To determine which ordered pairs are represented in the given table and equation, we need to analyze the equation [tex]\( c = 15.5 + 12f \)[/tex] and the table entries.
First, let's verify each ordered pair provided:
1. (7, 99.5)
- Given [tex]\( f = 7 \)[/tex], we calculate:
[tex]\[
15.5 + 12 \times 7 = 15.5 + 84 = 99.5
\][/tex]
- Hence, [tex]\( c = 99.5 \)[/tex]. So, the pair [tex]\( (7, 99.5) \)[/tex] is correct.
2. 15.5 + 12(3)
- This is not an ordered pair but a calculation.
- For [tex]\( f = 3 \)[/tex], we calculate:
[tex]\[
15.5 + 12 \times 3 = 15.5 + 36 = 51.5
\][/tex]
- So, [tex]\( c = 51.5 \)[/tex], which corresponds to the pair [tex]\( (3, 51.5) \)[/tex].
3. (75.5, 5)
- For [tex]\( f = 5 \)[/tex], we calculate:
[tex]\[
15.5 + 12 \times 5 = 15.5 + 60 = 75.5
\][/tex]
- So, [tex]\( c = 75.5 \)[/tex], but the order is reversed. The correct pair should be [tex]\( (5, 75.5) \)[/tex], not [tex]\( (75.5, 5) \)[/tex].
4. (3, 51.5)
- Given [tex]\( f = 3 \)[/tex], we calculate:
[tex]\[
15.5 + 12 \times 3 = 15.5 + 36 = 51.5
\][/tex]
- Hence, [tex]\( c = 51.5 \)[/tex]. So, the pair [tex]\( (3, 51.5) \)[/tex] is correct.
5. (123.5, 9)
- Given [tex]\( f = 9 \)[/tex], we calculate:
[tex]\[
15.5 + 12 \times 9 = 15.5 + 108 = 123.5
\][/tex]
- Hence, [tex]\( c = 123.5 \)[/tex]. So, the pair [tex]\( (9, 123.5) \)[/tex] is correct.
Summarizing, the ordered pairs represented in the table and equation are:
- [tex]\( (7, 99.5) \)[/tex]
- [tex]\( (3, 51.5) \)[/tex]
- [tex]\( (9, 123.5) \)[/tex]
The pairs [tex]\( (75.5, 5) \)[/tex] and the calculation [tex]\( 15.5 + 12(3) \)[/tex], do not match the form of an ordered pair but verify the computation needed.
Therefore, the correct ordered pairs are:
- [tex]\( (7, 99.5) \)[/tex]
- [tex]\( (3, 51.5) \)[/tex]
- [tex]\( (9, 123.5) \)[/tex]
