Homework 5*****Already A++ Rated Tutorial*****Use as Guide Paper*****

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1.     Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.

31-x = 1/27

 

 

 

A. {2}

 

 

B. {-7}

 

 

C. {4}

 

 

D. {3}

 
 

2.5 Points

   

2.     Perform the long division and write the partial fraction decomposition of the remainder term. 

x4 – x2 + 2/x3 - x2

 

 

 

A. x + 3 - 2/x - 1/x2 + 4x - 1

 

 

B. 2x + 1 - 2/x - 2/x + 2/x + 1

 

 

C. 2x + 1 - 2/x2 - 2/x + 5/x - 1

 

 

D. x + 1 - 2/x - 2/x2 + 2/x - 1

 
 

2.5 Points

   

3.     Solve each equation by either substitution or addition method.

https://study.ashworthcollege.edu/access/content/group/ddef570e-fc7d-4cb1-bd6e-3d3f5ab3f21b/v9/Images/Exam%20Images/Lesson%202/Lesson%202%20Exam%20Question%2010.JPG

x2 + 4y2 = 20 
x + 2y = 6

 

 

 

 

A. {(5, 2), (-4, 1)}

 

 

B. {(4, 2), (3, 1)}

 

 

C. {(2, 2), (4, 1)}

 

 

D. {(6, 2), (7, 1)}

 

 

 

2.5 Points

4.     Solve the following system by the addition method.

{2x + 3y = 6 
{2x – 3y = 6

 

 

 

A. {(4, 1)}

 

 

B. {(5, 0)}

 

 

C. {(2, 1)}

 

 

D. {(3, 0)}

 

 

0.0/ 2.5 Points

   

5.     Find the domain of following logarithmic function.

f(x) = ln (x - 2)2

 

 

 

A. (∞, 2)  (-2, -∞)

 

 

B. (-∞, 2)  (2, ∞)

 

 

C. (-∞, 1)  (3, ∞)

 

 

D. (2, -∞)  (2, ∞)

 
 

0.0/ 2.5 Points

   

6.     Find the domain of following logarithmic function.

f(x) = log (2 - x)

 

 

 

A. (∞, 4)

 

 

B. (∞, -12)

 

 

C. (-∞, 2)

 

 

D. (-∞, -3)

 
 

0.0/ 2.5 Points

   

7.     Perform the long division and write the partial fraction decomposition of the remainder term. 

x5 + 2/x2 - 1

 

 

 

A. x2 + x - 1/2(x + 1) + 4/2(x - 1)

 

 

 

B. x3 + x - 1/2(x + 1) + 3/2(x - 1)

 

C. x3 + x - 1/6(x - 2) + 3/2(x + 1)

 

D. x2 + x - 1/2(x + 1) + 4/2(x - 1)

 

 

 

0.0/ 2.5 Points

8.     Solve each equation by the substitution method.

https://study.ashworthcollege.edu/access/content/group/ddef570e-fc7d-4cb1-bd6e-3d3f5ab3f21b/v9/Images/Exam%20Images/Lesson%202/Lesson%202%20Exam%20Question%2010.JPG

x2 - 4y2 = -7 
3x2 + y2 = 31

 

 

 

 

A. {(2, 2), (3, -2), (-1, 2), (-4, -2)}

 

 

B. {(7, 2), (3, -2), (-4, 2), (-3, -1)}

 

 

C. {(4, 2), (3, -2), (-5, 2), (-2, -2)}

 

 

D. {(3, 2), (3, -2), (-3, 2), (-3, -2)}

 

 

 

0.0/ 2.5 Points

 

 

9.     Write the partial fraction decomposition for the following rational expression.

1/x2 – c2 (c ≠ 0)

 

 

 

A. 1/4c/x - c - 1/2c/x + c

 

 

B. 1/2c/x - c - 1/2c/x + c

 

 

C. 1/3c/x - c - 1/2c/x + c

 

 

D. 1/2c/x - c - 1/3c/x + c

 

 

 

0.0/ 2.5 Points

 

 

10.  Write the partial fraction decomposition for the following rational expression.
 
ax +b/(x – c)2 (c ≠ 0)

 

 

 

A. a/a – c +ac + b/(x – c)2

 

 

B. a/b – c +ac + b/(x – c)

 

 

C. a/a – b +ac + c/(x – c)2

 

 

D. a/a – b +ac + b/(x – c)

 

 

 

 

0.0/ 2.5 Points

11.  Write the form of the partial fraction decomposition of the rational expression. 
5x2 - 6x + 7/(x - 1)(x2 + 1)

 

 

 

A. A/x - 2 + Bx2 + C/x2 + 3

 

 

B. A/x - 4 + Bx + C/x2 + 1

 

 

C. A/x - 3 + Bx + C/x2 + 1

 

 

D. A/x - 1 + Bx + C/x2 + 1

 

 

 

 

0.0/ 2.5 Points

12.  Solve the following system.

https://study.ashworthcollege.edu/access/content/group/ddef570e-fc7d-4cb1-bd6e-3d3f5ab3f21b/v9/Images/Exam%20Images/Lesson%202/Lesson%202%20Exam%20Question%2010.JPG

3(2x+y) + 5z = -1 
2(x - 3y + 4z) = -9 
4(1 + x) = -3(z - 3y)

 

 

 

 

A. {(1, 1/3, 0)}

 

 

B. {(1/4, 1/3, -2)}

 

 

C. {(1/3, 1/5, -1)}

 

 

D. {(1/2, 1/3, -1)}

 

 

 

 

 

0.0/ 2.5 Points

13.  Write the partial fraction decomposition for the following rational expression.

4/2x2 - 5x – 3

 

 

 

A. 4/6(x - 2) - 8/7(4x + 1)

 

 

B. 4/7(x - 3) - 8/7(2x + 1)

 

 

C. 4/7(x - 2) - 8/7(3x + 1)

 

 

D. 4/6(x - 2) - 8/7(3x + 1)

 

 

14.  Use properties of logarithms to expand the following logarithmic expression as much as possible.
 
Logb (√xy/ z3)

 

 

 

A. 1/2 logbx - 6 logby + 3 logbz

 

 

B. 1/2 logb x - 9 logb y - 3 logb z

 

 

C. 1/2 logb x + 3 logb y + 6 logb z

 

 

D. 1/2 logb x + 3 logb y - 3 logb z

 

 

 

2.5 Points

15.  Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.

3 ln x – 1/3 ln y

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