Example Problems

Simplify the expression
3
2
æ
4 c  − 6
25 d −4
ö
­­
èø

A junior and a senior each simultaneously pick an interger at random from 1 to 10, inclusive. Find the probability that the "junior's number is even and the senior's number is divisble by 3." Give your answer in the form of a common fraction.

Solve the equatoin
\x + 8
 = 3 − i

Rationalize the denominator in the expression
3
\
x 2 y 2
3
\
x
 − 
3
\
y

Solve the equation
4
x 2 + 2 x − 15
 + 
5
x 2 − x − 6
 = 
3
x 2 + 7 x + 10
for x.

Find the sum of the infinite geometric series
­
Σ 4 · 0.6 n − 1
k = 1­
.

Machine C can do a job in 20 hours. Machine D can do this job in 15 hours. If machine C works alone for 2 hours and then Machine D works alone for 3 hours, how many additional hours are needed to complete the job with both machines at work?

Find the sum of the solutions to the equation
x 2 − 3 x
 = −4 x + 6
.

don't worry, the problems aren't as hard as they look and for those who think this is a snap, then see Mr. Darnall in Room 355.