To determine which elements in the given set are integers, we need to evaluate each element individually and verify if it is an integer. The set provided is:
[tex]\[
-3, 3.7, 9, -7.34, 2.83, 5, \frac{56}{7}, -1
\][/tex]
Let's check each element one by one.
1. -3: This is clearly an integer.
2. 3.7: This number has a decimal part, so it is not an integer.
3. 9: This is a whole number without any decimal part, so it is an integer.
4. -7.34: This number has a decimal part, so it is not an integer.
5. 2.83: This number has a decimal part, so it is not an integer.
6. 5: This is a whole number without any decimal part, so it is an integer.
7. [tex]\(\frac{56}{7}\)[/tex]: We need to calculate this division to determine if it is an integer.
[tex]\[
\frac{56}{7} = 8
\][/tex]
As [tex]\(8\)[/tex] is a whole number, it is an integer.
8. -1: This is a whole number without any decimal part, so it is an integer.
From this examination, the integers in the set are:
[tex]\[
-3, 9, 5, 8, -1
\][/tex]
Let's match this set of integers to the options provided in the question:
A) [tex]\(-3, 9, 5, \frac{56}{7}, -1\)[/tex]
B) [tex]\(3.7, -7.34, 2.83\)[/tex]
C) [tex]\(-3, 3.7, -7.34, -1\)[/tex]
D) [tex]\(3.7, 9, 2.83, 5, \frac{56}{7}\)[/tex]
The correct answer is:
[tex]\[
\boxed{-3, 9, 5, \frac{56}{7}, -1}
\][/tex]
Hence, the correct option is A.
