To solve the given problem, let's break down the description and convert it into an algebraic expression step by step.
The description given is:
- The product of [tex]\(x\)[/tex] cubed and 5: Here, "x cubed" refers to [tex]\(x^3\)[/tex]. Multiplying [tex]\(x^3\)[/tex] by 5 gives us [tex]\(5x^3\)[/tex].
- Divided by the sum of 2 times [tex]\(x\)[/tex] and 7: "2 times [tex]\(x\)[/tex]" refers to [tex]\(2x\)[/tex]. Adding 7 to [tex]\(2x\)[/tex] yields [tex]\(2x + 7\)[/tex].
So, putting these two parts together, we get the expression:
[tex]\[
\frac{5x^3}{2x + 7}
\][/tex]
To determine which of the given options matches this expression, let's examine each one:
A. [tex]\(\frac{5x^3}{2x + 7}\)[/tex]: This matches our derived expression exactly.
B. [tex]\(\frac{5x^8}{2} + x + 7\)[/tex]: This expression does not match our derived expression.
C. [tex]\(\frac{5x^3}{2x} + 7\)[/tex]: This expression does not match our derived expression because of the addition of 7 outside the fraction.
D. [tex]\(\frac{5x^3}{2(x + 7)}\)[/tex]: This expression does not match our derived expression because [tex]\(2(x + 7)\)[/tex] is not the same as [tex]\(2x + 7\)[/tex].
Thus, the correct algebraic form of the described expression is:
[tex]\[
\boxed{\frac{5x^3}{2x + 7}}
\][/tex]
So, the correct option is A.
