Question

the figure below is an oblique triangular prism. the expression below represents the volume of the figure written in standard form. what are the missing values? $ax^{b}+cx$ $a =$ $b =$ $c =$

Explanation:

Step1: Recall volume formula for triangular - prism

The volume formula for a triangular prism is $V = Bh$, where $B$ is the area of the base and $h$ is the height of the prism. The base of the given triangular prism is a triangle with base length $2x$ and height $x$, and the height of the prism is $x^{2}+3$.

Step2: Calculate the area of the base

The area of a triangle $B=\frac{1}{2}\times base\times height$. For the base - triangle, with base $2x$ and height $x$, we have $B=\frac{1}{2}\times(2x)\times x=x^{2}$.

Step3: Calculate the volume of the prism

Using the volume formula $V = Bh$, substitute $B = x^{2}$ and $h=x^{2}+3$. Then $V=x^{2}(x^{2}+3)$.

Step4: Expand the expression

Using the distributive property $a(b + c)=ab+ac$, we get $V=x^{2}\cdot x^{2}+x^{2}\cdot3=x^{4}+3x^{2}$.
Comparing with the form $ax^{b}+cx$, we have $a = 1$, $b = 4$, and $c = 3$.

Answer:

$a = 1$
$b = 4$
$c = 3$