When the Celsius temperature is 15degrees, the corresponding Fahrenheit temperature is 59degrees. When the Celsius temperature is 75degrees, the corresponding Fahrenheit temperature is 167 degrees . Let C represent the Celsius temperature and F the Fahrenheit temperature. a. Express F as an exact linear function of C. b. Solve the equation in part a for C, thus expressing C as a function of F. c. For what temperature is FequalsC?

(a)

(b)

(c) -40 degree

Step-by-step explanation:

(a)

A linear function is of the form

Given:

Temperature in Fahrenheit is given as 'F' and in Celsius is 'C'.

So, the linear relation is of the form , where, 'm' and 'b' are real numbers.

Now, when

When

Now, plugging these values in the above equation and solving for 'm' and 'b', we have:

Now, plugging 'm' value in first equation to get 'b' value, we have:

Therefore, the equation expressed for 'F' in terms of 'C' is given as:

(b)

In order to solve for 'C', we isolate 'C' from the above equation.

Add -32 both sides. This gives,

Divide both sides by 1.8. This gives,

Therefore, the equation solved for 'C' is

(c)

Let the temperature be 'x' when F = C.

Therefore,

Therefore, at -40 degree, the temperature in Fahrenheit equals that in Celsius.

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation:

step-by-step explanation:

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