Question

the formula used to convert a temperature from degrees fahrenheit (°f) to celsius (°c) is: ( c = \frac{5}{9}(f - 32) ) for which of the following ( c ) values temperatures is this celsius and fahrenheit temperature the same? select the correct answer. a. -7k b. 8 c. -11.5 d. 5 12

Explanation:

Step1: Set C = F in formula

Let $C = F = x$. Substitute into $C = \frac{5}{9}(F - 32)$:
$$x = \frac{5}{9}(x - 32)$$

Step2: Multiply both sides by 9

Eliminate the denominator:
$$9x = 5(x - 32)$$

Step3: Expand right-hand side

Distribute the 5:
$$9x = 5x - 160$$

Step4: Isolate x terms

Subtract $5x$ from both sides:
$$9x - 5x = -160$$
$$4x = -160$$

Step5: Solve for x

Divide both sides by 4:
$$x = \frac{-160}{4} = -40$$

Answer:

A. $-40^\circ$