Question

determining missing values in expressions for volume
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 = $
(options for c: 1, 2, 3, 4)

Explanation:

Step1: Recall prism volume formula

Volume = Base Area × Length

Step2: Calculate triangular base area

The triangular base has base $2$ and height $2x$.
Area = $\frac{1}{2} \times 2 \times 2x = 2x$

Step3: Identify prism length

The length of the prism is $x^2 + 3$.

Step4: Compute total volume

Multiply base area by length:
$V = 2x \times (x^2 + 3) = 2x^3 + 6x$

Step5: Match to given form $ax^b + cx$

Compare terms: $2x^3 + 6x = ax^b + cx$

Answer:

$a=2$, $b=3$, $c=6$