The relationship between temperatures measured in Fahrenheit, and in Celsius can be represented using an equation.
- The equation is: [tex]5F=9C + 160[/tex].
- The temperature in degrees Celsius when temperature in degrees Fahrenheit is 39, is 3.9
First, we calculate the slope (m) of the table
From the table (see attachment), we have:
[tex](F_1,C_1) = (-13,-25)[/tex]
[tex](F_2,C_2) = (-4,-20)[/tex]
Calculate the slope (m)
[tex]m = \frac{C_2 - C_1}{F_2-F_1}[/tex]
So, we have:
[tex]m = \frac{-20--25}{-4--13}[/tex]
[tex]m = \frac{5}{9}[/tex]
The equation is then calculated using:
[tex]C = m(F -F_1) + C_1[/tex]
So, we have:
[tex]C = \frac{5}{9}(F - -13) -25[/tex]
[tex]C = \frac{5}{9}(F +13) -25[/tex]
Multiply through by 9
[tex]9C = 5(F +13) -225[/tex]
Open bracket
[tex]9C = 5F +65 -225[/tex]
[tex]9C = 5F -160[/tex]
Rewrite as:
[tex]5F=9C + 160[/tex]
To calculate the value of C for F = 39, we have:
[tex]C = \frac{5}{9}(F +13) -25[/tex]
[tex]C = \frac 59(39 + 13) - 25[/tex]
[tex]C = \frac 59(52) - 25[/tex]
[tex]C = \frac{260}{9} - 25[/tex]
[tex]C = \frac{260-25\times 9}{9}[/tex]
[tex]C = \frac{35}{9}[/tex]
[tex]C = 3.9[/tex]
Read more about equations and tables at:
https://brainly.com/question/16911650
