D)  $5(x-2)(x-6)$

Question 4

Choose the one alternative that best completes the statement or answers the question.
-If $x$ varies inversely as $y^{2}$, and $x=6$ when $y=20$, find $x$ when $y=4$.

Accepted Answer

A)  5 
B)  150 
C)  96 
D)  180 
A)  5 
B)  150 
C)  96 
D)  180

Question 5

Find all numbers not in the domain of the function
-$f(x)=\frac{x-7}{5-x}$

Accepted Answer

A)  5,7 
B)  None 
C)  -5 
D)  5 
A)  5,7 
B)  None 
C)  -5 
D)  5

Question 6

Add or subtract as indicated. Write the answer in lowest terms.
-$\frac{2 a b}{a^{2}-b^{2}}-\frac{b}{a-b}+4$

Accepted Answer

A)  $\frac{2 a b-b+4}{a+b+1}$ 
B)  $\frac{(a-b)(5 a+5 b)}{a^{2}-b^{2}}$ 
C)  $\frac{4 a+5 b}{a+b}$ 
D)  $\frac{4 a+5 b}{a^{2}-b^{2}}$ 
A)  $\frac{2 a b-b+4}{a+b+1}$ 
B)  $\frac{(a-b)(5 a+5 b)}{a^{2}-b^{2}}$ 
C)  $\frac{4 a+5 b}{a+b}$ 
D)  $\frac{4 a+5 b}{a^{2}-b^{2}}$

Question 7

Choose the equivalent form of the given formula for lateral area of a cone. $\mathrm{A}=\pi \mathrm{rs}$

Accepted Answer

A)  $s=\frac{\pi \mathrm{A}}{\mathrm{r}}$ 
B)  $\mathrm{r}=\frac{\pi \mathrm{A}}{\mathrm{s}}$ 
C)  $r=\frac{A}{\pi s}$ 
D)  $\mathrm{s}=\frac{\mathrm{r}}{\pi \mathrm{A}}$ 
A)  $s=\frac{\pi \mathrm{A}}{\mathrm{r}}$ 
B)  $\mathrm{r}=\frac{\pi \mathrm{A}}{\mathrm{s}}$ 
C)  $r=\frac{A}{\pi s}$ 
D)  $\mathrm{s}=\frac{\mathrm{r}}{\pi \mathrm{A}}$

Question 8

$\frac{4}{5 x}+\frac{1}{2 x}=-\frac{1}{10}$

Accepted Answer

A)  $\{-14\}$ 
B)  $\varnothing$ 
C)  $\{13\}$ 
D)  $\{-13\}$ 
A)  $\{-14\}$ 
B)  $\varnothing$ 
C)  $\{13\}$ 
D)  $\{-13\}$

Question 9

Choose the one alternative that best completes the statement or answers the question.
Simplify the complex fraction
-$\frac{\frac{6}{y}}{\frac{7}{y+3}}$

Accepted Answer

A)  $42 y(y+3)$ 
B)  $\frac{y+3}{42 y}$ 
C)  $\frac{6(y+3)}{7 y}$ 
D)  $\frac{7 y}{6(y+3)}$ 
A)  $42 y(y+3)$ 
B)  $\frac{y+3}{42 y}$ 
C)  $\frac{6(y+3)}{7 y}$ 
D)  $\frac{7 y}{6(y+3)}$

Question 10

Perform the indicated operation and express in lowest terms.
-$\frac{125 x^{3}+125 x^{2} y}{25 x^{2}+50 x y+25 y^{2}}-\frac{125 x y^{2}+125 y^{3}}{25 x^{2}+50 x y+25 y^{2}}$

Accepted Answer

A)  $\frac{x-y}{25 x^{2}+25 x y+25 y^{2}}$ 
B)  $5 y-5 x$ 
C)  $\frac{5 x^{2}-5 y^{2}}{5 x+5 y}$ 
D)  $5 x-5 y$ 
A)  $\frac{x-y}{25 x^{2}+25 x y+25 y^{2}}$ 
B)  $5 y-5 x$ 
C)  $\frac{5 x^{2}-5 y^{2}}{5 x+5 y}$ 
D)  $5 x-5 y$

Question 11

Assume that the expressions given are denominators of fractions. Find the least common denominator.
-$7 y+14, y^{2}-4, y$

