Question 1

Perform the indicated operations and write your result in lowest terms.

Accepted Answer

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

Question 2

Solve the given equation.

Accepted Answer

A)  No solution 
B)  -6, 6 
C)  -6 
D)  6 
A)  No solution 
B)  -6, 6 
C)  -6 
D)  6 B

Question 3

Find the indicated value for the given rational expression.

Accepted Answer

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

Question 4

Reduce the given expression to lowest terms.

Accepted Answer

A)  z + 11 
B)    
C)  z2 + 121 
D)  z - 11 
A)  z + 11 
B)    
C)  z2 + 121 
D)  z - 11

Question 5

Among 100 college students, 45 said they study 11 or more hours per week while the rest said they did not. What is the ratio of those students who study at least 11 hours per week to those that do not?

Accepted Answer

A)  9 to 11 
B)  20 to 11 
C)  9 to 20 
D)  11 to 9 
A)  9 to 11 
B)  20 to 11 
C)  9 to 20 
D)  11 to 9

Question 6

A veterinarian is studying parasitic infections in German shepherds. Of the dogs studied, she discovered that one-third of the male German shepherds had some type of parasitic infection while one-fourth of the females had some type of parasitic infection. Furthermore, she found that one-sixth of the male dogs sampled were infected with the heartworm parasite and one-eighth of the females were infected with the heartworm parasite. What fraction of the parasitic infections were heartworm parasites? Assume that the study sampled the same number of males as females.

Accepted Answer

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

Question 7

Solve the equation for y.

Accepted Answer

A)  y = 7x - 33 
B)  y = 7x - 38 
C)  y = 7x - 34 
D)  y = 7x - 42 
A)  y = 7x - 33 
B)  y = 7x - 38 
C)  y = 7x - 34 
D)  y = 7x - 42

Question 8

Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator.

Accepted Answer

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

Question 9

Marta averaged   miles per hour for the x hours in which she drove home. Later, she drove another   hour at the same rate to her parents' home. How many miles did she drive to her parents' house?

Accepted Answer

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

Question 10

For the given ratio, find and equivalent ratio of integers in lowest terms.

Accepted Answer

A)  39 
B)    
C)    
D)    
A)  39 
B)    
C)    
D)

Question 11

David hires a septic system contractor to dig trenches for his new septic tank. The cost to hire the contractor is a fixed cost of $150 plus an additional $80 per hour. Which expression below describes the average cost of an x-hour job?

Accepted Answer

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

Question 12

Find the least common multiple of the given terms. r2 - 8r - 9, r2 - 18r + 81

Accepted Answer

A)  (r - 9) 
B)  (r + 1)(r - 9) 
C)  (r + 1)(r - 9)2 
D)  (r + 1)(r - 9)(r + 9) 
A)  (r - 9) 
B)  (r + 1)(r - 9) 
C)  (r + 1)(r - 9)2 
D)  (r + 1)(r - 9)(r + 9)

Question 13

Brandi bought a total of 6 lb of flounder and shrimp and paid $16 for the flounder and $16 for the shrimp. If the price per pound of the shrimp is twice that of the flounder, how many pounds of each did she buy?

Accepted Answer

A)  3 lb shrimp and 3 lb flounder 
B)  1 lb shrimp and 5 lb flounder 
C)  2 lb shrimp and 4 lb flounder 
D)  4 lb shrimp and 2 lb flounder 
A)  3 lb shrimp and 3 lb flounder 
B)  1 lb shrimp and 5 lb flounder 
C)  2 lb shrimp and 4 lb flounder 
D)  4 lb shrimp and 2 lb flounder

Question 14

Reduce the expression to lowest terms.

Accepted Answer

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

Question 15

Jimbo biked 20 miles at x mph. He then increased his speed by 6 mph and biked another 30 miles. Write a rational expression for Jimbo's total travel time.

Accepted Answer

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

Question 16

Solve the equation.

