To determine which formula correctly converts temperatures from degrees Celsius to degrees Fahrenheit, we can evaluate each formula with a test value and examine the results.
Let's use 0 degrees Celsius as our test value:
1. Formula 1: [tex]\({ }^{\circ} F = (9 / 5 \times{ }^{\circ} C) + 32\)[/tex]
- Substituting [tex]\( { }^{\circ} C = 0 \)[/tex]:
[tex]\[
{ }^{\circ} F = \left( \frac{9}{5} \times 0 \right) + 32 = 0 + 32 = 32
\][/tex]
- Result: [tex]\( 32^{\circ} F \)[/tex]
2. Formula 2: [tex]\({ }^{\circ} F = (5 / 9 \times ({ }^{\circ} C - 32)) \)[/tex]
- Substituting [tex]\( { }^{\circ} C = 0 \)[/tex]:
[tex]\[
{ }^{\circ} F = \frac{5}{9} \times (0 - 32) = \frac{5}{9} \times -32 \approx -17.78
\][/tex]
- Result: [tex]\( -17.78^{\circ} F \)[/tex]
3. Formula 3: [tex]\({ }^{\circ} F = { }^{\circ} C - 273 \)[/tex]
- Substituting [tex]\( { }^{\circ} C = 0 \)[/tex]:
[tex]\[
{ }^{\circ} F = 0 - 273 = -273
\][/tex]
- Result: [tex]\( -273^{\circ} F \)[/tex]
4. Formula 4: [tex]\({ }^{\circ} F = { }^{\circ} C + 273 \)[/tex]
- Substituting [tex]\( { }^{\circ} C = 0 \)[/tex]:
[tex]\[
{ }^{\circ} F = 0 + 273 = 273
\][/tex]
- Result: [tex]\( 273^{\circ} F \)[/tex]
From the evaluated results:
- The first formula gives us [tex]\( 32^{\circ} F \)[/tex], which is the correct conversion result for [tex]\( 0^{\circ} C \)[/tex] to [tex]\( ^{∘}F \)[/tex].
- The other formulas give us incorrect results when converting from Celsius to Fahrenheit.
Thus, the correct formula for converting from degrees Celsius to degrees Fahrenheit is:
[tex]\[ { }^{\circ} F = (9 / 5 \times{ }^{\circ} C) + 32 \][/tex]
So, the correct choice is:
[tex]\[ { }^{\circ} F = (9 / 5 \times{ }^{\circ} C) + 32 \][/tex]
