Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
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].
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 appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.