Answer:
C. 272
Step-by-step explanation:
Since we know 85% of the students participated last year we can assume the same amount will participate this year so to find the answer you simply do the total number of students (320) multiplied by 85% or .85 to get the best guess of how many students will participate this year.
Answer:
Your number is (3 sqrt(2)) / sqrt(2) = 3, and is a rational number indeed. I don't know exactly how to interpret the rest of the question. If r is a positive rational number and p is some positive real number, then sqrt(r^2 p) / sqrt(p) is always rational, being equal r. Possibly your question refers to situtions in which sqrt(c) is not uniquely determined, as for c negative real number or complex non-real number. In those situations a discussion is necessary. Also, in general expressions the discussion is necesary, because the denominator must be different from 0, and so on.
Step-by-step explanation:
1 step: 
,

, then

.
2 step: 
, then




and

will have form

.
3 step: Solve this system

and dividing first equation on second we obtain

. So,

and

,

- the common ratio.
4 step: Insert

into equation

and obtain

, from where

.
9 and 3 are the only common factors between 54 and 90
102/87 = 3*34/(3*29) = 34/29