Find solutions to your questions with the help of IDNLearn.com's expert community. Join our community to receive prompt and reliable responses to your questions from knowledgeable professionals.

The formula used to convert degrees Celsius to degrees Fahrenheit is [tex]\( F = \frac{9}{5}C + 32 \)[/tex].

Convert [tex]\( 77^{\circ} F \)[/tex] to degrees Celsius. Solve the formula for [tex]\( C \)[/tex], and then use it to convert the temperature.

Which is the correct formula and conversion?
A. [tex]\( C = \frac{5}{9}(F - 32) \)[/tex]; conversion: [tex]\( 77^{\circ} F = 139^{\circ} C \)[/tex]
B. [tex]\( C = 5F - 32 \)[/tex]; conversion: [tex]\( 77^{\circ} F = 225^{\circ} C \)[/tex]
C. [tex]\( C = \frac{9}{3}F - 32 \)[/tex]; conversion: [tex]\( 77^{\circ} F = 25^{\circ} C \)[/tex]
D. [tex]\( C = \frac{5}{9}(F - 32) \)[/tex]; conversion: [tex]\( 77^{\circ} F = 25^{\circ} C \)[/tex]


Sagot :

To convert [tex]\( 77^\circ \text{F} \)[/tex] to degrees Celsius, we must first rearrange the given formula [tex]\( F = \frac{9}{5}C + 32 \)[/tex] to solve for [tex]\( C \)[/tex].

1. Start with the equation:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]

2. Subtract 32 from both sides to isolate the term containing [tex]\( C \)[/tex]:
[tex]\[ F - 32 = \frac{9}{5}C \][/tex]

3. Multiply both sides by the reciprocal of [tex]\( \frac{9}{5} \)[/tex], which is [tex]\( \frac{5}{9} \)[/tex], to solve for [tex]\( C \)[/tex]:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]

Now, use this formula to convert [tex]\( 77^\circ \text{F} \)[/tex] to degrees Celsius.

4. Substitute [tex]\( 77 \)[/tex] for [tex]\( F \)[/tex] in the formula:
[tex]\[ C = \frac{5}{9}(77 - 32) \][/tex]

5. Calculate the difference inside the parentheses:
[tex]\[ 77 - 32 = 45 \][/tex]

6. Multiply by [tex]\( \frac{5}{9} \)[/tex]:
[tex]\[ C = \frac{5}{9} \times 45 \][/tex]

7. Perform the multiplication:
[tex]\[ C = 25.0 \][/tex]

Therefore, the correct conversion of [tex]\( 77^\circ \text{F} \)[/tex] is [tex]\( 25^\circ \text{C} \)[/tex].

Among the given choices, the correct formula and conversion are:
D. [tex]\( C = \frac{5}{9}(F - 32) \)[/tex]; conversion: [tex]\( 77^\circ \text{F} = 25^\circ \text{C} \)[/tex].
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.