Let's solve the expression step-by-step:
Given:
[tex]\[ f = -4 \][/tex]
[tex]\[ g = 5 \][/tex]
[tex]\[ h = \frac{3}{4} \][/tex]
We need to evaluate the expression:
[tex]\[ -8h - 2 \left(5 + f^3\right) + 7g^2 \][/tex]
1. Calculate the first term:
[tex]\[ -8h \][/tex]
[tex]\[ h = \frac{3}{4} \][/tex]
[tex]\[ -8 \times \frac{3}{4} = -6 \][/tex]
2. Calculate the second term:
[tex]\[ -2 \left(5 + f^3\right) \][/tex]
[tex]\[ f = -4 \][/tex]
[tex]\[ f^3 = (-4)^3 = -64 \][/tex]
[tex]\[ 5 + f^3 = 5 + (-64) = 5 - 64 = -59 \][/tex]
[tex]\[ -2 \times -59 = 118 \][/tex]
3. Calculate the third term:
[tex]\[ 7g^2 \][/tex]
[tex]\[ g = 5 \][/tex]
[tex]\[ g^2 = 5^2 = 25 \][/tex]
[tex]\[ 7 \times 25 = 175 \][/tex]
Finally, sum up all the terms:
[tex]\[ -6 + 118 + 175 = 287 \][/tex]
Therefore, the value of the expression is [tex]\( 287 \)[/tex]. So, the correct answer is:
[tex]\[ \boxed{287} \][/tex]