Accepted Answer

A)  $14 y(y+2)^{2}(y-2)$ 
B)  $14 y\left(y^{2}+2\right)\left(y^{2}-2\right)$ 
C)  $7 y(y+2)(y-2)$ 
D)  $y(y+2)(y-2)$ 
A)  $14 y(y+2)^{2}(y-2)$ 
B)  $14 y\left(y^{2}+2\right)\left(y^{2}-2\right)$ 
C)  $7 y(y+2)(y-2)$ 
D)  $y(y+2)(y-2)$

Question 12

Choose the one alternative that best completes the statement or answers the question.
-For a fixed amount of principal, the simple interest varies jointly with the rate and the time. If the simple interest is $\$ 1200$ when the rate is $4 \%$ and the time is 6 years, find the simple interest when the rate is $5 \%$ and the time is 10 years.

Accepted Answer

A)  $\$ 5000$ 
B)  $\$ 2750$ 
C)  $\$ 250$ 
D)  $\$ 2500$ 
A)  $\$ 5000$ 
B)  $\$ 2750$ 
C)  $\$ 250$ 
D)  $\$ 2500$

Question 13

Tell whether or not the rational expressions are equivalent.
-$\frac{-2 x^{3}+7 x^{2}+15 x}{x^{2}-8 x+15}, \frac{(-x)(2 x+3)}{x+3}$

Accepted Answer

A) True 
 B)False

Question 14

Find all numbers not in the domain of the function
-$f(x)=\frac{x^{2}-64}{x^{2}+4 x-32}$

Accepted Answer

A)  $8,-8$ 
B)  $8,-4$ 
C)  0 
D)  $-8,4$ 
A)  $8,-8$ 
B)  $8,-4$ 
C)  0 
D)  $-8,4$

Question 15

Tell whether or not the rational expressions are equivalent.
-$\frac{5 m+5}{m^{2}-1}, \frac{5}{m-1}$

Accepted Answer

A) True 
 B)False

Question 16

Graph the rational function. Give the equations of the vertical and horizontal asymptotes.
-$f(x)=-\frac{1}{x}$

Accepted Answer

A) $ x=-2 ; y=0 $
  
B) $ x=0 ; y=0 $
  
C) $ x=0 ; y=0 $
  
D) $ x=0 ; y=-3 $
  
A) $ x=-2 ; y=0 $
  
B) $ x=0 ; y=0 $
  
C) $ x=0 ; y=0 $
  
D) $ x=0 ; y=-3 $

Question 17

$\frac{2}{t}=\frac{t}{5 t-12}$

Accepted Answer

A)  $\{6,4\}$ 
B)  $\{6\}$ 
C)  $\varnothing$ 
D)  $\{0,16\}$ 
A)  $\{6,4\}$ 
B)  $\{6\}$ 
C)  $\varnothing$ 
D)  $\{0,16\}$

Question 18

Express the rational expression in lowest terms.
-$\frac{y^{2}+2 y-8}{y^{2}-2 y-24}$

Accepted Answer

A)  $\frac{2 y-1}{-2 y-3}$ 
B)  $\frac{y-2}{y-6}$ 
C)  $\frac{2 y-8}{-2 y-24}$ 
D)  $-\frac{y^{2}+2 y-8}{y^{2}-2 y-24}$ 
A)  $\frac{2 y-1}{-2 y-3}$ 
B)  $\frac{y-2}{y-6}$ 
C)  $\frac{2 y-8}{-2 y-24}$ 
D)  $-\frac{y^{2}+2 y-8}{y^{2}-2 y-24}$

Question 19

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 80 miles in the same time that Dana travels 68 miles. If Chuck's rate of travel is $6 \mathrm{mph}$ more than Dana's, and they travel the same length of time, at what speed does Chuck travel?

Accepted Answer

A)  $40 \mathrm{mph}$ 
B)  $38 \mathrm{mph}$ 
C)  $42 \mathrm{mph}$ 
D)  $34 \mathrm{mph}$ 
A)  $40 \mathrm{mph}$ 
B)  $38 \mathrm{mph}$ 
C)  $42 \mathrm{mph}$ 
D)  $34 \mathrm{mph}$

Question 20

Determine whether the equation represents direct, inverse, joint, or combined variation.
-$y=\frac{4}{x}$

Accepted Answer

A)  Inverse 
B)  Combined 
C)  Direct 
D)  Joint 
A)  Inverse 
B)  Combined 
C)  Direct 
D)  Joint

Solve the problem. Round your answer, as needed. -A machine can fill 4352 cartons of milk in 0.5 hour. How many cartons of milk can it fill per hour?

