Given the equation [tex]F=\frac{9}{5} C+32[/tex] where [tex]C[/tex] is the temperature in degrees Celsius and [tex]F[/tex] is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:
[tex]\left(-10, F_1\right),\left(-30, F_2\right)[/tex]
Step 1 of 2: Compute the missing [tex]y[/tex] values so that each ordered pair will satisfy the given equation.
Answer (1)
Substitute C = − 10 into the equation F = 5 9 C + 32 to find F 1 , which gives F 1 = 14 .
Substitute C = − 30 into the equation F = 5 9 C + 32 to find F 2 , which gives F 2 = − 22 .
The ordered pairs that satisfy the equation are ( − 10 , 14 ) and ( − 30 , − 22 ) .
The missing y values are F 1 = 14 , F 2 = − 22 .
Explanation
Understanding the Problem We are given the equation F = 5 9 C + 32 , which converts Celsius to Fahrenheit. We need to find the Fahrenheit temperatures F 1 and F 2 corresponding to C = − 10 and C = − 30 , respectively.
Calculating F1 First, let's find F 1 when C = − 10 . We substitute C = − 10 into the equation: F 1 = 5 9 ( − 10 ) + 32
Simplifying F1 Now, we simplify the expression: F 1 = 5 9 × ( − 10 ) + 32 = 9 × ( − 2 ) + 32 = − 18 + 32 = 14
So, F 1 = 14 .
Calculating F2 Next, let's find F 2 when C = − 30 . We substitute C = − 30 into the equation: F 2 = 5 9 ( − 30 ) + 32
Simplifying F2 Now, we simplify the expression: F 2 = 5 9 × ( − 30 ) + 32 = 9 × ( − 6 ) + 32 = − 54 + 32 = − 22 So, F 2 = − 22 .
Final Answer Therefore, the missing y values are F 1 = 14 and F 2 = − 22 .
Examples
Understanding the conversion between Celsius and Fahrenheit is useful in many real-life situations. For example, when traveling to a country that uses Celsius, you can convert the temperature to Fahrenheit to better understand how hot or cold it is. Similarly, scientists and engineers often need to convert between these two scales in their work. The formula F = 5 9 C + 32 allows for quick and accurate conversions, which is essential in many applications.
