Alan

2^(3x-1)*4^(2x+3)=8^(3-x)

We can write 4ⁿ as (2²)ⁿ → 2²ⁿ  and 8ⁿ as (2³)ⁿ → 2³ⁿ

so 2^(3x-1)*4^(2x+3)=8^(3-x)  becomes   2^(3x-1)*2^(4x+6) = 2^(9-3x)

Since 2^a*2^b = 2^a+b we can further write  2^(3x-1+4x+6) = 2^(9-3x)  or  2^{(7x + 5)} = 2^{(9 - 3x)}

From this it is clear that 7x + 5 = 9 - 3x   so  10x = 4  or x = 4/10 → 0.4

3(-3) - 5y=30

Simplify

-9 - 5y = 30

Add 9 to both sides

- 5y = 39

Divide both sides by -5

y = -39/5

2 in 25 as a percentage is (2/25)*100  →  200/25 →  8%

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There are 26 juniors of whom 16 preferred morning classes, so the probability is 16/26 = 0.615

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Use atan (Press 2nd then atan on the calculator on the home page here)

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As follows:

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See image below:

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If the rectangle's corners are labelled HIJK in clockwise sequence, say, then HJ and IK are both diagonals, so we'd have:

x = 2x - 7 so that x = 7.

Let the distance from house to barn be L.  Distance = speed*time, so

L = 300*t1      (1)  where t1 is time to get from house to barn

L = 400*t2      (2)  where t2 is time to get from barn to house

t1 + t2 = 7      (3)

From (1) and (2) we have  300*t1 = 400*t2  so, dividing both sides by 400 we have t2 = 3*t1/4.  Put this into (3) to get:

t1 + 3*t1/4 = 7   or   7*t1/4 = 7  or  t1 = 4

t1 is the time they crawled, so crawling time = 4 minutes. 

This expression factors as  (x - 1)(x + 7)

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