Question

13. The Celsius to Fahrenheit formula: F: 9/5C + 32
Solve this formula for C. Check all answers that are true.

Answer 1

To solve the Celsius to Fahrenheit formula \( F = \frac{9}{5}C + 32 \) for \( C \), we can follow these steps:

1. Subtract 32 from both sides:
\[
F - 32 = \frac{9}{5}C
\]

2. Multiply both sides by \(\frac{5}{9}\) to isolate \( C \):
\[
C = \frac{5}{9}(F - 32)
\]

Thus, the formula for converting Fahrenheit to Celsius is:
\[
C = \frac{5}{9}(F - 32)
\]

### Checks for True Answers:
- The computed formula correctly transforms Fahrenheit values back into Celsius.
- If you substitute an appropriate \( F \) into \( C = \frac{5}{9}(F - 32) \), it will yield the corresponding Celsius temperature.

To check whether this is true for specific Fahrenheit values:
- Example: Let’s assume \( F = 32 \) (freezing point of water).
\[
C = \frac{5}{9}(32 - 32) = \frac{5}{9}(0) = 0
\]
The answer checks out since \( 32°F = 0°C \).

- Example: Let’s take \( F = 212 \) (boiling point of water).
\[
C = \frac{5}{9}(212 - 32) = \frac{5}{9}(180) = 100
\]
The answer checks out since \( 212°F = 100°C \).

### Conclusion:
The correct rearranged formula is \( C = \frac{5}{9}(F - 32) \), and it is valid for converting Fahrenheit back to Celsius.