Alan

(h + 5)^2 = h^2 + 2*5*h + 5^2 = h^2 + 10h + 25

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Suppose he had N hats on Monday.

On Tuesday he had N + 8 hats.

On Wednesday he had (N + 8)/2 hats.

On Thursday (N + 8)/2 = 20

Multiply both sides by 2

N + 8 = 40

Subtract 8 from both sides

N = 32  

This is how many hats he had on Monday.

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You could just write this as 

$$x^{\frac{3}{4}}$$

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To get slope intercept form isolate the y, so:

3x + 5y = -5

Subtract 3x from both sides:

5y = -3x - 5

Divide all terms by 5:

y = -(3/5)x - 1

This is now in slope intercept form, where the slope is -(3/5) and the y intercept is -1.

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For part a) I think there are only 15 sets of 3 pairs.  If the players are numbered 1 to 6 then the sets are as follows:

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Not quite anonymous!  Volume of sphere is 

$$Volume = \frac{4}{3}\pi r^3$$

Note the r-cubed not squared.

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Work out the slope of each option from (y2 - y1)/(x2 - x1):

a. slope = (2 - 5)/(-4 - 0) = -3/-4 = 3/4

b. slope = (1 - 2)/(-4 - 0) = -1/-4 = 1/4

c. slope = (-2 - 0)/(0 - 0) = -2/0 ⇒ vertical line

d. slope = (-2 - -2)/(-4 - 0) = 0/-4 = 0 ⇒ horizontal line

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In general g^a*g^b = g^a+b, so g⁴*g⁴ = g⁴⁺⁴ = g⁸

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