Answer :
We start with the conversion formula that relates degrees Fahrenheit ([tex]$F$[/tex]) to degrees Celsius ([tex]$C$[/tex]):
[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]
Given that [tex]$F = 50^\circ$[/tex], we substitute into the formula:
[tex]$$
C = \frac{5}{9}(50 - 32) = \frac{5}{9} \times 18 = 10.
$$[/tex]
Thus, the correct Celsius temperature is [tex]$10^\circ C$[/tex].
Now, let’s examine the two alternative expressions provided:
1. Option A:
[tex]$$
\frac{5}{9}(50) - 5(32)
$$[/tex]
First, compute [tex]$\frac{5}{9}(50)$[/tex]:
[tex]$$
\frac{5}{9} \times 50 = \frac{250}{9} \quad \text{(approximately }27.78\text{)}.
$$[/tex]
Then compute [tex]$5(32)$[/tex]:
[tex]$$
5 \times 32 = 160.
$$[/tex]
Now subtract:
[tex]$$
\frac{250}{9} - 160 \approx 27.78 - 160 \approx -132.22.
$$[/tex]
This result, approximately [tex]$-132.22$[/tex], does not equal [tex]$10$[/tex].
2. Option B:
[tex]$$
5(50) - \frac{32}{9}
$$[/tex]
First, compute [tex]$5(50)$[/tex]:
[tex]$$
5 \times 50 = 250.
$$[/tex]
Then compute [tex]$\frac{32}{9}$[/tex]:
[tex]$$
\frac{32}{9} \approx 3.56.
$$[/tex]
Now subtract:
[tex]$$
250 - \frac{32}{9} \approx 250 - 3.56 \approx 246.44.
$$[/tex]
This result, approximately [tex]$246.44$[/tex], also does not equal [tex]$10$[/tex].
Since neither Option A nor Option B produces the correct conversion value of [tex]$10^\circ C$[/tex], we conclude that neither expression is equivalent to the original conversion formula.
Therefore, the final answer is that none of the given expressions correctly convert [tex]$50^\circ F$[/tex] to degrees Celsius.
[tex]$$
C = \frac{5}{9}(F - 32).
$$[/tex]
Given that [tex]$F = 50^\circ$[/tex], we substitute into the formula:
[tex]$$
C = \frac{5}{9}(50 - 32) = \frac{5}{9} \times 18 = 10.
$$[/tex]
Thus, the correct Celsius temperature is [tex]$10^\circ C$[/tex].
Now, let’s examine the two alternative expressions provided:
1. Option A:
[tex]$$
\frac{5}{9}(50) - 5(32)
$$[/tex]
First, compute [tex]$\frac{5}{9}(50)$[/tex]:
[tex]$$
\frac{5}{9} \times 50 = \frac{250}{9} \quad \text{(approximately }27.78\text{)}.
$$[/tex]
Then compute [tex]$5(32)$[/tex]:
[tex]$$
5 \times 32 = 160.
$$[/tex]
Now subtract:
[tex]$$
\frac{250}{9} - 160 \approx 27.78 - 160 \approx -132.22.
$$[/tex]
This result, approximately [tex]$-132.22$[/tex], does not equal [tex]$10$[/tex].
2. Option B:
[tex]$$
5(50) - \frac{32}{9}
$$[/tex]
First, compute [tex]$5(50)$[/tex]:
[tex]$$
5 \times 50 = 250.
$$[/tex]
Then compute [tex]$\frac{32}{9}$[/tex]:
[tex]$$
\frac{32}{9} \approx 3.56.
$$[/tex]
Now subtract:
[tex]$$
250 - \frac{32}{9} \approx 250 - 3.56 \approx 246.44.
$$[/tex]
This result, approximately [tex]$246.44$[/tex], also does not equal [tex]$10$[/tex].
Since neither Option A nor Option B produces the correct conversion value of [tex]$10^\circ C$[/tex], we conclude that neither expression is equivalent to the original conversion formula.
Therefore, the final answer is that none of the given expressions correctly convert [tex]$50^\circ F$[/tex] to degrees Celsius.
