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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?

\begin{tabular}{|c|c|}
\hline
Time [tex]$(t)$[/tex] & Calories [tex]$(c)$[/tex] \\
\hline
-5 & -27.5 \\
\hline
0 & 0 \\
\hline
5 & 27.5 \\
\hline
10 & 55 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline
Time [tex]$(t)$[/tex] & Calories [tex]$(c)$[/tex] \\
\hline
0 & 0 \\
\hline
5 & 27.5 \\
\hline
10 & 55 \\
\hline
15 & 82.5 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline
Time [tex]$(t)$[/tex] & Calories [tex]$(c)$[/tex] \\
\hline
-20 & -110 \\
\hline
-15 & -82.5 \\
\hline
-10 & -55 \\
\hline
-5 & -27.5 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To determine which table(s) match the equation [tex]\( c = 5.5t \)[/tex], we will check each table to see if the given pairs of time [tex]\( t \)[/tex] and calories [tex]\( c \)[/tex] satisfy this equation.

First Table:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time } (t) & \text{Calories } (c) \\ \hline -5 & -27.5 \\ 0 & 0 \\ 5 & 27.5 \\ 10 & 55 \\ \hline \end{array} \][/tex]

1. For [tex]\( t = -5 \)[/tex]: [tex]\( c = 5.5 \times (-5) = -27.5 \)[/tex] (matches)
2. For [tex]\( t = 0 \)[/tex]: [tex]\( c = 5.5 \times 0 = 0 \)[/tex] (matches)
3. For [tex]\( t = 5 \)[/tex]: [tex]\( c = 5.5 \times 5 = 27.5 \)[/tex] (matches)
4. For [tex]\( t = 10 \)[/tex]: [tex]\( c = 5.5 \times 10 = 55 \)[/tex] (matches)

All pairs in the first table match the equation [tex]\( c = 5.5t \)[/tex].

Second Table:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time } (t) & \text{Calories } (c) \\ \hline 0 & 0 \\ 5 & 27.5 \\ 10 & 55 \\ 15 & 82.5 \\ \hline \end{array} \][/tex]

1. For [tex]\( t = 0 \)[/tex]: [tex]\( c = 5.5 \times 0 = 0 \)[/tex] (matches)
2. For [tex]\( t = 5 \)[/tex]: [tex]\( c = 5.5 \times 5 = 27.5 \)[/tex] (matches)
3. For [tex]\( t = 10 \)[/tex]: [tex]\( c = 5.5 \times 10 = 55 \)[/tex] (matches)
4. For [tex]\( t = 15 \)[/tex]: [tex]\( c = 5.5 \times 15 = 82.5 \)[/tex] (matches)

All pairs in the second table match the equation [tex]\( c = 5.5t \)[/tex].

Third Table:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time } (t) & \text{Calories } (c) \\ \hline -20 & -110 \\ -15 & -82.5 \\ -10 & -55 \\ -5 & -27.5 \\ \hline \end{array} \][/tex]

1. For [tex]\( t = -20 \)[/tex]: [tex]\( c = 5.5 \times (-20) = -110 \)[/tex] (matches)
2. For [tex]\( t = -15 \)[/tex]: [tex]\( c = 5.5 \times (-15) = -82.5 \)[/tex] (matches)
3. For [tex]\( t = -10 \)[/tex]: [tex]\( c = 5.5 \times (-10) = -55 \)[/tex] (matches)
4. For [tex]\( t = -5 \)[/tex]: [tex]\( c = 5.5 \times (-5) = -27.5 \)[/tex] (matches)

All pairs in the third table match the equation [tex]\( c = 5.5t \)[/tex].

Conclusion:
All three tables satisfy the equation [tex]\( c = 5.5t \)[/tex]. Therefore, the tables that match are:
1. The first table
2. The second table
3. The third table
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