High School

Type the correct answer in each box. If necessary, round your answers to the nearest tenth.

Use the conversion formulas for Celsius and Fahrenheit to find the missing values in the table.

[tex]
\[
\begin{array}{|c|c|}
\hline
\multicolumn{2}{|c|}{\text{Temperature}} \\
\hline
\text{Degrees Celsius} & \text{Degrees Fahrenheit} \\
\hline
10 & \square \\
\hline
\square & 87 \\
\hline
-5 & \square \\
\hline
\square & 10 \\
\hline
\end{array}
\]
[/tex]

Conversion formulas:
- To convert Celsius to Fahrenheit: [tex] F = \frac{9}{5}C + 32 [/tex]
- To convert Fahrenheit to Celsius: [tex] C = \frac{5}{9}(F - 32) [/tex]

Answer :

To convert temperatures between Celsius and Fahrenheit, we use two main formulas:

1. Celsius to Fahrenheit:
[tex]\( F = C \times \frac{9}{5} + 32 \)[/tex]

2. Fahrenheit to Celsius:
[tex]\( C = (F - 32) \times \frac{5}{9} \)[/tex]

Let's use these formulas to fill in the missing values in the table:

1. Convert 10 degrees Celsius to Fahrenheit:
[tex]\[
F = 10 \times \frac{9}{5} + 32 = 50.0
\][/tex]
So, 10 degrees Celsius is 50.0 degrees Fahrenheit.

2. Convert 87 degrees Fahrenheit to Celsius:
[tex]\[
C = (87 - 32) \times \frac{5}{9} \approx 30.6
\][/tex]
Rounding to the nearest tenth, 87 degrees Fahrenheit is approximately 30.6 degrees Celsius.

3. Convert -5 degrees Celsius to Fahrenheit:
[tex]\[
F = -5 \times \frac{9}{5} + 32 = 23.0
\][/tex]
So, -5 degrees Celsius is 23.0 degrees Fahrenheit.

4. Convert 10 degrees Fahrenheit to Celsius:
[tex]\[
C = (10 - 32) \times \frac{5}{9} \approx -12.2
\][/tex]
Rounding to the nearest tenth, 10 degrees Fahrenheit is approximately -12.2 degrees Celsius.

With these calculations, the completed table is:

[tex]\[
\begin{array}{|c|c|}
\hline
\text{Degrees Celsius} & \text{Degrees Fahrenheit} \\
\hline
10 & 50.0 \\
\hline
30.6 & 87 \\
\hline
-5 & 23.0 \\
\hline
-12.2 & 10 \\
\hline
\end{array}
\][/tex]