Madelyn simplified the expression 3(4y) + 6 + 2y using the following steps:
3(4y) + 6 + 2y
v
12y + 6 + 2y
v
12y + 2y + 6
v
14y + 6
which property did she use in simplifying?
-commutative property of multiplication
-commutative property of addition
-associative property of multiplication
-associative property of addition

As part of an annual fundraiser to raise money for diabetes research, diane joined a bikeathon. the track she biked on was 1,920 yards long. diane biked 38.5 laps. her sponsors agreed to donate an amount of money for each mile she biked. how many miles did she bike? first fill in the blanks on the left side using the ratios shown. then write your answer. given ratios: 5280ft / 1 mi , 1 mi /5280 ft , 1,920 yards / 1 lap , 1 lap / 1,920 yards , 3 ft / 1 yard , 1 yard / 3 ft. blanks: 38.5 laps / 1 yard x (blank) x (blank) x (blank) = (blank) miles i'm really confused on how to do this, and the explanations aren't exactly . if you could walk me through how to do this, it would be greatly appreciated.

F(x)=x/2-2 and g(x)=2x^2+x-3 find (f+g)(x)

Suppose that one doll house uses the 1 inch scale, meaning that 1 inch on the doll house corresponds to 1/2 foot for life-sized objects. if the doll house is 108 inches wide, what is the width of the full-sized house that it's modeled after? in inches and feet.