Question

select the correct answer.
which equation shows a correct evaluation of ((mn)(4))?
(m(x) = 4x - 5)
(n(x) = 2x + 11)
a. ((mn)(4) = 8(4)^2 - 6(4) - 55)
b. ((mn)(4) = 8(4)^2 - 55)
c. ((mn)(4) = 8(4)^2 + 34(4) - 55)
d. ((mn)(4) = 8(4) - 55)

Explanation:

Step1: Recall function multiplication

To find \((mn)(x)\), we multiply \(m(x)\) and \(n(x)\). Given \(m(x) = 4x - 5\) and \(n(x)=2x + 11\), so \((mn)(x)=(4x - 5)(2x + 11)\).

Step2: Expand the product

Using the distributive property (FOIL method):
\[

$$\begin{align*} (4x - 5)(2x + 11)&=4x\times2x+4x\times11-5\times2x-5\times11\\ &=8x^{2}+44x - 10x-55\\ &=8x^{2}+34x - 55 \end{align*}$$

\]

Step3: Evaluate at \(x = 4\)

Now, substitute \(x = 4\) into \((mn)(x)\): \((mn)(4)=8(4)^{2}+34(4)-55\)

Answer:

C. \((mn)(4)=8(4)^{2}+34(4)-55\)