To convert [tex]\( 77^\circ \text{F} \)[/tex] to degrees Celsius, we must first rearrange the given formula [tex]\( F = \frac{9}{5}C + 32 \)[/tex] to solve for [tex]\( C \)[/tex].
1. Start with the equation:
[tex]\[
F = \frac{9}{5}C + 32
\][/tex]
2. Subtract 32 from both sides to isolate the term containing [tex]\( C \)[/tex]:
[tex]\[
F - 32 = \frac{9}{5}C
\][/tex]
3. Multiply both sides by the reciprocal of [tex]\( \frac{9}{5} \)[/tex], which is [tex]\( \frac{5}{9} \)[/tex], to solve for [tex]\( C \)[/tex]:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
Now, use this formula to convert [tex]\( 77^\circ \text{F} \)[/tex] to degrees Celsius.
4. Substitute [tex]\( 77 \)[/tex] for [tex]\( F \)[/tex] in the formula:
[tex]\[
C = \frac{5}{9}(77 - 32)
\][/tex]
5. Calculate the difference inside the parentheses:
[tex]\[
77 - 32 = 45
\][/tex]
6. Multiply by [tex]\( \frac{5}{9} \)[/tex]:
[tex]\[
C = \frac{5}{9} \times 45
\][/tex]
7. Perform the multiplication:
[tex]\[
C = 25.0
\][/tex]
Therefore, the correct conversion of [tex]\( 77^\circ \text{F} \)[/tex] is [tex]\( 25^\circ \text{C} \)[/tex].
Among the given choices, the correct formula and conversion are:
D. [tex]\( C = \frac{5}{9}(F - 32) \)[/tex]; conversion: [tex]\( 77^\circ \text{F} = 25^\circ \text{C} \)[/tex].
