Question 1

Which of the following is the correct graph of   ?

Accepted Answer

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

Question 2

Solve:

Accepted Answer

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

Question 3

Solve: (x - 7)2 = 100

Accepted Answer

A)  {-3, 17} 
B)  {3, 17} 
C)  {-3, 3} 
D)  {17, 17} 
A)  {-3, 17} 
B)  {3, 17} 
C)  {-3, 3} 
D)  {17, 17} A

Question 4

The monthly profit P in dollars that Carla makes on the sale of x automobiles is determined by the formula P = x2 + 3x - 54. For what values of x is her profit positive?

Accepted Answer

A)  6, 7, ... 
B)  1, 2, ..., 7 
C)  7, 8, ... 
D)  1, 2, ..., 6 
A)  6, 7, ... 
B)  1, 2, ..., 7 
C)  7, 8, ... 
D)  1, 2, ..., 6

Question 5

Find all real solutions of the given equation. (x2 + 1)2 - 18(x2 + 1) = -17

Accepted Answer

A)  {5, 3} 
B)  {0, 5, 3} 
C)  {0, ±4} 
D)  {±16} 
A)  {5, 3} 
B)  {0, 5, 3} 
C)  {0, ±4} 
D)  {±16}

Question 6

Solve the inequality. Graph the solution set. x2 - 12x + 32 < 0

Accepted Answer

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

Question 7

Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime. 10x2 + 10x + 6

Accepted Answer

A)  The expression is prime. 
B)  (x + 10)(x + 6) 
C)  (10x + 6)(x + 10) 
D)  (10x + 10)(x + 6) 
A)  The expression is prime. 
B)  (x + 10)(x + 6) 
C)  (10x + 6)(x + 10) 
D)  (10x + 10)(x + 6)

Question 8

Solve the given inequality and express the solution in interval notation.

Accepted Answer

A)    
B)  (-10, 0]F1F1F1S1F1F1F10[0, 1) 
C)  [-10, 1) 
D)  (-10, 1] 
A)    
B)  (-10, 0]F1F1F1S1F1F1F10[0, 1) 
C)  [-10, 1) 
D)  (-10, 1]

Question 9

Find all real and imaginary solutions to the equation. b4 - 2401 = 0

Accepted Answer

A)    
B)  {0, ±7i} 
C)  {±7, ±7i} 
D)  {±7} 
A)    
B)  {0, ±7i} 
C)  {±7, ±7i} 
D)  {±7}

Question 10

Solve by factoring: x2 - x - 42 = 0

Accepted Answer

A)  {-7, -6} 
B)  {-7, 6} 
C)  {-6, 7} 
D)  {6, 7} 
A)  {-7, -6} 
B)  {-7, 6} 
C)  {-6, 7} 
D)  {6, 7}

Question 11

Solve by completing the square. 3x2 - 8x + 2 = 0

Accepted Answer

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

Question 12

A battery manufacturing plant spends C dollars per hour to produce "D"-size batteries. An efficiency consultant has determined that C is related to the number of batteries produced per hour, x, according to the equation C(x) = 0.01x2 - 2.4x + 224. What number of batteries per hour minimizes the cost?

Accepted Answer

A)  224 batteries 
B)  130 batteries 
C)  80 batteries 
D)  120 batteries 
A)  224 batteries 
B)  130 batteries 
C)  80 batteries 
D)  120 batteries

Question 13

Find all real solutions of the given equation. x2/3 - 2x1/3 - 15 = 0

Accepted Answer

A)  {±3, ±5} 
B)  {-27, 125} 
C)  {-3, 5} 
D)    
A)  {±3, ±5} 
B)  {-27, 125} 
C)  {-3, 5} 
D)

Question 14

Terrence paddles his canoe upstream a distance of 4 miles. He completes the return trip in 30 minutes less that the upstream journey. If the current flows at 4 miles per hour, what is Terrence's speed in still water?

Accepted Answer

A)    mph 
B)    mph 
C)  No real solution. 
D)    mph 
A)    mph 
B)    mph 
C)  No real solution. 
D)    mph

Question 15

Solve the given inequality and express the solution in interval notation. x2 + 9x F1F1F1S1F1F1F10 0

Accepted Answer

A)  (-F1F1F1S1F1F1F10, 0]F1F1F1S1F1F1F10[9, F1F1F1S1F1F1F10) 
B)  [0, F1F1F1S1F1F1F10) 
C)  [-9, 0] 
D)  (-F1F1F1S1F1F1F10, -9]F1F1F1S1F1F1F10[0, F1F1F1S1F1F1F10) 
A)  (-F1F1F1S1F1F1F10, 0]F1F1F1S1F1F1F10[9, F1F1F1S1F1F1F10) 
B)  [0, F1F1F1S1F1F1F10) 
C)  [-9, 0] 
D)  (-F1F1F1S1F1F1F10, -9]F1F1F1S1F1F1F10[0, F1F1F1S1F1F1F10)

