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Functions [tex] p [/tex] and [tex] q [/tex] are defined by these equations:

[tex]\[
\begin{array}{l}
p(x) = 5x + 30 \\
q(x) = 11x - 24
\end{array}
\][/tex]

What is [tex] (q - p)(6) [/tex]?

A. -42
B. 42
C. 18
D. -18

Sagot :

GinnyAnsweridn
To solve the problem, we want to determine the value of [tex]\((q - p)(6)\)[/tex] given the functions [tex]\(p(x) = 5x + 30\)[/tex] and [tex]\(q(x) = 11x - 24\)[/tex].

Here's the step-by-step process:

1. Evaluate [tex]\(p(x)\)[/tex] at [tex]\(x = 6\)[/tex]:
[tex]\[ p(6) = 5(6) + 30 = 30 + 30 = 60 \][/tex]

2. Evaluate [tex]\(q(x)\)[/tex] at [tex]\(x = 6\)[/tex]:
[tex]\[ q(6) = 11(6) - 24 = 66 - 24 = 42 \][/tex]

3. Calculate [tex]\((q - p)(6)\)[/tex]:
[tex]\[ (q - p)(6) = q(6) - p(6) \][/tex]
Substituting the evaluated values from steps 1 and 2:
[tex]\[ (q - p)(6) = 42 - 60 = -18 \][/tex]

Thus, the value of [tex]\((q - p)(6)\)[/tex] is [tex]\(-18\)[/tex]. Therefore, the correct answer is:

D. -18
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