Find the best solutions to your problems with the help of IDNLearn.com. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.
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.
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.