Question 16

Find b2 - 4ac and the number of real solutions for the given equation. x2 + 3x + 4 = 0

Accepted Answer

A)  -7, 2 
B)  25, 0 
C)  -7, 0 
D)  25, 2 
A)  -7, 2 
B)  25, 0 
C)  -7, 0 
D)  25, 2

Question 17

If an object is given an initial velocity of v0 feet per second from a height of s0 feet, then its height S after t seconds is given by the formula   . A rock is thrown into the air at 14 feet per second from a height of 7 feet. How long does it take to reach the earth?

Accepted Answer

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

Question 18

Find all intercepts for the graph of the parabola. f(x) = 25 - x2

Accepted Answer

A)  (0, 0), (5, 25) 
B)  (0, 25), (-5, 0), (5, 0) 
C)  (25, 0), (0, -5), (0, 5) 
D)  (0, 25), (5, 0) 
A)  (0, 0), (5, 25) 
B)  (0, 25), (-5, 0), (5, 0) 
C)  (25, 0), (0, -5), (0, 5) 
D)  (0, 25), (5, 0)

Question 19

Write a quadratic equation that has the solutions -10 and 3.

Accepted Answer

A)  x2 + 7x - 30 = 0 
B)  x2 + 30 = 0 
C)  x2 - 60x - 30 = 0 
D)  x2 + 60x - 30 = 0 
A)  x2 + 7x - 30 = 0 
B)  x2 + 30 = 0 
C)  x2 - 60x - 30 = 0 
D)  x2 + 60x - 30 = 0

Question 20

Solve:

Accepted Answer

A)    
B)  {4, 9} 
C)  {-4, -9} 
D)  {9} 
A)    
B)  {4, 9} 
C)  {-4, -9} 
D)  {9}

Exam 10: Section 1: Quadratic Equations and Inequalities

Which of the following is the correct graph of ?

Solve:

Solve: (x - 7)2 = 100

The monthly profit P in dollars that Carla makes on the sale of x automobiles is determined by the formula P = x2 + 3x - 54. For what values of x is her profit positive?

Find all real solutions of the given equation. (x2 + 1)2 - 18(x2 + 1) = -17

Solve the inequality. Graph the solution set. x2 - 12x + 32 < 0

Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime. 10x2 + 10x + 6

Solve the given inequality and express the solution in interval notation.

Find all real and imaginary solutions to the equation. b4 - 2401 = 0

Solve by factoring: x2 - x - 42 = 0

Solve by completing the square. 3x2 - 8x + 2 = 0

Find all real solutions of the given equation. x2/3 - 2x1/3 - 15 = 0

Terrence paddles his canoe upstream a distance of 4 miles. He completes the return trip in 30 minutes less that the upstream journey. If the current flows at 4 miles per hour, what is Terrence's speed in still water?

Solve the given inequality and express the solution in interval notation. x2 + 9x  0

Find b2 - 4ac and the number of real solutions for the given equation. x2 + 3x + 4 = 0

If an object is given an initial velocity of v0 feet per second from a height of s0 feet, then its height S after t seconds is given by the formula . A rock is thrown into the air at 14 feet per second from a height of 7 feet. How long does it take to reach the earth?

Find all intercepts for the graph of the parabola. f(x) = 25 - x2

Write a quadratic equation that has the solutions -10 and 3.

Solve:

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 1: Rational Expressions

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 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

Filters

Solve: (x - 7)² = 100

The monthly profit P in dollars that Carla makes on the sale of x automobiles is determined by the formula P = x² + 3x - 54. For what values of x is her profit positive?

Find all real solutions of the given equation. (x² + 1)² - 18(x² + 1) = -17

Solve the inequality. Graph the solution set. x² - 12x + 32 < 0

Use the discriminant to determine whether the given quadratic polynomial can be factored, then factor it if it is not prime. 10x² + 10x + 6

Find all real and imaginary solutions to the equation. b⁴ - 2401 = 0

Solve by factoring: x² - x - 42 = 0

Solve by completing the square. 3x² - 8x + 2 = 0

Find all real solutions of the given equation. x^2/3 - 2x^1/3 - 15 = 0

Solve the given inequality and express the solution in interval notation. x² + 9x  0

Find b² - 4ac and the number of real solutions for the given equation. x² + 3x + 4 = 0

If an object is given an initial velocity of v₀ feet per second from a height of s₀ feet, then its height S after t seconds is given by the formula . A rock is thrown into the air at 14 feet per second from a height of 7 feet. How long does it take to reach the earth?

Find all intercepts for the graph of the parabola. f(x) = 25 - x²