Question 1

Complete the rewriting of the given series using the new index as indicated.   (2i + 1) =

Accepted Answer

A) 
  (2i + 1) =
  (2j + 2) 
B) 
  (2i + 1) =
  (2j + 3) 
C) 
  (2i + 1) =
  (2j + 4) 
D) 
  (2i + 1) =
  (2j + 3) 
A) 
  (2i + 1) =
  (2j + 2) 
B) 
  (2i + 1) =
  (2j + 3) 
C) 
  (2i + 1) =
  (2j + 4) 
D) 
  (2i + 1) =
  (2j + 3)

Question 2

List all terms of the finite sequence an = n + 4 for 1 ≤ n ≤ 5.

Accepted Answer

A)  5, 9, 13, 17, 21 
B)  4, 5, 6, 7, 8 
C)  5, 6, 7, 8, 9 
D)  4, 8, 12, 16, 20 
A)  5, 9, 13, 17, 21 
B)  4, 5, 6, 7, 8 
C)  5, 6, 7, 8, 9 
D)  4, 8, 12, 16, 20

Question 3

Solve the given system of equations. y = x2
Y = 6

Accepted Answer

A)  Ø 
B)  {(-6, 36), (6, 36)} 
C)    
D)    
A)  Ø 
B)  {(-6, 36), (6, 36)} 
C)    
D)

Question 4

Find the sum of the given infinite geometric series. 16 + 12 + 9 + ...

Accepted Answer

A)  "64" 
B)  "F1F1F1S1F1F1F10" 
C)  "68" 
D)  "60" 
A)  "64" 
B)  "F1F1F1S1F1F1F10" 
C)  "68" 
D)  "60"

Question 5

Write the expression without negative exponents.

Accepted Answer

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

Question 6

Conrad builds picnic tables and porch swings which he sells at flea markets. A picnic table requires six 2F1F1F1S1F1F1F104's and nine 1F1F1F1S1F1F1F106's. A swing uses three 2F1F1F1S1F1F1F104's and six 1F1F1F1S1F1F1F106's. Conrad currently has 108 2F1F1F1S1F1F1F104's and 180 1F1F1F1S1F1F1F106's in his inventory. If tables sell for $50 and swings sell for $30, how many of each item should Conrad make in order to maximize his revenue?

Accepted Answer

A)  15 picnic tables and 10 porch swings 
B)  0 picnic tables and 30 porch swings 
C)  18 picnic tables and 0 porch swings 
D)  12 picnic tables and 12 porch swings 
A)  15 picnic tables and 10 porch swings 
B)  0 picnic tables and 30 porch swings 
C)  18 picnic tables and 0 porch swings 
D)  12 picnic tables and 12 porch swings

Question 7

Solve the inequality. Graph the solution set. x2 + 10x + 21 ≥ 0

Accepted Answer

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

Question 8

Write the given equation in the form y = a(x - h)2 + k and identify the vertex, focus, and directrix. y = 3x2 - 8x + 5

Accepted Answer

A)  Vertex:
  ; Focus:
  ; Directrix:
  
B)  Vertex:
  ; Focus:
  ; Directrix:
  
C)  Vertex:
  ; Focus:
  ; Directrix:
  
D)  Vertex:
  ; Focus:
  ; Directrix:
  
A)  Vertex:
  ; Focus:
  ; Directrix:
  
B)  Vertex:
  ; Focus:
  ; Directrix:
  
C)  Vertex:
  ; Focus:
  ; Directrix:
  
D)  Vertex:
  ; Focus:
  ; Directrix:

Question 9

How are the graphs of   and   related?

Accepted Answer

A)  The graph of g(x) is the same as that of f(x), but translated upward by 4 units. 
B)  The graph of g(x) is the same as that of f(x), but translated downward by 4 units. 
C)  The graph of g(x) is the same as that of f(x), but translated 4 units to the right. 
D)  The graph of g(x) is the same as that of f(x), but translated 4 units to the left. 
A)  The graph of g(x) is the same as that of f(x), but translated upward by 4 units. 
B)  The graph of g(x) is the same as that of f(x), but translated downward by 4 units. 
C)  The graph of g(x) is the same as that of f(x), but translated 4 units to the right. 
D)  The graph of g(x) is the same as that of f(x), but translated 4 units to the left.

Question 10

Solve 4-6x - 10 = 16-4x - 1.

Accepted Answer

A)  {5} 
B)  {-4} 
C)  {6} 
D)  {4} 
A)  {5} 
B)  {-4} 
C)  {6} 
D)  {4}

Question 11

Solve the absolute value inequality and graph the solution. |x - 1| F1F1F1S1F1F1F10 2

Accepted Answer

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

Question 12

Raphael can load a large shipping truck in 12 hours. Working together, Raphael and Jana can load the same truck in 3 hours. How long would it take Jana to load the truck by herself?

