To convert [tex]\( 77^{\circ} F \)[/tex] to degrees Celsius, we'll start by deriving the correct formula from the given Fahrenheit to Celsius relationship.
We know the formula to convert Celsius to Fahrenheit is:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
To find the formula to convert Fahrenheit to Celsius, we need to solve this equation for [tex]\( C \)[/tex].
First, subtract 32 from both sides:
[tex]\[ F - 32 = \frac{9}{5}C \][/tex]
Next, multiply both sides by [tex]\(\frac{5}{9}\)[/tex] to isolate [tex]\(C\)[/tex]:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
Now that we have the correct formula for converting Fahrenheit to Celsius:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
Let's apply this formula to convert [tex]\( 77^{\circ} F \)[/tex] to degrees Celsius:
[tex]\[ C = \frac{5}{9}(77 - 32) \][/tex]
[tex]\[ C = \frac{5}{9}(45) \][/tex]
[tex]\[ C = 25 \][/tex]
So the correct formula is:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
And the conversion of [tex]\( 77^{\circ} F \)[/tex] is:
[tex]\[ 77^{\circ} F = 25^{\circ} C \][/tex]
Thus, the correct option is:
C. [tex]\(C = \frac{5}{9}(F - 32)\)[/tex]; conversion: [tex]\(77^{\circ} F = 25^{\circ} C\)[/tex]
