\( 11 v^{2}+2 v^{2}=13 v^{2} \) \( 7 v^{2}-32 v=-25 \mid 13 v^{2}-23 \) 13. Find the sum of \( 14 z^{2} \) and \( -9 z^{2} \).

Let's start with the equations provided. First, the equation \( 11 v^{2} + 2 v^{2} = 13 v^{2} \) is a straightforward demonstration of combining like terms, which is foundational in algebra. This kind of simplification is crucial when solving equations because it allows you to isolate variables more effectively. Now, looking at the second part, \( 7 v^{2} - 32 v = -25 \mid 13 v^{2} - 23 \), it suggests we have two expressions to consider. Upon simplification, one might factor or rearrange to isolate \( v \). As for the final part, to find the sum of \( 14 z^{2} \) and \( -9 z^{2} \), simply combine the coefficients of \( z^{2} \): \( 14 z^{2} + (-9 z^{2}) = 5 z^{2} \). Stay curious about these equations; algebra is like a puzzle waiting for you to solve it!