To solve the problem, let's break it down step-by-step.
1. Define the functions [tex]\( h(x) \)[/tex] and [tex]\( k(x) \)[/tex]:
[tex]\[
h(x) = x^2 - 3
\][/tex]
[tex]\[
k(x) = 5 + x
\][/tex]
2. Calculate [tex]\( h(7) \)[/tex]:
We substitute [tex]\( x = 7 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[
h(7) = 7^2 - 3
\][/tex]
Calculate [tex]\( 7^2 \)[/tex]:
[tex]\[
7^2 = 49
\][/tex]
Then subtract 3:
[tex]\[
49 - 3 = 46
\][/tex]
So, [tex]\( h(7) = 46 \)[/tex].
3. Calculate [tex]\( k(h(7)) \)[/tex], which is [tex]\( k(46) \)[/tex]:
We substitute [tex]\( x = 46 \)[/tex] into the function [tex]\( k(x) \)[/tex]:
[tex]\[
k(46) = 5 + 46
\][/tex]
Adding the numbers together:
[tex]\[
5 + 46 = 51
\][/tex]
So, [tex]\( k(46) = 51 \)[/tex].
Therefore, the value of [tex]\( k(h(7)) \)[/tex] is [tex]\( 51 \)[/tex].
The correct answer is:
[tex]\[ \boxed{51} \][/tex]
