Use the formula [tex]C=\frac{5}{9}(F-32)[/tex] for conversion between Fahrenheit and Celsius to convert each temperature.

a. Convert [tex]84^{\circ} F[/tex] to Celsius
b. Convert [tex]-10^{\circ} F[/tex] to Celsius
c. Convert [tex]45^{\circ} C[/tex] to Fahrenheit

a. [tex]84^{\circ} F = \square^{\circ} C[/tex]
(Type an integer or decimal rounded to the nearest tenth as needed.)

Sure! Let's go through each part of the temperature conversion:

### a. Convert 84°F to Celsius
To convert from Fahrenheit to Celsius, we use the formula:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]

For [tex]\( 84^\circ F \)[/tex]:
[tex]\[ C = \frac{5}{9}(84 - 32) \][/tex]
[tex]\[ C = \frac{5}{9}(52) \][/tex]
[tex]\[ C = \frac{5 \times 52}{9} \][/tex]
[tex]\[ C = \frac{260}{9} \][/tex]
[tex]\[ C \approx 28.9 \][/tex]

So, [tex]\( 84^{\circ} F \)[/tex] is approximately [tex]\( 28.9^{\circ} C \)[/tex].

### b. Convert -10°F to Celsius
Using the same formula:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]

For [tex]\(-10^\circ F\)[/tex]:
[tex]\[ C = \frac{5}{9}(-10 - 32) \][/tex]
[tex]\[ C = \frac{5}{9}(-42) \][/tex]
[tex]\[ C = \frac{5 \times -42}{9} \][/tex]
[tex]\[ C = \frac{-210}{9} \][/tex]
[tex]\[ C \approx -23.3 \][/tex]

So, [tex]\(-10^{\circ} F\)[/tex] is approximately [tex]\(-23.3^{\circ} C\)[/tex].

### c. Convert 45°C to Fahrenheit
To convert from Celsius to Fahrenheit, use the reverse formula:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]

For [tex]\( 45^\circ C \)[/tex]:
[tex]\[ F = \frac{9}{5} \times 45 + 32 \][/tex]
[tex]\[ F = 9 \times 9 + 32 \][/tex]
[tex]\[ F = 81 + 32 \][/tex]
[tex]\[ F = 113.0 \][/tex]

So, [tex]\( 45^{\circ} C \)[/tex] is [tex]\( 113.0^{\circ} F \)[/tex].

These are the temperature conversions for each given case.