Question

select the correct answer.
what is the value of this expression when ( c = -4 ) and ( d = 10 )?
( \frac{1}{4}left(c^{3}+d^{2}
ight) )

a. 2

b. 9

c. 21

d. 41

Explanation:

Step1: Substitute \( c = -4 \) and \( d = 10 \) into the expression

First, calculate \( c^3 \) and \( d^2 \). For \( c = -4 \), \( c^3 = (-4)^3 = -64 \). For \( d = 10 \), \( d^2 = 10^2 = 100 \).

Step2: Calculate the sum inside the parentheses

Add the results from Step 1: \( c^3 + d^2 = -64 + 100 = 36 \).

Step3: Multiply by \( \frac{1}{4} \)

Now, multiply the sum by \( \frac{1}{4} \): \( \frac{1}{4} \times 36 = 9 \).

Answer:

B. 9