Alright, let's simplify the given expression step by step:
Given expression:
[tex]\[ -2x^2 + 8x - 9 + 4x + 7x^2 + 2 \][/tex]
To simplify it, we need to combine the like terms. Like terms are terms that have the same variable raised to the same power.
1. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-2x^2 + 7x^2 = 5x^2
\][/tex]
2. Combine the [tex]\(x\)[/tex] terms:
[tex]\[
8x + 4x = 12x
\][/tex]
3. Combine the constant terms:
[tex]\[
-9 + 2 = -7
\][/tex]
So, by combining all of the like terms, the expression simplifies to:
[tex]\[ 5x^2 + 12x - 7 \][/tex]
Therefore, the equivalent expression is:
[tex]\[ \boxed{5x^2 + 12x - 7} \][/tex]
So, the correct option is:
[tex]\[ \text{B. } 5x^2 + 12x - 7 \][/tex]
