What is the only temperature that is the same in Fahrenheit and Celsius?

What is the only temperature that is the same in Fahrenheit and Celsius?

• A. 0 degrees
• B. 32 degrees
• C. 40 below
• D. 100 degrees

Answer: (C)

To determine the temperature that is the same in both Fahrenheit and Celsius, we can use the formula that relates the two temperature scales: \[ F = \frac{9}{5}C + 32 \] Where \( F \) is the temperature in Fahrenheit and \( C \) is the temperature in Celsius. To find the point where these two values are equal, we set \( F = C \): \[ C = \frac{9}{5}C + 32 \] Rearranging gives us: \[ C - \frac{9}{5}C = 32 \] This simplifies to: \[ \frac{-4}{5}C = 32 \] Multiplying both sides by \(-\frac{5}{4}\): \[ C = -40 \] This means that at \(-40\) degrees, the Celsius and Fahrenheit scales coincide. Since the question provides options, the only option that aligns with this calculated result is "40 below," indicating \(-40\) degrees. Understanding the other options can clarify why they do not represent this special point of equivalence. For instance, 0 degrees Celsius is equivalent to 32 degrees Fahrenheit, while 100 degrees Celsius converts to 212 degrees Fahrenheit

To determine the temperature that is the same in both Fahrenheit and Celsius, we can use the formula that relates the two temperature scales:

[ F = \frac{9}{5}C + 32 ]

Where ( F ) is the temperature in Fahrenheit and ( C ) is the temperature in Celsius. To find the point where these two values are equal, we set ( F = C ):

[ C = \frac{9}{5}C + 32 ]

Rearranging gives us:

[ C - \frac{9}{5}C = 32 ]

This simplifies to:

[ \frac{-4}{5}C = 32 ]

Multiplying both sides by (-\frac{5}{4}):

[ C = -40 ]

This means that at (-40) degrees, the Celsius and Fahrenheit scales coincide. Since the question provides options, the only option that aligns with this calculated result is "40 below," indicating (-40) degrees.

Understanding the other options can clarify why they do not represent this special point of equivalence. For instance, 0 degrees Celsius is equivalent to 32 degrees Fahrenheit, while 100 degrees Celsius converts to 212 degrees Fahrenheit