Question

select the correct answer.
what is the value of this expression when c = -4 and d = 10?
\\(\frac{1}{4}(c^3 + d^2)\\)
\\(\circ\\) a. 2
\\(\circ\\) b. 9
\\(\circ\\) c. 21
\\(\circ\\) d. 41

Explanation:

Step1: Substitute the values of c and d

Substitute \( c = - 4 \) and \( d = 10 \) into the expression \( \frac{1}{4}(c^{3}+d^{2}) \). First, calculate \( c^{3} \) and \( d^{2} \) separately.
For \( c^{3} \), when \( c=-4 \), we have \( (-4)^{3}=(-4)\times(-4)\times(-4)=-64 \).
For \( d^{2} \), when \( d = 10 \), we have \( 10^{2}=10\times10 = 100 \).

Step2: Calculate the sum inside the parentheses

Now, find the sum of \( c^{3} \) and \( d^{2} \), that is \( -64 + 100=36 \).

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

Multiply the result from Step 2 by \( \frac{1}{4} \), so \( \frac{1}{4}\times36 = 9 \).

Answer:

B. 9