Answer:
-480
Step-by-step explanation:
If f varies directly as g, and inversely as h, then we can write the variation equation:
, where k is the constant of variation.
If g=56 when h=-2 and f=-7, then we substitute these values into the formula to find the value of k.
![-7=\frac{k(56)}{-2}](https://tex.z-dn.net/?f=-7%3D%5Cfrac%7Bk%2856%29%7D%7B-2%7D)
![-7\times -2=56k](https://tex.z-dn.net/?f=-7%5Ctimes%20-2%3D56k)
![k=\frac{14}{56}=\frac{1}{4}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B14%7D%7B56%7D%3D%5Cfrac%7B1%7D%7B4%7D)
The equation now becomes:
![f=\frac{g}{4h}](https://tex.z-dn.net/?f=f%3D%5Cfrac%7Bg%7D%7B4h%7D)
if f=10 and h=-12, then;
![10=\frac{g}{-48}](https://tex.z-dn.net/?f=10%3D%5Cfrac%7Bg%7D%7B-48%7D)
![g=-48\times 10=-480](https://tex.z-dn.net/?f=g%3D-48%5Ctimes%2010%3D-480)
The correct answer is B.
<span>Not all functions will have intercepts</span>
Do you have a picture I'll show you
A proportional relationship is a relationship between variables such that the amount of one variable is a multiple of the other variable
A table showing the amount of sugar in different sizes of orange juice is presented as follows;
![\begin{array}{|c|cc|}\mathbf{Amount \ of \ orange \ juice, \ x}&&\mathbf{Quantity \ of \, sugar\ (g), \ f(x)}\\3&&8.25\\6&&16.5\\9&&24.75\\12&&33\\15&&41.25\end{array}\right]](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7Cc%7Ccc%7C%7D%5Cmathbf%7BAmount%20%5C%20of%20%5C%20orange%20%5C%20juice%2C%20%5C%20x%7D%26%26%5Cmathbf%7BQuantity%20%5C%20of%20%5C%2C%20sugar%5C%20%28g%29%2C%20%5C%20f%28x%29%7D%5C%5C3%26%268.25%5C%5C6%26%2616.5%5C%5C9%26%2624.75%5C%5C12%26%2633%5C%5C15%26%2641.25%5Cend%7Barray%7D%5Cright%5D)
Reason:
The given parameter are;
12 ounces of orange juice contains 33 grams of sugar
Therefore, we have;
The amount of sugar per ounce of orange juice is given as follows;
![1 \ ounce \ of \ orange \ juice \ contains, \dfrac{33 \ grams }{12 } = 2.75 \, grams \, of \, sugar](https://tex.z-dn.net/?f=1%20%5C%20ounce%20%5C%20of%20%5C%20orange%20%5C%20juice%20%5C%20contains%2C%20%20%5Cdfrac%7B33%20%5C%20grams%20%7D%7B12%20%7D%20%3D%202.75%20%5C%2C%20grams%20%5C%2C%20of%20%5C%2C%20sugar)
Therefore, there are 2.75 grams of sugar per ounce of orange juice
which gives;
The amount of sugar in different sizes of orange juice, f(x) = 2.75·x
Where <em>x</em> represents the amount of orange juice, and f(x) represents the amount of sugar in the orange juice
A table showing the amount of sugar present in different sizes of orange juice is given as follows;
![\begin{array}{|c|cc|}\mathbf{Amount \ of \ orange \ juice, \ x}&&\mathbf{Quantity \ of \, sugar\ (g), \ f(x)}\\3&&8.25\\6&&16.5\\9&&24.75\\12&&33\\15&&41.25\end{array}\right]](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7Cc%7Ccc%7C%7D%5Cmathbf%7BAmount%20%5C%20of%20%5C%20orange%20%5C%20juice%2C%20%5C%20x%7D%26%26%5Cmathbf%7BQuantity%20%5C%20of%20%5C%2C%20sugar%5C%20%28g%29%2C%20%5C%20f%28x%29%7D%5C%5C3%26%268.25%5C%5C6%26%2616.5%5C%5C9%26%2624.75%5C%5C12%26%2633%5C%5C15%26%2641.25%5Cend%7Barray%7D%5Cright%5D)
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