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In which table does [tex][tex]$y$[/tex][/tex] vary directly with [tex][tex]$x$[/tex][/tex]?

A.
\begin{tabular}{|c|c|}
\hline[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 1 & -2 \\
\hline 2 & -4 \\
\hline 3 & -16 \\
\hline
\end{tabular}

B.
\begin{tabular}{|c|c|}
\hline [tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 1 & -5 \\
\hline 2 & 18 \\
\hline 3 & 41 \\
\hline
\end{tabular}

C.
\begin{tabular}{|c|c|}
\hline[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 1 & 26 \\
\hline 2 & 52 \\
\hline 3 & 78 \\
\hline
\end{tabular}

D.
\begin{tabular}{|c|c|}
\hline [tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 1 & -7 \\
\hline 2 & -1 \\
\hline 3 & 6 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To determine in which table [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], we must check for a consistent ratio [tex]\( \frac{y}{x} \)[/tex]. That is, if [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], then [tex]\( \frac{y}{x} \)[/tex] should yield the same constant value for all pairs [tex]\((x, y)\)[/tex] in the table.

Let's analyze each table:

Table A:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & -2 \\ 2 & -4 \\ 3 & -16 \\ \hline \end{array} \][/tex]

Calculating the ratio [tex]\( \frac{y}{x} \)[/tex] for each pair:
[tex]\[ \frac{-2}{1} = -2, \quad \frac{-4}{2} = -2, \quad \frac{-16}{3} \approx -5.33 \][/tex]

The ratio [tex]\( \frac{y}{x} \)[/tex] is not consistent, so [tex]\( y \)[/tex] does not vary directly with [tex]\( x \)[/tex] in Table A.

Table B:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & -5 \\ 2 & 18 \\ 3 & 41 \\ \hline \end{array} \][/tex]

Calculating the ratio [tex]\( \frac{y}{x} \)[/tex] for each pair:
[tex]\[ \frac{-5}{1} = -5, \quad \frac{18}{2} = 9, \quad \frac{41}{3} \approx 13.67 \][/tex]

The ratio [tex]\( \frac{y}{x} \)[/tex] is not consistent, so [tex]\( y \)[/tex] does not vary directly with [tex]\( x \)[/tex] in Table B.

Table C:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & 26 \\ 2 & 52 \\ 3 & 78 \\ \hline \end{array} \][/tex]

Calculating the ratio [tex]\( \frac{y}{x} \)[/tex] for each pair:
[tex]\[ \frac{26}{1} = 26, \quad \frac{52}{2} = 26, \quad \frac{78}{3} = 26 \][/tex]

The ratio [tex]\( \frac{y}{x} \)[/tex] is consistent at 26 for all pairs. Therefore, [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex] in Table C.

Table D:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & -7 \\ 2 & -1 \\ 3 & 6 \\ \hline \end{array} \][/tex]

Calculating the ratio [tex]\( \frac{y}{x} \)[/tex] for each pair:
[tex]\[ \frac{-7}{1} = -7, \quad \frac{-1}{2} = -0.5, \quad \frac{6}{3} = 2 \][/tex]

The ratio [tex]\( \frac{y}{x} \)[/tex] is not consistent, so [tex]\( y \)[/tex] does not vary directly with [tex]\( x \)[/tex] in Table D.

In summary, the correct table in which [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex] is:

Table C:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & 26 \\ 2 & 52 \\ 3 & 78 \\ \hline \end{array} \][/tex]

Therefore, the correct answer is [tex]\( \boxed{3} \)[/tex].
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