Question

the time spent dancing (minutes) and the amount of calories burned can be modeled by the equation $c = 5.5t$. which table of values matches the equation and includes only viable solutions? three tables of time (t) and calories (c) values are shown: first table: t=-5, c=-27.5; t=0, c=0; t=5, c=27.5; t=10, c=55. second table: t=0, c=0; t=5, c=27.5; t=10, c=55; t=15, c=82.5. third table: t=-20, c=-110; t=-15, c=-82.5; t=-10, c=-55; t=-5, c=-27.5

Explanation:

Step1: Identify viable t-values

Time spent dancing cannot be negative, so $t \geq 0$.

Step2: Validate equation for t-values

For $t=0$: $c=5.5(0)=0$
For $t=5$: $c=5.5(5)=27.5$
For $t=10$: $c=5.5(10)=55$
For $t=15$: $c=5.5(15)=82.5$

Step3: Eliminate invalid tables

Tables with negative $t$ values are non-viable, so only the second table has valid, positive/zero time values that fit the equation.

Answer:

The second table:

Time (t)	Calories (c)
5	27.5
10	55
15	82.5