To determine which expression represents Jonah's earnings, let's carefully analyze the given information step by step.
We are given:
- Let [tex]\( k \)[/tex] be Karen's salary.
- Jonah earned [tex]$5 more than half of Karen's salary.
To express Jonah's earnings algebraically, we need to break down the information provided:
1. Half of Karen's salary: Half of Karen's salary \( k \) can be written as \( \frac{1}{2} k \).
2. $[/tex]5 more than half of Karen's salary: Adding 5 to half of Karen's salary can be written as [tex]\( \frac{1}{2} k + 5 \)[/tex].
Now let's examine each of the given expressions to find which one matches our derived expression [tex]\( \frac{1}{2} k + 5 \)[/tex]:
1. [tex]\(\frac{1}{2}(k+5)\)[/tex]: This expression represents half of the quantity [tex]\( k + 5 \)[/tex], which is not what we need. It would mean taking half after adding [tex]$5, not adding $[/tex]5 after taking half.
2. [tex]\(\frac{1}{2} k + 5\)[/tex]: This matches our derived expression exactly. It represents half of Karen's salary plus [tex]$5, which correctly describes Jonah's earnings.
3. \(\frac{1}{2} + k + 5\): This expression adds half to Karen's salary plus $[/tex]5, which is not correct. It does not correctly reflect "half of Karen's salary plus [tex]$5".
4. \(\frac{1}{2} k > 5\): This is an inequality, not an expression for Jonah's earnings. It states that half of Karen's salary is greater than $[/tex]5, which does not describe the amount Jonah earns.
Thus, the correct expression that represents Jonah's earnings is:
[tex]\(\boxed{\frac{1}{2} k + 5}\)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{2} \][/tex]
