The relationship between Celsius(C)and Fahrenheit (F) degrees of measuring temperature is linear. Find an equation relating the two if 1o degrees C corresponds to 50 degrees Fand 50 degrees F and 30 degrees C corresponds to 86 degrees F. Use the equation to find the Celsius measure of 24 degrees F.

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If there's a linear relationship,

F = mC + n

50 = 10m + n
86 = 30m + n

36 = 20m
m = 9/5
n = 32

F = 9/5 C + 32
or
C = 5/9(F-32)

C(24) = 5/9(24-32)
= -40/9 = -4.44

To find an equation relating the Celsius (C) and Fahrenheit (F) degrees, we will use the two data points given:

Data point 1: 1 degree C corresponds to 50 degrees F:
C₁ = 1, F₁ = 50

Data point 2: 30 degrees C corresponds to 86 degrees F:
C₂ = 30, F₂ = 86

We can start by finding the slope of the line using the formula:

slope (m) = (F₂ - F₁) / (C₂ - C₁)

Substituting the values:
m = (86 - 50) / (30 - 1)
m = 36 / 29

Now that we have the slope, we can use the point-slope formula to find the equation of the line:

F - F₁ = m(C - C₁)

Substituting the values:
F - 50 = (36 / 29)(C - 1)

To find the Celsius measure for 24 degrees F, we can rearrange the equation and substitute F = 24:

24 - 50 = (36 / 29)(C - 1)

-26 = (36 / 29)(C - 1)

Multiplying both sides by 29:
-754 = 36(C - 1)

Dividing both sides by 36:
-754 / 36 = C - 1

C - 1 = -20.944

Adding 1 to both sides:
C = -20.944 + 1
C ≈ -19.944

Therefore, the Celsius measure of 24 degrees F is approximately -19.944 degrees Celsius.

To find the equation relating Celsius (C) to Fahrenheit (F), we need to use the two data points mentioned in the problem.

First, let's use the data point where 10 degrees C corresponds to 50 degrees F. We can express this relationship using the equation:

F = m*C + b

where F is Fahrenheit, C is Celsius, m is the slope of the line, and b is the y-intercept.

Plugging in the values, we get:

50 = m*10 + b [Equation 1]

Now, let's use the second data point where 30 degrees C corresponds to 86 degrees F. Applying the same equation:

86 = m*30 + b [Equation 2]

We now have a system of two equations with two variables (m and b). To solve for m and b, we can subtract equation 1 from equation 2:

(86 - 50) = (m*30 - m*10) + (b - b)
36 = 20m

Dividing both sides by 20:

m = 36/20
m = 9/5

Now, substituting this value of m into equation 1:

50 = (9/5)*10 + b

Simplifying:

50 = 90/5 + b
50 = 18 + b
b = 50 - 18
b = 32

Therefore, the equation relating Celsius (C) to Fahrenheit (F) is:

F = (9/5)*C + 32

To find the Celsius measure of 24 degrees F using this equation, we can plug in the value for F and solve for C:

24 = (9/5)*C + 32

Subtracting 32 from both sides:

24 - 32 = (9/5)*C
-8 = (9/5)*C

Dividing both sides by (9/5):

C = (-8) / (9/5)
C = -8 * (5/9)
C = -40/9
C ≈ -4.44 degrees Celsius

Therefore, the Celsius measure of 24 degrees Fahrenheit is approximately -4.44 degrees Celsius.