Answer:
B) 9
Step-by-step explanation:
According to the statement, we have the following relationship:
[tex]y \propto x[/tex]
[tex]y = k\cdot x[/tex] (Eq. 1)
Where:
[tex]k[/tex] - Proportionality constant, dimensionless.
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
Such constant is eliminated by constructing this relationship:
[tex]\frac{y_{2}}{y_{1}} = \frac{x_{2}}{x_{1}}[/tex]
[tex]x_{2} = \left(\frac{y_{2}}{y_{1}} \right)\cdot x_{1}[/tex] (Eq. 2)
If we know that [tex]y_{1} = 56[/tex], [tex]x_{1} = 6[/tex] and [tex]y_{2} = 84[/tex], then the value of [tex]x_{2}[/tex] is:
[tex]x_{2} = \left(\frac{84}{56} \right)\cdot (6)[/tex]
[tex]x_{2} = 9[/tex]
Hence, the correct answer is B.
