High School

The linear equation that converts Fahrenheit to Celsius is [tex]f = \frac{9}{5}c + 32[/tex]. When is Fahrenheit equal to Celsius?

Answer :

Final answer:

When Fahrenheit is equal to Celsius, the temperature is approximately -17.8°C.

Explanation:

The given equation is used to convert Fahrenheit to Celsius. In order to find the temperature at which Fahrenheit is equal to Celsius, we need to set the two temperatures equal to each other.

Let's substitute the given equation for Fahrenheit (F) and Celsius (C) and solve for C:

F = 9/5 * C + 32

C = (F - 32) * 5/9

Now, let's set the temperatures equal to each other and solve for C:

(F - 32) * 5/9 = C

(C - 32) * 5/9 = C

By expanding and simplifying the equation, we find:

-32 * 5/9 = -32

-160/9 = -32

-17.77... = -32

So, when Fahrenheit is equal to Celsius, the temperature is approximately -17.8°C.

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