To convert from Fahrenheit to Celsius, we start with the given formula that converts Celsius ([tex]\(C\)[/tex]) to Fahrenheit ([tex]\(F\)[/tex]):
[tex]\[ F = \frac{9}{5} C + 32 \][/tex]
We need to solve this formula for [tex]\(C\)[/tex] to convert Fahrenheit to Celsius. Let's rearrange the formula step-by-step.
1. Subtract 32 from both sides:
[tex]\[ F - 32 = \frac{9}{5} C \][/tex]
2. Multiply both sides by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ \left( F - 32 \right) \times \frac{5}{9} = C \][/tex]
So, the formula to convert Fahrenheit to Celsius is:
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
Now, we can use this formula to convert [tex]\(59^\circ F\)[/tex] to Celsius:
1. Substitute [tex]\(F = 59\)[/tex] into the formula:
[tex]\[ C = \frac{5}{9} (59 - 32) \][/tex]
2. Calculate the value inside the parentheses first:
[tex]\[ 59 - 32 = 27 \][/tex]
3. Multiply by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ C = \frac{5}{9} \times 27 \][/tex]
4. Simplify the fraction:
[tex]\[ C = \frac{5 \times 27}{9} = \frac{135}{9} = 15 \][/tex]
Thus, the conversion gives:
[tex]\[ 59^\circ F = 15^\circ C \][/tex]
Now, let's identify the correct formula and conversion from the given choices:
A. [tex]\( C = \frac{5}{9} F - 32 \)[/tex]; conversion: [tex]\( 59^\circ F = 15^\circ C \)[/tex] - Incorrect formula
B. [tex]\( C = \frac{5}{9} (F - 32) \)[/tex]; conversion: [tex]\( 59^\circ F = 15^\circ C \)[/tex] - Correct formula and conversion
C. [tex]\( C = \frac{5}{9} F - 32 \)[/tex]; conversion: [tex]\( 59^\circ F = 135^\circ C \)[/tex] - Incorrect formula and conversion
D. [tex]\( C = \frac{5}{9} (F - 32) \)[/tex]; conversion: [tex]\( 59^\circ F = 106^\circ C \)[/tex] - Incorrect conversion
The correct choice is:
[tex]\[ \boxed{B} \][/tex]
