The formula [tex]F = \frac{9}{5} C + 32[/tex] may be used to convert Celsius temperatures to Fahrenheit.

What is the range of Celsius temperatures if the Fahrenheit range is [tex]-23^\circ F[/tex] to [tex]80^\circ F[/tex]?

The corresponding Celsius range would be [tex]\square^\circ C[/tex] to [tex]\square^\circ C[/tex].

Round Celsius temperature answers to 2 decimal places.

To find the corresponding range of Celsius temperatures when given a range in Fahrenheit from [tex]\(-23^\circ F\)[/tex] to [tex]\(80^\circ F\)[/tex], we will use the formula to convert Fahrenheit to Celsius. The formula is:

[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]

Let's apply this formula step by step to convert the given Fahrenheit temperatures into Celsius.

1. Convert [tex]\(-23^\circ F\)[/tex] to Celsius:

- Start with the formula: [tex]\(C = \frac{5}{9}(F - 32)\)[/tex].
- Substitute [tex]\(-23\)[/tex] for [tex]\(F\)[/tex]:
[tex]\[
C = \frac{5}{9}(-23 - 32)
\][/tex]
- Simplify inside the parentheses:
[tex]\[
-23 - 32 = -55
\][/tex]
- Now, plug in and calculate:
[tex]\[
C = \frac{5}{9} \times -55
\][/tex]
[tex]\[
C = \frac{-275}{9} \approx -30.56
\][/tex]

So, [tex]\(-23^\circ F\)[/tex] is approximately [tex]\(-30.56^\circ C\)[/tex].

2. Convert [tex]\(80^\circ F\)[/tex] to Celsius:

- Use the same formula: [tex]\(C = \frac{5}{9}(F - 32)\)[/tex].
- Substitute [tex]\(80\)[/tex] for [tex]\(F\)[/tex]:
[tex]\[
C = \frac{5}{9}(80 - 32)
\][/tex]
- Simplify inside the parentheses:
[tex]\[
80 - 32 = 48
\][/tex]
- Now, plug in and calculate:
[tex]\[
C = \frac{5}{9} \times 48
\][/tex]
[tex]\[
C = \frac{240}{9} \approx 26.67
\][/tex]

Therefore, [tex]\(80^\circ F\)[/tex] is approximately [tex]\(26.67^\circ C\)[/tex].

Conclusion:

The corresponding Celsius range is approximately [tex]\(-30.56^\circ C\)[/tex] to [tex]\(26.67^\circ C\)[/tex].