IDNLearn.com: Your go-to resource for finding expert answers. Our community is here to provide the comprehensive and accurate answers you need to make informed decisions.
Sagot :
To complete the table based on the given domain and function [tex]\( y = -\frac{2}{3} x + 7 \)[/tex], let's find the corresponding [tex]\( y \)[/tex] values for given [tex]\( x \)[/tex] values, and vice versa where needed.
1. For [tex]\( x = -6 \)[/tex]:
[tex]\[ y = -\frac{2}{3}(-6) + 7 = 4 + 7 = 11.0 \][/tex]
Therefore, the value of [tex]\( y \)[/tex] when [tex]\( x = -6 \)[/tex] is [tex]\( 11.0 \)[/tex].
2. For [tex]\( y = 5 \)[/tex]:
[tex]\[ 5 = -\frac{2}{3} x + 7 \][/tex]
[tex]\[ -\frac{2}{3} x = 5 - 7 = -2 \][/tex]
[tex]\[ x = -2 \div -\frac{2}{3} = -2 \times -\frac{3}{2} = 3.0 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 5 \)[/tex] is [tex]\( 3.0 \)[/tex].
3. For [tex]\( x = 15 \)[/tex]:
[tex]\[ y = -\frac{2}{3} (15) + 7 = -10 + 7 = -3.0 \][/tex]
Therefore, the value of [tex]\( y \)[/tex] when [tex]\( x = 15 \)[/tex] is [tex]\( -3.0 \)[/tex].
4. For [tex]\( y = 15 \)[/tex]:
[tex]\[ 15 = -\frac{2}{3} x + 7 \][/tex]
[tex]\[ -\frac{2}{3} x = 15 - 7 = 8 \][/tex]
[tex]\[ x = 8 \div -\frac{2}{3} = 8 \times -\frac{3}{2} = -12.0 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 15 \)[/tex] is [tex]\( -12.0 \)[/tex].
Now, we can complete the table:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -6 & 11.0 \\ \hline 3.0 & 5 \\ \hline 15 & -3.0 \\ \hline -12.0 & 15 \\ \hline \end{tabular} \][/tex]
1. For [tex]\( x = -6 \)[/tex]:
[tex]\[ y = -\frac{2}{3}(-6) + 7 = 4 + 7 = 11.0 \][/tex]
Therefore, the value of [tex]\( y \)[/tex] when [tex]\( x = -6 \)[/tex] is [tex]\( 11.0 \)[/tex].
2. For [tex]\( y = 5 \)[/tex]:
[tex]\[ 5 = -\frac{2}{3} x + 7 \][/tex]
[tex]\[ -\frac{2}{3} x = 5 - 7 = -2 \][/tex]
[tex]\[ x = -2 \div -\frac{2}{3} = -2 \times -\frac{3}{2} = 3.0 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 5 \)[/tex] is [tex]\( 3.0 \)[/tex].
3. For [tex]\( x = 15 \)[/tex]:
[tex]\[ y = -\frac{2}{3} (15) + 7 = -10 + 7 = -3.0 \][/tex]
Therefore, the value of [tex]\( y \)[/tex] when [tex]\( x = 15 \)[/tex] is [tex]\( -3.0 \)[/tex].
4. For [tex]\( y = 15 \)[/tex]:
[tex]\[ 15 = -\frac{2}{3} x + 7 \][/tex]
[tex]\[ -\frac{2}{3} x = 15 - 7 = 8 \][/tex]
[tex]\[ x = 8 \div -\frac{2}{3} = 8 \times -\frac{3}{2} = -12.0 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 15 \)[/tex] is [tex]\( -12.0 \)[/tex].
Now, we can complete the table:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -6 & 11.0 \\ \hline 3.0 & 5 \\ \hline 15 & -3.0 \\ \hline -12.0 & 15 \\ \hline \end{tabular} \][/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.