Question

the formula used to convert degrees celsius to degrees fahrenheit is $f=\frac{9}{5}c + 32$. convert $59^{circ}f$ to degrees celsius. solve the formula for $c$, and then use it to convert the temperature. which is the correct formula and conversion? a. $c=\frac{9}{5}(f - 32)$; conversion: $59^{circ}f = 106^{circ}c$ b. $c=\frac{5}{9}f - 32$; conversion: $59^{circ}f = 135^{circ}c$ c. $c=\frac{5}{9}f - 32$; conversion: $59^{circ}f = 15^{circ}c$ d. $c=\frac{5}{9}(f - 32)$; conversion: $59^{circ}f = 15^{circ}c$

Explanation:

Step1: Solve the formula \(F=\frac{9}{5}C + 32\) for \(C\)

Subtract 32 from both sides: \(F - 32=\frac{9}{5}C\).
Multiply both sides by \(\frac{5}{9}\): \(C=\frac{5}{9}(F - 32)\).

Step2: Convert \(F = 59\) to Celsius

Substitute \(F = 59\) into \(C=\frac{5}{9}(F - 32)\):
\(C=\frac{5}{9}(59 - 32)=\frac{5}{9}\times27 = 15\).

Answer:

D. \(C=\frac{5}{9}(F - 32)\); conversion: \(59^{\circ}F = 15^{\circ}C\)