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What is the value of this expression when [tex]\(c=-4\)[/tex] and [tex]\(d=10\)[/tex]?

[tex]\[ \frac{1}{4}\left(c^3+d^2\right) \][/tex]

A. 2

B. 9

C. 21

D. 41

Sagot :

GinnyAnswer
Let's begin by plugging in the given values [tex]\(c = -4\)[/tex] and [tex]\(d = 10\)[/tex] into the expression [tex]\(\frac{1}{4}(c^3 + d^2)\)[/tex].

1. Calculate [tex]\(c^3\)[/tex]:
[tex]\[ c^3 = (-4)^3 = -64 \][/tex]

2. Calculate [tex]\(d^2\)[/tex]:
[tex]\[ d^2 = (10)^2 = 100 \][/tex]

3. Add the results from steps 1 and 2:
[tex]\[ c^3 + d^2 = -64 + 100 = 36 \][/tex]

4. Now, multiply the result by [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[ \frac{1}{4}(c^3 + d^2) = \frac{1}{4}(36) = 9 \][/tex]

So, the value of the expression is [tex]\(9\)[/tex].

Therefore, the correct answer is:
B. 9
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