Here is a formula to convert degrees Celsius [tex]$\left({ }^{\circ} C \right)$[/tex] to degrees Fahrenheit:

[tex]\[ F = 1.8C + 32 \][/tex]

Where [tex]$ F $[/tex] is the number of degrees Fahrenheit, and [tex]$ C $[/tex] is the number of degrees Celsius.

1. If the temperature in degrees Celsius is [tex]$-5$[/tex], what is the temperature in degrees Fahrenheit?

2. Which temperature is the same in degrees Celsius as it is in degrees Fahrenheit?

We start with the conversion formula from Celsius to Fahrenheit:
[tex]$$
F = 1.8C + 32.
$$[/tex]

1. To find the Fahrenheit temperature when the Celsius temperature is [tex]$-5^\circ C$[/tex], substitute [tex]$C = -5$[/tex] into the formula:
[tex]$$
F = 1.8(-5) + 32.
$$[/tex]
First, multiply:
[tex]$$
1.8 \times (-5) = -9.
$$[/tex]
Then add 32:
[tex]$$
F = -9 + 32 = 23.
$$[/tex]
So, the temperature in Fahrenheit is [tex]$23^\circ F$[/tex].

2. Next, to find the temperature at which the numerical value in Celsius equals the numerical value in Fahrenheit, set [tex]$C = F$[/tex]. Replace [tex]$F$[/tex] in the conversion formula by [tex]$C$[/tex]:
[tex]$$
C = 1.8C + 32.
$$[/tex]
Subtract [tex]$1.8C$[/tex] from both sides to isolate the term containing [tex]$C$[/tex]:
[tex]$$
C - 1.8C = 32.
$$[/tex]
Combine like terms:
[tex]$$
-0.8C = 32.
$$[/tex]
Divide both sides by [tex]$-0.8$[/tex] to solve for [tex]$C$[/tex]:
[tex]$$
C = \frac{32}{-0.8} = -40.
$$[/tex]
Therefore, the temperature that is the same in both Celsius and Fahrenheit is [tex]$-40^\circ$[/tex].

In summary:
- Converting [tex]$-5^\circ C$[/tex] gives [tex]$23^\circ F$[/tex].
- The temperature that is the same in both units is [tex]$-40^\circ$[/tex].