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MATH 095
Intermediate Algebra
Spring 2009
Turn in FINAL DRAFTS of these problems. Your finished product should be easy to
read and contain how you reached your answers (show work). Use a highlighter to
show your final answers.
1. Carpenters stabilize wall frames with a diagonal brace, as shown in the figure.
The length of the brace is given by L  H 2  W 2 .
a. Solve the formula for H .
b. If the bottom of the brace is attached 9 feet from the corner and the
brace is 12 feet long, how far up the corner post should it be nailed? Give
your answer to the nearest tenth of a foot.
2. Find, explain, and correct the errors in this student’s work. Be sure to determine
the correct answers.
7x  4  8  x
7 x  4  64  x 2
0  x 2  7 x  60
a.
0  ( x  5)( x  12)
x  5  0 or
x  12  0
x  5
x  12
or
b.
2  9  7i   67i 
 42i
3. Consider the rectangular electronic billboard on the right. Find the perimeter and
the area for the billboard. Leave your answers as simplified radicals.
4. Solve each equation.
a.
x4  x2
b. 3 x  1  1  0
c.
x2  9x  3   x
d. 7 x  11  5  0
5. Simplify each expression.
x 1 3  x5 6
a.
x
3 5 1
 x y 
b.   2 1 2 
 2 xy 
c. r 1 2 r  r 3 2
d.

a 

13 4
a2 3
6. Perform the indicated operations. Give answers in standard form.
a. (5  4i)  (9  3i )
b. (2  3i )(1  i )
c.
d.
 25   81
3i
2i
7. Explain how to rationalize the denominator. Use an example in your explanation.
8. Find the exact length of side b in the figure.
9. Perform the indicated operations. Assume that all variables represent positive
real numbers.
a.
 13  2 
2
b. 8 80  3 45
c. 2 54 x3  5 96 x3
d.
3
5

2
16
Self-Reflection
Write a short (one or two paragraphs) self-reflection of this homework assignment.
What were your strengths? What were some areas in which you could improve?