To solve for [tex]\( F \)[/tex] in the given relationship between the temperature in degrees Celsius ([tex]\( C \)[/tex]) and degrees Fahrenheit ([tex]\( F \)[/tex]), we need to isolate [tex]\( F \)[/tex] on one side of the equation. The equation provided is:
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
Here are the steps to solve for [tex]\( F \)[/tex]:
1. Start with the given equation:
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
2. To eliminate the fraction, multiply both sides of the equation by [tex]\( \frac{9}{5} \)[/tex]:
[tex]\[ \left( \frac{9}{5} \right) C = F - 32 \][/tex]
3. Now, add 32 to both sides of the equation to isolate [tex]\( F \)[/tex]:
[tex]\[ \left( \frac{9}{5} \right) C + 32 = F \][/tex]
Therefore, the correct formula that solves for [tex]\( F \)[/tex] is:
[tex]\[ F = \frac{9}{5} C + 32 \][/tex]
So, the correct answer is:
[tex]\[ O \quad F = \frac{9}{5} C + 32 \][/tex]
This matches the first choice given.
