a right rectangular prism has a height of 9 inches. the length of the prisms base is x inches, which is 7…

a right rectangular prism has a height of 9 inches. the length of the prisms base is x inches, which is 7 inches more than the width of the prisms base. which function v gives the volume of the prism, in cubic inches, in terms of the length of the prisms base? (a) v(x)=x(x + 9)(x + 7) (b) v(x)=x(x + 9)(x - 7) (c) v(x)=9x(x + 7) (d) v(x)=9x(x - 7)

a right rectangular prism has a height of 9 inches. the length of the prisms base is x inches, which is 7 inches more than the width of the prisms base. which function v gives the volume of the prism, in cubic inches, in terms of the length of the prisms base? (a) v(x)=x(x + 9)(x + 7) (b) v(x)=x(x + 9)(x - 7) (c) v(x)=9x(x + 7) (d) v(x)=9x(x - 7)

Answer

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - prism is $V = l\times w\times h$, where $l$ is the length of the base, $w$ is the width of the base, and $h$ is the height.

Step2: Identify given values

We are given that $h = 9$ inches, $l=x$ inches, and the length $x$ is 7 inches more than the width. So, if the width is $w$, then $x=w + 7$, and $w=x - 7$.

Step3: Substitute values into formula

Substitute $l=x$, $w=x - 7$, and $h = 9$ into the volume formula $V=l\times w\times h$. We get $V(x)=9\times x\times(x - 7)$.

Answer:

D. $V(x)=9x(x - 7)$