problems 3 - 6\nsort the cards based on whether they represent a proportional relationship or not.\nthe…

problems 3 - 6\nsort the cards based on whether they represent a proportional relationship or not.\nthe volume, v, of a rectangular prism whose height is 12 centimeters and whose base is a square with side lengths of s centimeters: v = 12s².\nthe remaining length, l, of a 120 - inch rope after x inches have been cut off: 120 - x = l.\nthe total cost, t, after 8% sales tax is added to an items price p: 1.08p = t.\nthe number of marbles, x, each sister gets after m marbles are shared equally among four sisters: x = m/4.\nproportional\nnot proportional

problems 3 - 6\nsort the cards based on whether they represent a proportional relationship or not.\nthe volume, v, of a rectangular prism whose height is 12 centimeters and whose base is a square with side lengths of s centimeters: v = 12s².\nthe remaining length, l, of a 120 - inch rope after x inches have been cut off: 120 - x = l.\nthe total cost, t, after 8% sales tax is added to an items price p: 1.08p = t.\nthe number of marbles, x, each sister gets after m marbles are shared equally among four sisters: x = m/4.\nproportional\nnot proportional

Answer

Explanation:

Step1: Recall proportional - relationship definition

A proportional relationship is of the form $y = kx$ ($k$ is a non - zero constant), and when $x = 0$, $y=0$.

Step2: Analyze $V = 12s^{2}$

It is not of the form $y = kx$. For example, when $s = 0$, $V = 0$, but the relationship is quadratic. So it is not proportional.

Step3: Analyze $120−x = L$

When $x = 0$, $L = 120\neq0$. It is not of the form $y = kx$. So it is not proportional.

Step4: Analyze $1.08p=t$

It can be written as $t = 1.08p$, where $k = 1.08$. When $p = 0$, $t = 0$. So it is proportional.

Step5: Analyze $x=\frac{m}{4}$

It can be written as $x=\frac{1}{4}m$, where $k=\frac{1}{4}$. When $m = 0$, $x = 0$. So it is proportional.

Answer:

Proportional: The total cost $t$ after 8% sales tax is added to an item's price $p$ ($1.08p = t$), The number of marbles $x$ each sister gets after $m$ marbles are shared equally among four sisters ($x=\frac{m}{4}$) Not Proportional: The volume $V$ of a rectangular prism whose height is 12 centimeters and whose base is a square with side lengths of $s$ centimeters ($V = 12s^{2}$), The remaining length $L$ of a 120 - inch rope after $x$ inches have been cut off ($120−x = L$)