A scientist uses the expression [tex]$\frac{5}{9}(F-32)$[/tex] to convert temperature. What is the temperature, in [tex]${}^{\\circ} F$[/tex], of a substance at [tex]$-25^{\\circ} C$[/tex]?
A. -13
B. 18
C. 13
D. -32
Answer (2)
Substitute the given Celsius temperature, − 25 , into the conversion formula: − 25 = 9 5 ( F − 32 ) .
Multiply both sides by 5 9 to get − 45 = F − 32 .
Add 32 to both sides to isolate F : F = − 45 + 32 .
Simplify to find the Fahrenheit temperature: − 13 .
Explanation
Understanding the Problem We are given the formula to convert Fahrenheit to Celsius: C = 9 5 ( F − 32 ) , where C is the temperature in Celsius and F is the temperature in Fahrenheit. We are given that the temperature in Celsius is − 2 5 ∘ C , and we want to find the corresponding temperature in Fahrenheit.
Substituting the Value Substitute C = − 25 into the formula: − 25 = 9 5 ( F − 32 ) .
Multiplying by the Inverse To solve for F , first multiply both sides of the equation by 5 9 : 5 9 × ( − 25 ) = 5 9 × 9 5 ( F − 32 ) − 45 = F − 32
Isolating F Now, add 32 to both sides of the equation: − 45 + 32 = F − 32 + 32 − 13 = F
Final Answer Therefore, the temperature in Fahrenheit is − 1 3 ∘ F .
Examples
Temperature conversion is a common task in many fields, such as cooking, weather forecasting, and scientific research. For example, if a recipe calls for an oven temperature in Fahrenheit but you only have a Celsius thermometer, you would need to convert the temperature. Similarly, weather reports often provide temperatures in both Celsius and Fahrenheit, so understanding the conversion formula is useful for interpreting the information. In scientific research, accurate temperature measurements are crucial, and scientists may need to convert between different temperature scales depending on the context.
The temperature of a substance at -25°C is -13°F. The conversion formula used is F = 5 9 C + 32 . Thus, the answer is -13.
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