Answer :
Given the equation [tex]\( c = 5.5t \)[/tex], we need to determine which table of values correctly follows this relationship between the time spent dancing (minutes) and the number of calories burned.
Let's examine each table one by one:
### Table 1
[tex]\[ \begin{tabular}{|c|c|} \hline Time $(t)$ & Calories $(c)$ \\ \hline -5 & -27.5 \\ \hline 0 & 0 \\ \hline 5 & 27.5 \\ \hline 10 & 55 \\ \hline \end{tabular} \][/tex]
Using the equation [tex]\( c = 5.5t \)[/tex], let's verify each pair:
- For [tex]\( t = -5 \)[/tex], [tex]\( c = 5.5 \times -5 = -27.5 \)[/tex].
- For [tex]\( t = 0 \)[/tex], [tex]\( c = 5.5 \times 0 = 0 \)[/tex].
- For [tex]\( t = 5 \)[/tex], [tex]\( c = 5.5 \times 5 = 27.5 \)[/tex].
- For [tex]\( t = 10 \)[/tex], [tex]\( c = 5.5 \times 10 = 55 \)[/tex].
All values in Table 1 satisfy the equation. Thus, Table 1 is a possible match.
### Table 2
[tex]\[ \begin{tabular}{|c|c|} \hline Time $(t)$ & Calories $(c)$ \\ \hline 0 & 0 \\ \hline 5 & 27.5 \\ \hline 10 & 55 \\ \hline 15 & 82.5 \\ \hline \end{tabular} \][/tex]
Using the equation [tex]\( c = 5.5t \)[/tex], let's verify each pair:
- For [tex]\( t = 0 \)[/tex], [tex]\( c = 5.5 \times 0 = 0 \)[/tex].
- For [tex]\( t = 5 \)[/tex], [tex]\( c = 5.5 \times 5 = 27.5 \)[/tex].
- For [tex]\( t = 10 \)[/tex], [tex]\( c = 5.5 \times 10 = 55 \)[/tex].
- For [tex]\( t = 15 \)[/tex], [tex]\( c = 5.5 \times 15 = 82.5 \)[/tex].
All values in Table 2 also satisfy the equation. Thus, Table 2 is a possible match.
### Table 3
[tex]\[ \begin{tabular}{|c|c|} \hline Time $(t)$ & Calories $(c)$ \\ \hline -20 & -110 \\ \hline -15 & -82.5 \\ \hline -10 & -55 \\ \hline -5 & -27.5 \\ \hline \end{tabular} \][/tex]
Using the equation [tex]\( c = 5.5t \)[/tex], let's verify each pair:
- For [tex]\( t = -20 \)[/tex], [tex]\( c = 5.5 \times -20 = -110 \)[/tex].
- For [tex]\( t = -15 \)[/tex], [tex]\( c = 5.5 \times -15 = -82.5 \)[/tex].
- For [tex]\( t = -10 \)[/tex], [tex]\( c = 5.5 \times -10 = -55 \)[/tex].
- For [tex]\( t = -5 \)[/tex], [tex]\( c = 5.5 \times -5 = -27.5 \)[/tex].
All values in Table 3 satisfy the equation. Thus, Table 3 is a possible match too.
### Conclusion:
Upon evaluating each table, we find that all three tables contain values that satisfy the equation [tex]\( c = 5.5t \)[/tex]. Therefore, any of the tables could be considered correct. However, only Table 1 was initially identified as matching the equation and including all valid solutions.
Thus, the table of values that matches the equation [tex]\( c = 5.5t \)[/tex] and includes only viable solutions is:
[tex]\[ \begin{tabular}{|c|c|} \hline Time $(t)$ & Calories $(c)$ \\ \hline -5 & -27.5 \\ \hline 0 & 0 \\ \hline 5 & 27.5 \\ \hline 10 & 55 \\ \hline \end{tabular} \][/tex]
Let's examine each table one by one:
### Table 1
[tex]\[ \begin{tabular}{|c|c|} \hline Time $(t)$ & Calories $(c)$ \\ \hline -5 & -27.5 \\ \hline 0 & 0 \\ \hline 5 & 27.5 \\ \hline 10 & 55 \\ \hline \end{tabular} \][/tex]
Using the equation [tex]\( c = 5.5t \)[/tex], let's verify each pair:
- For [tex]\( t = -5 \)[/tex], [tex]\( c = 5.5 \times -5 = -27.5 \)[/tex].
- For [tex]\( t = 0 \)[/tex], [tex]\( c = 5.5 \times 0 = 0 \)[/tex].
- For [tex]\( t = 5 \)[/tex], [tex]\( c = 5.5 \times 5 = 27.5 \)[/tex].
- For [tex]\( t = 10 \)[/tex], [tex]\( c = 5.5 \times 10 = 55 \)[/tex].
All values in Table 1 satisfy the equation. Thus, Table 1 is a possible match.
### Table 2
[tex]\[ \begin{tabular}{|c|c|} \hline Time $(t)$ & Calories $(c)$ \\ \hline 0 & 0 \\ \hline 5 & 27.5 \\ \hline 10 & 55 \\ \hline 15 & 82.5 \\ \hline \end{tabular} \][/tex]
Using the equation [tex]\( c = 5.5t \)[/tex], let's verify each pair:
- For [tex]\( t = 0 \)[/tex], [tex]\( c = 5.5 \times 0 = 0 \)[/tex].
- For [tex]\( t = 5 \)[/tex], [tex]\( c = 5.5 \times 5 = 27.5 \)[/tex].
- For [tex]\( t = 10 \)[/tex], [tex]\( c = 5.5 \times 10 = 55 \)[/tex].
- For [tex]\( t = 15 \)[/tex], [tex]\( c = 5.5 \times 15 = 82.5 \)[/tex].
All values in Table 2 also satisfy the equation. Thus, Table 2 is a possible match.
### Table 3
[tex]\[ \begin{tabular}{|c|c|} \hline Time $(t)$ & Calories $(c)$ \\ \hline -20 & -110 \\ \hline -15 & -82.5 \\ \hline -10 & -55 \\ \hline -5 & -27.5 \\ \hline \end{tabular} \][/tex]
Using the equation [tex]\( c = 5.5t \)[/tex], let's verify each pair:
- For [tex]\( t = -20 \)[/tex], [tex]\( c = 5.5 \times -20 = -110 \)[/tex].
- For [tex]\( t = -15 \)[/tex], [tex]\( c = 5.5 \times -15 = -82.5 \)[/tex].
- For [tex]\( t = -10 \)[/tex], [tex]\( c = 5.5 \times -10 = -55 \)[/tex].
- For [tex]\( t = -5 \)[/tex], [tex]\( c = 5.5 \times -5 = -27.5 \)[/tex].
All values in Table 3 satisfy the equation. Thus, Table 3 is a possible match too.
### Conclusion:
Upon evaluating each table, we find that all three tables contain values that satisfy the equation [tex]\( c = 5.5t \)[/tex]. Therefore, any of the tables could be considered correct. However, only Table 1 was initially identified as matching the equation and including all valid solutions.
Thus, the table of values that matches the equation [tex]\( c = 5.5t \)[/tex] and includes only viable solutions is:
[tex]\[ \begin{tabular}{|c|c|} \hline Time $(t)$ & Calories $(c)$ \\ \hline -5 & -27.5 \\ \hline 0 & 0 \\ \hline 5 & 27.5 \\ \hline 10 & 55 \\ \hline \end{tabular} \][/tex]
