Question

the formula used to convert degrees celsius to degrees fahrenheit is $f = \frac{9}{5}c + 32$. convert 68°f to degrees celsius. solve the formula for c, and then use it to convert the temperatur which is the correct formula and conversion? \\(\bigcirc\\) a. $c = \frac{5}{9}(f - 32)$; conversion: $68^\circ f = 122^\circ c$ \\(\bigcirc\\) b. $c = \frac{5}{9}f - 32$; conversion: $68^\circ f = 180^\circ c$ \\(\bigcirc\\) c. $c = \frac{5}{9}(f - 32)$; conversion: $68^\circ f = 20^\circ c$ \\(\bigcirc\\) d. $c = \frac{5}{9}f - 32$; conversion: $68^\circ f = 20^\circ c$

Explanation:

Step1: Isolate $F-32$

Start with given formula:
$$F = \frac{9}{5}C + 32$$
Subtract 32 from both sides:
$$F - 32 = \frac{9}{5}C$$

Step2: Solve for $C$

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

Step3: Substitute $F=68$

Plug value into rearranged formula:
$$C = \frac{5}{9}(68 - 32)$$

Step4: Calculate the result

Simplify the expression:
$$C = \frac{5}{9}(36) = 20$$

Answer:

C. $C = \frac{5}{9}(F - 32)$; conversion: $68^\circ\text{F} = 20^\circ\text{C}$