hadanicolemanuela
Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

The time spent dancing (minutes) and the amount of calories burned can be modeled by the equation [tex]\(c = 5.5t\)[/tex]. Which table of values matches the equation and includes only viable solutions?

[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]

[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]

[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]

Sagot :

GinnyAnswer
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]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.