To simplify the given expression [tex]\((9x^2 - 2x + 7) + (4x^2 + 7x + 2)\)[/tex], let's follow the steps:
1. Combine the [tex]\(x^2\)[/tex] terms:
- The [tex]\(x^2\)[/tex] terms in the expressions are [tex]\(9x^2\)[/tex] and [tex]\(4x^2\)[/tex].
- Add these together: [tex]\(9x^2 + 4x^2 = 13x^2\)[/tex].
2. Combine the [tex]\(x\)[/tex] terms:
- The [tex]\(x\)[/tex] terms in the expressions are [tex]\(-2x\)[/tex] and [tex]\(7x\)[/tex].
- Add these together: [tex]\(-2x + 7x = 5x\)[/tex].
3. Combine the constant terms:
- The constants in the expressions are [tex]\(7\)[/tex] and [tex]\(2\)[/tex].
- Add these together: [tex]\(7 + 2 = 9\)[/tex].
Combining these results, the simplified expression is:
[tex]\[ 13x^2 + 5x + 9 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{13x^2 + 5x + 9} \][/tex]
Therefore, the correct choice is:
C. [tex]\(13 x^2 + 5 x + 9\)[/tex]
