To find the value of the expression [tex]\(-8h - 2\left(5 + f^3\right) + 7g^2\)[/tex] when [tex]\( f = -4 \)[/tex], [tex]\( g = 5 \)[/tex], and [tex]\( h = \frac{3}{4} \)[/tex], we can break down the problem into parts and solve it step-by-step. Let's solve it systematically:
1. Substitute the values into the expression:
- [tex]\( f = -4 \)[/tex]
- [tex]\( g = 5 \)[/tex]
- [tex]\( h = \frac{3}{4} \)[/tex]
2. Calculate each individual term in the expression:
- Calculate [tex]\(-8h\)[/tex]:
[tex]\[
-8h = -8 \times \frac{3}{4} = -8 \times 0.75 = -6.0
\][/tex]
- Calculate [tex]\( 2\left(5 + f^3\right) \)[/tex]:
First, find [tex]\( f^3 \)[/tex]:
[tex]\[
f^3 = (-4)^3 = -64
\][/tex]
Next, find [tex]\( 5 + f^3 \)[/tex]:
[tex]\[
5 + f^3 = 5 + (-64) = 5 - 64 = -59
\][/tex]
Then, compute [tex]\( 2\left(-59\right) \)[/tex]:
[tex]\[
2\left(-59\right) = 2 \times -59 = -118
\][/tex]
- Calculate [tex]\( 7g^2 \)[/tex]:
First, find [tex]\( g^2 \)[/tex]:
[tex]\[
g^2 = 5^2 = 25
\][/tex]
Next, multiply by 7:
[tex]\[
7g^2 = 7 \times 25 = 175
\][/tex]
3. Combine all the calculated parts together:
[tex]\[
-8h - 2\left(5 + f^3\right) + 7g^2 = -6.0 - 118 + 175
\][/tex]
4. Calculate the final value:
[tex]\[
-6.0 - 118 + 175 = -124 + 175 = 51
\][/tex]
Therefore, the value of the expression is [tex]\( 287.0 \)[/tex].
