Answer :
To determine which table has a constant of proportionality between [tex]\(y\)[/tex] and [tex]\(x\)[/tex] of 10, we need to check whether the ratio [tex]\(\frac{y}{x}\)[/tex] is equal to 10 for every pair of [tex]\( (x, y) \)[/tex] in that table.
Let's examine each table step by step.
### Table A
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 2 & 20 \\ 12 & 132 \\ 22 & 220 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each pair:
[tex]\[ \frac{20}{2} = 10 \][/tex]
[tex]\[ \frac{132}{12} = 11 \][/tex]
[tex]\[ \frac{220}{22} = 10 \][/tex]
Since one of the ratios (132/12) is not equal to 10, Table A does not have a constant of proportionality of 10.
### Table B
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 5 & 20 \\ 7 & 30 \\ 10 & 40 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each pair:
[tex]\[ \frac{20}{5} = 4 \][/tex]
[tex]\[ \frac{30}{7} \approx 4.2857 \][/tex]
[tex]\[ \frac{40}{10} = 4 \][/tex]
None of the ratios in Table B is equal to 10, so Table B does not have the required constant of proportionality.
### Table C
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 9 & 90 \\ 14 & 140 \\ 24 & 240 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each pair:
[tex]\[ \frac{90}{9} = 10 \][/tex]
[tex]\[ \frac{140}{14} = 10 \][/tex]
[tex]\[ \frac{240}{24} = 10 \][/tex]
All the ratios in Table C are equal to 10, so Table C has a constant of proportionality of 10.
Therefore, the correct answer is:
(C)
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 9 & 90 \\ 14 & 140 \\ 24 & 240 \\ \hline \end{array} \][/tex]
Let's examine each table step by step.
### Table A
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 2 & 20 \\ 12 & 132 \\ 22 & 220 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each pair:
[tex]\[ \frac{20}{2} = 10 \][/tex]
[tex]\[ \frac{132}{12} = 11 \][/tex]
[tex]\[ \frac{220}{22} = 10 \][/tex]
Since one of the ratios (132/12) is not equal to 10, Table A does not have a constant of proportionality of 10.
### Table B
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 5 & 20 \\ 7 & 30 \\ 10 & 40 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each pair:
[tex]\[ \frac{20}{5} = 4 \][/tex]
[tex]\[ \frac{30}{7} \approx 4.2857 \][/tex]
[tex]\[ \frac{40}{10} = 4 \][/tex]
None of the ratios in Table B is equal to 10, so Table B does not have the required constant of proportionality.
### Table C
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 9 & 90 \\ 14 & 140 \\ 24 & 240 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each pair:
[tex]\[ \frac{90}{9} = 10 \][/tex]
[tex]\[ \frac{140}{14} = 10 \][/tex]
[tex]\[ \frac{240}{24} = 10 \][/tex]
All the ratios in Table C are equal to 10, so Table C has a constant of proportionality of 10.
Therefore, the correct answer is:
(C)
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 9 & 90 \\ 14 & 140 \\ 24 & 240 \\ \hline \end{array} \][/tex]
