Question

The formula D=MV
represents the density in grams per centimeters cubed for an object with a mass of M grams and a volume of V cubic centimeters. The mass of an object is given by the function f(x)=2x2+9x+4
. The volume of the object is given by the function g(x)=x+4
. What function represents the density of the object?

Enter the missing values.

(1 point)
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Remaining Attempts : 3

Answer 1

To find the density function \( D \), we need to substitute the functions \( f(x) \) for mass \( M \) and \( g(x) \) for volume \( V \) into the formula \( D = \frac{M}{V} \).

Given:
- Mass function: \( f(x) = 2x^2 + 9x + 4 \)
- Volume function: \( g(x) = x + 4 \)

We can express the density \( D \) as follows:

\[
D(x) = \frac{f(x)}{g(x)} = \frac{2x^2 + 9x + 4}{x + 4}
\]

This function represents the density of the object in terms of \( x \). Therefore, the function for density is:

\[
D(x) = \frac{2x^2 + 9x + 4}{x + 4}
\]

This is the function that represents the density of the object.