Add or subtract as indicated. Write the answer in lowest terms. - $\frac{2}{r}+\frac{3}{r+6}$

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $x^{2}+4 x-12,5 x+30$

Choose the one alternative that best completes the statement or answers the question. -If $x$ varies inversely as $y^{2}$ , and $x=6$ when $y=20$ , find $x$ when $y=4$ .

Find all numbers not in the domain of the function - $f(x)=\frac{x-7}{5-x}$

Add or subtract as indicated. Write the answer in lowest terms. - $\frac{2 a b}{a^{2}-b^{2}}-\frac{b}{a-b}+4$

Choose the equivalent form of the given formula for lateral area of a cone. $\mathrm{A}=\pi \mathrm{rs}$

$\frac{4}{5 x}+\frac{1}{2 x}=-\frac{1}{10}$

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - $\frac{\frac{6}{y}}{\frac{7}{y+3}}$

Perform the indicated operation and express in lowest terms. - $\frac{125 x^{3}+125 x^{2} y}{25 x^{2}+50 x y+25 y^{2}}-\frac{125 x y^{2}+125 y^{3}}{25 x^{2}+50 x y+25 y^{2}}$

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $7 y+14, y^{2}-4, y$

Tell whether or not the rational expressions are equivalent. - $\frac{-2 x^{3}+7 x^{2}+15 x}{x^{2}-8 x+15}, \frac{(-x)(2 x+3)}{x+3}$

Find all numbers not in the domain of the function - $f(x)=\frac{x^{2}-64}{x^{2}+4 x-32}$

Tell whether or not the rational expressions are equivalent. - $\frac{5 m+5}{m^{2}-1}, \frac{5}{m-1}$

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - $f(x)=-\frac{1}{x}$ $Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - f(x)=-\frac{1}{x}$

$\frac{2}{t}=\frac{t}{5 t-12}$

Express the rational expression in lowest terms. - $\frac{y^{2}+2 y-8}{y^{2}-2 y-24}$

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 80 miles in the same time that Dana travels 68 miles. If Chuck's rate of travel is $6 \mathrm{mph}$ more than Dana's, and they travel the same length of time, at what speed does Chuck travel?

Determine whether the equation represents direct, inverse, joint, or combined variation. - $y=\frac{4}{x}$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 7: Rational Expressions and Functions

Solve the problem. Round your answer, as needed. -A machine can fill 4352 cartons of milk in 0.5 hour. How many cartons of milk can it fill per hour?

Add or subtract as indicated. Write the answer in lowest terms. - 2r+3r+6\frac{2}{r}+\frac{3}{r+6}r2​+r+63​

Assume that the expressions given are denominators of fractions. Find the least common denominator. - x2+4x−12,5x+30x^{2}+4 x-12,5 x+30x2+4x−12,5x+30

Choose the one alternative that best completes the statement or answers the question. -If xxx varies inversely as y2y^{2}y2 , and x=6x=6x=6 when y=20y=20y=20 , find xxx when y=4y=4y=4 .

Find all numbers not in the domain of the function - f(x)=x−75−xf(x)=\frac{x-7}{5-x}f(x)=5−xx−7​

Add or subtract as indicated. Write the answer in lowest terms. - 2aba2−b2−ba−b+4\frac{2 a b}{a^{2}-b^{2}}-\frac{b}{a-b}+4a2−b22ab​−a−bb​+4

Choose the equivalent form of the given formula for lateral area of a cone. A=πrs\mathrm{A}=\pi \mathrm{rs}A=πrs

45x+12x=−110\frac{4}{5 x}+\frac{1}{2 x}=-\frac{1}{10}5x4​+2x1​=−101​

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - 6y7y+3\frac{\frac{6}{y}}{\frac{7}{y+3}}y+37​y6​​

