Get expert insights and community support for your questions on IDNLearn.com. Get thorough and trustworthy answers to your queries from our extensive network of knowledgeable professionals.
Sagot :
To determine which table represents a proportional relationship with a constant of proportionality equal to 0.8, we need to evaluate each table.
1. Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 4 & 8 & 10 \\ \hline y & 0 & 0.5 & 1 & 1.25 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each [tex]\(x \neq 0\)[/tex]:
- For [tex]\(x = 4\)[/tex], [tex]\(\frac{y}{x} = \frac{0.5}{4} = 0.125\)[/tex]
- For [tex]\(x = 8\)[/tex], [tex]\(\frac{y}{x} = \frac{1}{8} = 0.125\)[/tex]
- For [tex]\(x = 10\)[/tex], [tex]\(\frac{y}{x} = \frac{1.25}{10} = 0.125\)[/tex]
The constant of proportionality is 0.125, not 0.8.
2. Table 2:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 5 & 10 & 12.5 \\ \hline y & 0 & 4 & 8 & 10 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each [tex]\(x \neq 0\)[/tex]:
- For [tex]\(x = 5\)[/tex], [tex]\(\frac{y}{x} = \frac{4}{5} = 0.8\)[/tex]
- For [tex]\(x = 10\)[/tex], [tex]\(\frac{y}{x} = \frac{8}{10} = 0.8\)[/tex]
- For [tex]\(x = 12.5\)[/tex], [tex]\(\frac{y}{x} = \frac{10}{12.5} = 0.8\)[/tex]
The constant of proportionality is indeed 0.8 for Table 2.
3. Table 3:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 4 & 8 & 10 \\ \hline y & 0.8 & 0.8 & 0.8 & 0.8 \\ \hline \end{array} \][/tex]
This table cannot represent a proportional relationship, as when [tex]\(x\)[/tex] changes, [tex]\(y\)[/tex] remains constant.
4. Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 5 & 10 & 12.5 \\ \hline y & 0.8 & 10.8 & 20.8 & 25.8 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each [tex]\(x \neq 0\)[/tex]:
- For [tex]\(x = 5\)[/tex], [tex]\(\frac{y}{x} = \frac{10.8}{5} = 2.16\)[/tex]
- For [tex]\(x = 10\)[/tex], [tex]\(\frac{y}{x} = \frac{20.8}{10} = 2.08\)[/tex]
- For [tex]\(x = 12.5\)[/tex], [tex]\(\frac{y}{x} = \frac{25.8}{12.5} = 2.064\)[/tex]
The constant of proportionality is not consistent and is not 0.8.
Therefore, the table that represents a proportional relationship with a constant of proportionality equal to 0.8 is:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 5 & 10 & 12.5 \\ \hline y & 0 & 4 & 8 & 10 \\ \hline \end{array} \][/tex]
So, the answer is Table 2.
1. Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 4 & 8 & 10 \\ \hline y & 0 & 0.5 & 1 & 1.25 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each [tex]\(x \neq 0\)[/tex]:
- For [tex]\(x = 4\)[/tex], [tex]\(\frac{y}{x} = \frac{0.5}{4} = 0.125\)[/tex]
- For [tex]\(x = 8\)[/tex], [tex]\(\frac{y}{x} = \frac{1}{8} = 0.125\)[/tex]
- For [tex]\(x = 10\)[/tex], [tex]\(\frac{y}{x} = \frac{1.25}{10} = 0.125\)[/tex]
The constant of proportionality is 0.125, not 0.8.
2. Table 2:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 5 & 10 & 12.5 \\ \hline y & 0 & 4 & 8 & 10 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each [tex]\(x \neq 0\)[/tex]:
- For [tex]\(x = 5\)[/tex], [tex]\(\frac{y}{x} = \frac{4}{5} = 0.8\)[/tex]
- For [tex]\(x = 10\)[/tex], [tex]\(\frac{y}{x} = \frac{8}{10} = 0.8\)[/tex]
- For [tex]\(x = 12.5\)[/tex], [tex]\(\frac{y}{x} = \frac{10}{12.5} = 0.8\)[/tex]
The constant of proportionality is indeed 0.8 for Table 2.
3. Table 3:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 4 & 8 & 10 \\ \hline y & 0.8 & 0.8 & 0.8 & 0.8 \\ \hline \end{array} \][/tex]
This table cannot represent a proportional relationship, as when [tex]\(x\)[/tex] changes, [tex]\(y\)[/tex] remains constant.
4. Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 5 & 10 & 12.5 \\ \hline y & 0.8 & 10.8 & 20.8 & 25.8 \\ \hline \end{array} \][/tex]
Calculate [tex]\(\frac{y}{x}\)[/tex] for each [tex]\(x \neq 0\)[/tex]:
- For [tex]\(x = 5\)[/tex], [tex]\(\frac{y}{x} = \frac{10.8}{5} = 2.16\)[/tex]
- For [tex]\(x = 10\)[/tex], [tex]\(\frac{y}{x} = \frac{20.8}{10} = 2.08\)[/tex]
- For [tex]\(x = 12.5\)[/tex], [tex]\(\frac{y}{x} = \frac{25.8}{12.5} = 2.064\)[/tex]
The constant of proportionality is not consistent and is not 0.8.
Therefore, the table that represents a proportional relationship with a constant of proportionality equal to 0.8 is:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 5 & 10 & 12.5 \\ \hline y & 0 & 4 & 8 & 10 \\ \hline \end{array} \][/tex]
So, the answer is Table 2.
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com. We’re committed to providing accurate answers, so visit us again soon.