Decide whether or not each equation represents a proportional relationship. A. The remaining length (L) of 120-inch rope after x inches have been cut off: 120−x=L b. The total cost (t) after 8% sales tax is added to an item's price (p): 1.08p=t c. The number of marbles each sister gets (x) when m marbles are shared equally among four sisters: x=m4 d. The volume (V) of a rectangular prism whose height is 12 cm and base is a square with side lengths s cm: V=12s2 Problem 3

Answer and Step-by-step explanation: An equation represents proportional relationship when dividing the quantities of the equation results in a quotient that is always the same. For example, in general:

Equation: y = mx

= m

m is a constant value, which means is the same.

A. Equation: 120 - x = L

Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.

B. Equation: 1.08p = t

Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.

C. Equation:

This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:

D. Equation:

This equation is NOT proportional because side length is squared, so it is not constant linearly.

(-1,0) and (4,0) are x-intercepts.

step-by-step explanation:

x-intercepts are all points on the x-axis.

points (-1,0) and (4,0) are both x -intercepts.

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11 -1> 1 -1+ a

-12 > a