Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To determine which table has a constant of proportionality between [tex]\(y\)[/tex] and [tex]\(x\)[/tex] of [tex]\(\frac{1}{6}\)[/tex], we need to check if the relationship between [tex]\(x\)[/tex] and [tex]\(y\)[/tex] in each table is described by the equation [tex]\( y = \frac{1}{6}x \)[/tex].
### Table A:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 15 & 5 \\ 19 \frac{1}{2} & 6 \frac{1}{2} \\ 36 & 12 \\ \hline \end{array} \][/tex]
Checking each pair:
1. For [tex]\( x = 15 \)[/tex], [tex]\( y = 5 \)[/tex]:
[tex]\[ \frac{1}{6} \times 15 = \frac{15}{6} = 2.5 \quad \text{(not 5)} \][/tex]
2. For [tex]\( x = 19 \frac{1}{2} = 19.5 \)[/tex], [tex]\( y = 6 \frac{1}{2} = 6.5 \)[/tex]:
[tex]\[ \frac{1}{6} \times 19.5 = \frac{19.5}{6} \approx 3.25 \quad \text{(not 6.5)} \][/tex]
3. For [tex]\( x = 36 \)[/tex], [tex]\( y = 12 \)[/tex]:
[tex]\[ \frac{1}{6} \times 36 = \frac{36}{6} = 6 \quad \text{(not 12)} \][/tex]
### Table B:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 12 & 2 \\ 13 \frac{1}{2} & 3 \frac{1}{2} \\ 24 & 14 \\ \hline \end{array} \][/tex]
Checking each pair:
1. For [tex]\( x = 12 \)[/tex], [tex]\( y = 2 \)[/tex]:
[tex]\[ \frac{1}{6} \times 12 = \frac{12}{6} = 2 \quad \text{(Correct)} \][/tex]
2. For [tex]\( x = 13 \frac{1}{2} = 13.5 \)[/tex], [tex]\( y = 3 \frac{1}{2} = 3.5 \)[/tex]:
[tex]\[ \frac{1}{6} \times 13.5 = \frac{13.5}{6} = 2.25 \quad \text{(not 3.5)} \][/tex]
3. For [tex]\( x = 24 \)[/tex], [tex]\( y = 14 \)[/tex]:
[tex]\[ \frac{1}{6} \times 24 = \frac{24}{6} = 4 \quad \text{(not 14)} \][/tex]
### Table C:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 18 & 3 \\ 27 & 4 \frac{1}{2} \\ 33 & 5 \frac{1}{2} \\ \hline \end{array} \][/tex]
Checking each pair:
1. For [tex]\( x = 18 \)[/tex], [tex]\( y = 3 \)[/tex]:
[tex]\[ \frac{1}{6} \times 18 = \frac{18}{6} = 3 \quad \text{(Correct)} \][/tex]
2. For [tex]\( x = 27 \)[/tex], [tex]\( y = 4 \frac{1}{2} = 4.5 \)[/tex]:
[tex]\[ \frac{1}{6} \times 27 = \frac{27}{6} = 4.5 \quad \text{(Correct)} \][/tex]
3. For [tex]\( x = 33 \)[/tex], [tex]\( y = 5 \frac{1}{2} = 5.5 \)[/tex]:
[tex]\[ \frac{1}{6} \times 33 = \frac{33}{6} = 5.5 \quad \text{(Correct)} \][/tex]
From this, we can conclude which table follows the given constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex]:
- Table A does not satisfy the condition.
- Table B does not satisfy the condition.
- Table C satisfies the condition.
Therefore, the table that has a constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] of [tex]\( \frac{1}{6} \)[/tex] is:
[tex]\[ \boxed{\text{Table C}} \][/tex]
### Table A:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 15 & 5 \\ 19 \frac{1}{2} & 6 \frac{1}{2} \\ 36 & 12 \\ \hline \end{array} \][/tex]
Checking each pair:
1. For [tex]\( x = 15 \)[/tex], [tex]\( y = 5 \)[/tex]:
[tex]\[ \frac{1}{6} \times 15 = \frac{15}{6} = 2.5 \quad \text{(not 5)} \][/tex]
2. For [tex]\( x = 19 \frac{1}{2} = 19.5 \)[/tex], [tex]\( y = 6 \frac{1}{2} = 6.5 \)[/tex]:
[tex]\[ \frac{1}{6} \times 19.5 = \frac{19.5}{6} \approx 3.25 \quad \text{(not 6.5)} \][/tex]
3. For [tex]\( x = 36 \)[/tex], [tex]\( y = 12 \)[/tex]:
[tex]\[ \frac{1}{6} \times 36 = \frac{36}{6} = 6 \quad \text{(not 12)} \][/tex]
### Table B:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 12 & 2 \\ 13 \frac{1}{2} & 3 \frac{1}{2} \\ 24 & 14 \\ \hline \end{array} \][/tex]
Checking each pair:
1. For [tex]\( x = 12 \)[/tex], [tex]\( y = 2 \)[/tex]:
[tex]\[ \frac{1}{6} \times 12 = \frac{12}{6} = 2 \quad \text{(Correct)} \][/tex]
2. For [tex]\( x = 13 \frac{1}{2} = 13.5 \)[/tex], [tex]\( y = 3 \frac{1}{2} = 3.5 \)[/tex]:
[tex]\[ \frac{1}{6} \times 13.5 = \frac{13.5}{6} = 2.25 \quad \text{(not 3.5)} \][/tex]
3. For [tex]\( x = 24 \)[/tex], [tex]\( y = 14 \)[/tex]:
[tex]\[ \frac{1}{6} \times 24 = \frac{24}{6} = 4 \quad \text{(not 14)} \][/tex]
### Table C:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 18 & 3 \\ 27 & 4 \frac{1}{2} \\ 33 & 5 \frac{1}{2} \\ \hline \end{array} \][/tex]
Checking each pair:
1. For [tex]\( x = 18 \)[/tex], [tex]\( y = 3 \)[/tex]:
[tex]\[ \frac{1}{6} \times 18 = \frac{18}{6} = 3 \quad \text{(Correct)} \][/tex]
2. For [tex]\( x = 27 \)[/tex], [tex]\( y = 4 \frac{1}{2} = 4.5 \)[/tex]:
[tex]\[ \frac{1}{6} \times 27 = \frac{27}{6} = 4.5 \quad \text{(Correct)} \][/tex]
3. For [tex]\( x = 33 \)[/tex], [tex]\( y = 5 \frac{1}{2} = 5.5 \)[/tex]:
[tex]\[ \frac{1}{6} \times 33 = \frac{33}{6} = 5.5 \quad \text{(Correct)} \][/tex]
From this, we can conclude which table follows the given constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex]:
- Table A does not satisfy the condition.
- Table B does not satisfy the condition.
- Table C satisfies the condition.
Therefore, the table that has a constant of proportionality between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] of [tex]\( \frac{1}{6} \)[/tex] is:
[tex]\[ \boxed{\text{Table C}} \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