Accepted Answer

A)  -1, -2 
B)  1, -2 
C)  1, 2 
D)  1 
A)  -1, -2 
B)  1, -2 
C)  1, 2 
D)  1

Question 17

Perform the indicated operations and write your result in lowest terms.

Accepted Answer

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

Question 18

Perform the indicated operations and write your result in lowest terms.

Accepted Answer

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

Question 19

Build the rational expression into an equivalent rational expression with the indicated denominator.

Accepted Answer

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

Question 20

Cora can paddle her canoe 14 miles in the same time that Susan's motorboat covers 42 miles. If Susan's boat travels 14 mph faster than Cora's canoe, then how fast is Susan's boat?

Accepted Answer

A)  23 mph 
B)  21 mph 
C)  7 mph 
D)  22 mph 
A)  23 mph 
B)  21 mph 
C)  7 mph 
D)  22 mph

Exam 6: Section 1: Rational Expressions

Perform the indicated operations and write your result in lowest terms.

Solve the given equation.

Find the indicated value for the given rational expression.

Reduce the given expression to lowest terms.

Among 100 college students, 45 said they study 11 or more hours per week while the rest said they did not. What is the ratio of those students who study at least 11 hours per week to those that do not?

Solve the equation for y.

Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator.

Marta averaged miles per hour for the x hours in which she drove home. Later, she drove another hour at the same rate to her parents' home. How many miles did she drive to her parents' house?

For the given ratio, find and equivalent ratio of integers in lowest terms.

David hires a septic system contractor to dig trenches for his new septic tank. The cost to hire the contractor is a fixed cost of $150 plus an additional $80 per hour. Which expression below describes the average cost of an x-hour job?

Find the least common multiple of the given terms. r2 - 8r - 9, r2 - 18r + 81

Brandi bought a total of 6 lb of flounder and shrimp and paid $16 for the flounder and $16 for the shrimp. If the price per pound of the shrimp is twice that of the flounder, how many pounds of each did she buy?

Reduce the expression to lowest terms.

Jimbo biked 20 miles at x mph. He then increased his speed by 6 mph and biked another 30 miles. Write a rational expression for Jimbo's total travel time.

Solve the equation.

Perform the indicated operations and write your result in lowest terms.

Perform the indicated operations and write your result in lowest terms.

Build the rational expression into an equivalent rational expression with the indicated denominator.

Cora can paddle her canoe 14 miles in the same time that Susan's motorboat covers 42 miles. If Susan's boat travels 14 mph faster than Cora's canoe, then how fast is Susan's boat?

Section 1: Real Numbers and Their Properties

Section 2: Real Numbers and Their Properties

Section 1: Linear Equations and Inequalities in One Variable

Section 2: Linear Equations and Inequalities in One Variable

Section 1: Linear Equations and Inequalities in Two Variables

Section 2: Linear Equations and Inequalities in Two Variables

Section 1: Exponents and Polynomials

Section 2: Exponents and Polynomials

Section 1: Factoring

Section 2: Factoring

Section 2: Rational Expressions

Section 1: Systems of Linear Equations

Section 2: Systems of Linear Equations

Section 1: More on Inequalities

Section 2: More on Inequalities

Section 1: Radicals and Rational Exponents

Section 2: Radicals and Rational Exponents

Section 1: Quadratic Equations and Inequalities

Section 2: Quadratic Equations and Inequalities

Section 1: Functions

Section 2: Functions

Section 1: Exponential and Logarithmic Functions

Section 2: Exponential and Logarithmic Functions

Section 1: Nonlinear Systems and the Conic Sections

Section 2: Nonlinear Systems and the Conic Sections

Section 1: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Section 2: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Mathematical Problem Set

Algebraic Equations and Problem Solving

Algebra and Math Problems

Algebraic Equation Practice

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Find the least common multiple of the given terms. r² - 8r - 9, r² - 18r + 81