Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To determine which table has a constant of proportionality between [tex]\(y\)[/tex] and [tex]\(x\)[/tex] of [tex]\(\frac{1}{6}\)[/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]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
