To convert [tex]\( 59^{\circ} F \)[/tex] to degrees Celsius, you need to solve the given formula for [tex]\( C \)[/tex]. The initial formula for converting Celsius to Fahrenheit is:
[tex]\[ F = \frac{9}{5} C + 32 \][/tex]
We need to express [tex]\( C \)[/tex] in terms of [tex]\( F \)[/tex]. To do this, follow these steps:
1. Subtract 32 from both sides of the formula to isolate the term involving [tex]\( C \)[/tex]:
[tex]\[ F - 32 = \frac{9}{5} C \][/tex]
2. Multiply both sides of the equation by [tex]\( \frac{5}{9} \)[/tex] to solve for [tex]\( C \)[/tex]:
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
Now that we have the correct formula, [tex]\( C = \frac{5}{9} (F - 32) \)[/tex], we can use it to convert [tex]\( 59^{\circ} F \)[/tex] to degrees Celsius:
[tex]\[ C = \frac{5}{9} (59 - 32) \][/tex]
Calculate the value inside the parenthesis first:
[tex]\[ 59 - 32 = 27 \][/tex]
Next, multiply by [tex]\( \frac{5}{9} \)[/tex]:
[tex]\[ C = \frac{5}{9} \times 27 \][/tex]
This simplifies to:
[tex]\[ C = 15 \][/tex]
So, [tex]\( 59^{\circ} F = 15^{\circ} C \)[/tex].
Reviewing the options:
A. [tex]\( C = \frac{5}{9} F - 32 \)[/tex]; conversion: [tex]\( 59^{\circ} F = 135^{\circ} C \)[/tex]
B. [tex]\( C = \frac{5}{9} (F - 32) \)[/tex]; conversion: [tex]\( 59^{\circ} F = 15^{\circ} C \)[/tex]
C. [tex]\( C = \frac{5}{9} F - 32 \)[/tex]; conversion: [tex]\( 59^{\circ} F = 15^{\circ} C \)[/tex]
D. [tex]\( C = \frac{5}{9} (F - 32) \)[/tex]; conversion: [tex]\( 59^{\circ} F = 106^{\circ} C \)[/tex]
The correct formula and conversion are given in Option B:
[tex]\[ C = \frac{5}{9} (F - 32); \quad 59^{\circ} F = 15^{\circ} C \][/tex]