Perform the indicated operation and express in lowest terms. - 125x3+125x2y25x2+50xy+25y2−125xy2+125y325x2+50xy+25y2\frac{125 x^{3}+125 x^{2} y}{25 x^{2}+50 x y+25 y^{2}}-\frac{125 x y^{2}+125 y^{3}}{25 x^{2}+50 x y+25 y^{2}}25x2+50xy+25y2125x3+125x2y​−25x2+50xy+25y2125xy2+125y3​

Assume that the expressions given are denominators of fractions. Find the least common denominator. - 7y+14,y2−4,y7 y+14, y^{2}-4, y7y+14,y2−4,y

Tell whether or not the rational expressions are equivalent. - −2x3+7x2+15xx2−8x+15,(−x)(2x+3)x+3\frac{-2 x^{3}+7 x^{2}+15 x}{x^{2}-8 x+15}, \frac{(-x)(2 x+3)}{x+3}x2−8x+15−2x3+7x2+15x​,x+3(−x)(2x+3)​

Find all numbers not in the domain of the function - f(x)=x2−64x2+4x−32f(x)=\frac{x^{2}-64}{x^{2}+4 x-32}f(x)=x2+4x−32x2−64​

Tell whether or not the rational expressions are equivalent. - 5m+5m2−1,5m−1\frac{5 m+5}{m^{2}-1}, \frac{5}{m-1}m2−15m+5​,m−15​

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - f(x)=−1xf(x)=-\frac{1}{x}f(x)=−x1​

2t=t5t−12\frac{2}{t}=\frac{t}{5 t-12}t2​=5t−12t​

Express the rational expression in lowest terms. - y2+2y−8y2−2y−24\frac{y^{2}+2 y-8}{y^{2}-2 y-24}y2−2y−24y2+2y−8​

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 80 miles in the same time that Dana travels 68 miles. If Chuck's rate of travel is 6mph6 \mathrm{mph}6mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel?

Determine whether the equation represents direct, inverse, joint, or combined variation. - y=4xy=\frac{4}{x}y=x4​

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Add or subtract as indicated. Write the answer in lowest terms. - $\frac{2}{r}+\frac{3}{r+6}$

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $x^{2}+4 x-12,5 x+30$

Choose the one alternative that best completes the statement or answers the question. -If $x$ varies inversely as $y^{2}$ , and $x=6$ when $y=20$ , find $x$ when $y=4$ .

Find all numbers not in the domain of the function - $f(x)=\frac{x-7}{5-x}$

Add or subtract as indicated. Write the answer in lowest terms. - $\frac{2 a b}{a^{2}-b^{2}}-\frac{b}{a-b}+4$

Choose the equivalent form of the given formula for lateral area of a cone. $\mathrm{A}=\pi \mathrm{rs}$

$\frac{4}{5 x}+\frac{1}{2 x}=-\frac{1}{10}$

Choose the one alternative that best completes the statement or answers the question. Simplify the complex fraction - $\frac{\frac{6}{y}}{\frac{7}{y+3}}$

Perform the indicated operation and express in lowest terms. - $\frac{125 x^{3}+125 x^{2} y}{25 x^{2}+50 x y+25 y^{2}}-\frac{125 x y^{2}+125 y^{3}}{25 x^{2}+50 x y+25 y^{2}}$

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $7 y+14, y^{2}-4, y$

Tell whether or not the rational expressions are equivalent. - $\frac{-2 x^{3}+7 x^{2}+15 x}{x^{2}-8 x+15}, \frac{(-x)(2 x+3)}{x+3}$

Find all numbers not in the domain of the function - $f(x)=\frac{x^{2}-64}{x^{2}+4 x-32}$

Tell whether or not the rational expressions are equivalent. - $\frac{5 m+5}{m^{2}-1}, \frac{5}{m-1}$

Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - $f(x)=-\frac{1}{x}$ $Graph the rational function. Give the equations of the vertical and horizontal asymptotes. - f(x)=-\frac{1}{x}$

$\frac{2}{t}=\frac{t}{5 t-12}$

Express the rational expression in lowest terms. - $\frac{y^{2}+2 y-8}{y^{2}-2 y-24}$

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 80 miles in the same time that Dana travels 68 miles. If Chuck's rate of travel is $6 \mathrm{mph}$ more than Dana's, and they travel the same length of time, at what speed does Chuck travel?

Determine whether the equation represents direct, inverse, joint, or combined variation. - $y=\frac{4}{x}$