1. Verify the property a x (b+c) =(a x b)+(a x c) by taking: 1) a = (1/4), b = 0, c = (-5/6)

We start by replacing a=1/4, b=0 and c=-5/6 on both sides of a x (b + c) = (a×b) + (a+c) and compare results

So in 1/4 x (0 + (-5/6)) we solve first the parenthesis (0 + (-5/6))=(-5/6)

Now we solve the product 1/4×(-5/6) = -5/24

Now we replace in the other side

(1/4 × 0) + (1/4 × (-5/6))

First parenthesis: (0) + (-5/24) = -5/24

We conclude that both sides are equal to -5/24! So the property verifies

(Btw this is called distributive property)

the answer is d

the answer is in the first quadrant, which make the y-int positive.

since the dots are going down, therefore the correlation is negative

i hope it is right.