Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To determine which table has a constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] of [tex]\( \frac{1}{5} \)[/tex], we need to check if the ratio [tex]\( \frac{y}{x} \)[/tex] is consistent and equals [tex]\( \frac{1}{5} \)[/tex] for each pair of values in the table.
Table A:
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 2 & \frac{4}{5} \\ 7 & \frac{14}{5} \\ 12 & \frac{24}{5} \\ \hline \end{array} \][/tex]
Calculate the constant of proportionality for each pair in Table A:
1. For [tex]\( x = 2 \)[/tex] and [tex]\( y = \frac{4}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{4}{5}}{2} = \frac{4}{5} \times \frac{1}{2} = \frac{4}{10} = \frac{2}{5} \][/tex]
2. For [tex]\( x = 7 \)[/tex] and [tex]\( y = \frac{14}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{14}{5}}{7} = \frac{14}{5} \times \frac{1}{7} = \frac{14}{35} = \frac{2}{5} \][/tex]
3. For [tex]\( x = 12 \)[/tex] and [tex]\( y = \frac{24}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{24}{5}}{12} = \frac{24}{5} \times \frac{1}{12} = \frac{24}{60} = \frac{2}{5} \][/tex]
The ratio [tex]\( \frac{y}{x} \)[/tex] is [tex]\( \frac{2}{5} \)[/tex] in all cases for Table A. Therefore, this table does not have the constant of proportionality of [tex]\( \frac{1}{5} \)[/tex].
Table B:
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 8 & \frac{8}{5} \\ 9 & \frac{9}{5} \\ 10 & 2 \\ \hline \end{array} \][/tex]
Calculate the constant of proportionality for each pair in Table B:
1. For [tex]\( x = 8 \)[/tex] and [tex]\( y = \frac{8}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{8}{5}}{8} = \frac{8}{5} \times \frac{1}{8} = \frac{8}{40} = \frac{1}{5} \][/tex]
2. For [tex]\( x = 9 \)[/tex] and [tex]\( y = \frac{9}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{9}{5}}{9} = \frac{9}{5} \times \frac{1}{9} = \frac{9}{45} = \frac{1}{5} \][/tex]
3. For [tex]\( x = 10 \)[/tex] and [tex]\( y = 2 \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{2}{10} = \frac{1}{5} \][/tex]
The ratio [tex]\( \frac{y}{x} \)[/tex] is [tex]\( \frac{1}{5} \)[/tex] in all cases for Table B. Therefore, this table has the constant of proportionality of [tex]\( \frac{1}{5} \)[/tex].
Table C:
[tex]\[ \begin{array}{|ll|} \hline x & y \\ \hline 3 & \frac{16}{5} \\ \hline \end{array} \][/tex]
Calculate the constant of proportionality for the given pair in Table C:
1. For [tex]\( x = 3 \)[/tex] and [tex]\( y = \frac{16}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{16}{5}}{3} = \frac{16}{5} \times \frac{1}{3} = \frac{16}{15} \][/tex]
The ratio [tex]\( \frac{y}{x} \)[/tex] is [tex]\( \frac{16}{15} \)[/tex] for Table C, which is not [tex]\( \frac{1}{5} \)[/tex].
Therefore, the table that has a constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] of [tex]\( \frac{1}{5} \)[/tex] is Table B.
Table A:
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 2 & \frac{4}{5} \\ 7 & \frac{14}{5} \\ 12 & \frac{24}{5} \\ \hline \end{array} \][/tex]
Calculate the constant of proportionality for each pair in Table A:
1. For [tex]\( x = 2 \)[/tex] and [tex]\( y = \frac{4}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{4}{5}}{2} = \frac{4}{5} \times \frac{1}{2} = \frac{4}{10} = \frac{2}{5} \][/tex]
2. For [tex]\( x = 7 \)[/tex] and [tex]\( y = \frac{14}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{14}{5}}{7} = \frac{14}{5} \times \frac{1}{7} = \frac{14}{35} = \frac{2}{5} \][/tex]
3. For [tex]\( x = 12 \)[/tex] and [tex]\( y = \frac{24}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{24}{5}}{12} = \frac{24}{5} \times \frac{1}{12} = \frac{24}{60} = \frac{2}{5} \][/tex]
The ratio [tex]\( \frac{y}{x} \)[/tex] is [tex]\( \frac{2}{5} \)[/tex] in all cases for Table A. Therefore, this table does not have the constant of proportionality of [tex]\( \frac{1}{5} \)[/tex].
Table B:
[tex]\[ \begin{array}{|cc|} \hline x & y \\ \hline 8 & \frac{8}{5} \\ 9 & \frac{9}{5} \\ 10 & 2 \\ \hline \end{array} \][/tex]
Calculate the constant of proportionality for each pair in Table B:
1. For [tex]\( x = 8 \)[/tex] and [tex]\( y = \frac{8}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{8}{5}}{8} = \frac{8}{5} \times \frac{1}{8} = \frac{8}{40} = \frac{1}{5} \][/tex]
2. For [tex]\( x = 9 \)[/tex] and [tex]\( y = \frac{9}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{9}{5}}{9} = \frac{9}{5} \times \frac{1}{9} = \frac{9}{45} = \frac{1}{5} \][/tex]
3. For [tex]\( x = 10 \)[/tex] and [tex]\( y = 2 \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{2}{10} = \frac{1}{5} \][/tex]
The ratio [tex]\( \frac{y}{x} \)[/tex] is [tex]\( \frac{1}{5} \)[/tex] in all cases for Table B. Therefore, this table has the constant of proportionality of [tex]\( \frac{1}{5} \)[/tex].
Table C:
[tex]\[ \begin{array}{|ll|} \hline x & y \\ \hline 3 & \frac{16}{5} \\ \hline \end{array} \][/tex]
Calculate the constant of proportionality for the given pair in Table C:
1. For [tex]\( x = 3 \)[/tex] and [tex]\( y = \frac{16}{5} \)[/tex]:
[tex]\[ \frac{y}{x} = \frac{\frac{16}{5}}{3} = \frac{16}{5} \times \frac{1}{3} = \frac{16}{15} \][/tex]
The ratio [tex]\( \frac{y}{x} \)[/tex] is [tex]\( \frac{16}{15} \)[/tex] for Table C, which is not [tex]\( \frac{1}{5} \)[/tex].
Therefore, the table that has a constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] of [tex]\( \frac{1}{5} \)[/tex] is Table B.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