Accepted Answer

A)  3 hours 
B)  5 hours 
C)  6 hours 
D)  4 hours 
A)  3 hours 
B)  5 hours 
C)  6 hours 
D)  4 hours

Question 13

Find the product. (2a + 6)(10a + 1)

Accepted Answer

A)  20a2 + 22a + 6 
B)  20a2 + 19a + 6 
C)  20a2 + 6a + 62 
D)  20a2 + 62a + 6 
A)  20a2 + 22a + 6 
B)  20a2 + 19a + 6 
C)  20a2 + 6a + 62 
D)  20a2 + 62a + 6

Question 14

Find four consecutive integers whose sum is 226.

Accepted Answer

A)  55, 57, 59, 61 
B)  56, 57, 58, 59 
C)  55, 56, 57, 58 
D)  54, 55, 56, 57 
A)  55, 57, 59, 61 
B)  56, 57, 58, 59 
C)  55, 56, 57, 58 
D)  54, 55, 56, 57

Question 15

Write a formula for the nth term of the given arithmetic sequence. 9, 14, 19, 24, 29, . . .

Accepted Answer

A)  an = 5n + 4 
B)  an = 4n - 5 
C)  an = 5n - 4 
D)  an = 6n - 5 
A)  an = 5n + 4 
B)  an = 4n - 5 
C)  an = 5n - 4 
D)  an = 6n - 5

Question 16

Find the imaginary solutions: 100x2 + 160x + 100 = 0

Accepted Answer

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

Question 17

Solve the given equation. 18c2 + 3c - 10 = 0

Accepted Answer

A)    
B)    
C)    
D)  -2, 3 
A)    
B)    
C)    
D)  -2, 3

Question 18

Graph the solution to the compound inequality.

Accepted Answer

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

Question 19

Use the binomial theorem to expand the given binomial. (y + 1)3

Accepted Answer

A)  y3 + y2 + y + 1 
B)  y3 + 1 
C)  y3 + 3y2 + 3y + 1 
D)  3y3 + 3y2 + 3y + 3 
A)  y3 + y2 + y + 1 
B)  y3 + 1 
C)  y3 + 3y2 + 3y + 1 
D)  3y3 + 3y2 + 3y + 3

Question 20

Find the x- and y-intercepts of 7x - 2y = -5 and use these intercepts to graph the equation.

Accepted Answer

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

Exam 18: Algebraic Equation Practice

Complete the rewriting of the given series using the new index as indicated. (2i + 1) =

List all terms of the finite sequence an = n + 4 for 1 ≤ n ≤ 5.

Solve the given system of equations. y = x2 Y = 6

Find the sum of the given infinite geometric series. 16 + 12 + 9 + ...

Write the expression without negative exponents.

Solve the inequality. Graph the solution set. x2 + 10x + 21 ≥ 0

Write the given equation in the form y = a(x - h)2 + k and identify the vertex, focus, and directrix. y = 3x2 - 8x + 5

How are the graphs of and related?

Solve 4-6x - 10 = 16-4x - 1.

Solve the absolute value inequality and graph the solution. |x - 1|  2

Raphael can load a large shipping truck in 12 hours. Working together, Raphael and Jana can load the same truck in 3 hours. How long would it take Jana to load the truck by herself?

Find the product. (2a + 6)(10a + 1)

Find four consecutive integers whose sum is 226.

Write a formula for the nth term of the given arithmetic sequence. 9, 14, 19, 24, 29, . . .

Find the imaginary solutions: 100x2 + 160x + 100 = 0

Solve the given equation. 18c2 + 3c - 10 = 0

Graph the solution to the compound inequality.

Use the binomial theorem to expand the given binomial. (y + 1)3

Find the x- and y-intercepts of 7x - 2y = -5 and use these intercepts to graph the equation.

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 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

Filters

List all terms of the finite sequence a_n = n + 4 for 1 ≤ n ≤ 5.

Solve the given system of equations. y = x² Y = 6

Solve the inequality. Graph the solution set. x² + 10x + 21 ≥ 0

Write the given equation in the form y = a(x - h)² + k and identify the vertex, focus, and directrix. y = 3x² - 8x + 5

Solve 4^-6^x^{- 10} = 16^-4^x^{- 1}.

Find the imaginary solutions: 100x² + 160x + 100 = 0

Solve the given equation. 18c² + 3c - 10 = 0

Use the binomial theorem to expand the given binomial. (y + 1)³