Answered

Join IDNLearn.com and start exploring the answers to your most pressing questions. Join our platform to receive prompt and accurate responses from experienced professionals in various fields.

Select the correct answer.

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 :

GinnyAnsweridn
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].
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.