Let's analyze the given function and the expressions step-by-step to determine which expression is equivalent to [tex]\((k + k)(4)\)[/tex]:
1. Understand the function [tex]\(k(x)\)[/tex]:
Given:
[tex]\[
k(x) = 5x - 6
\][/tex]
2. Evaluate the function [tex]\(k(x)\)[/tex] at [tex]\(x = 4\)[/tex]:
[tex]\[
k(4) = 5(4) - 6 = 20 - 6 = 14
\][/tex]
3. Understand what [tex]\((k + k)(4)\)[/tex] means:
[tex]\((k + k)(4)\)[/tex] is equivalent to:
[tex]\[
k(4) + k(4)
\][/tex]
Since we already found that [tex]\(k(4) = 14\)[/tex], we have:
[tex]\[
k(4) + k(4) = 14 + 14 = 28
\][/tex]
4. Now let's analyze each provided expression to see which one evaluates to 28:
- Expression 1: [tex]\(5(4 + 4) - 6\)[/tex]
[tex]\[
5(4 + 4) - 6 = 5(8) - 6 = 40 - 6 = 34
\][/tex]
This evaluates to 34, not 28.
- Expression 2: [tex]\(5(5(4) - 6) - 6\)[/tex]
[tex]\[
5(5(4) - 6) - 6 = 5(20 - 6) - 6 = 5(14) - 6 = 70 - 6 = 64
\][/tex]
This evaluates to 64, not 28.
- Expression 3: [tex]\(54 - 6 + 54 - 6\)[/tex]
[tex]\[
54 - 6 + 54 - 6 = 48 + 48 = 96
\][/tex]
This evaluates to 96, not 28.
- Expression 4: [tex]\(5(4) - 6 + 5(4) - 6\)[/tex]
[tex]\[
5(4) - 6 + 5(4) - 6 = 20 - 6 + 20 - 6 = 14 + 14 = 28
\][/tex]
This evaluates to 28, which matches our computed value for [tex]\((k + k)(4)\)[/tex].
Therefore, the expression that is equivalent to [tex]\((k + k)(4)\)[/tex] is:
[tex]\[
5(4) - 6 + 5(4) - 6
\][/tex]
