The temperature of a weather station was 12.8°F at midnight and fell 1.4°F each hour for six hours. Which of the following solutions are viable for (h,T) where h is the number of hours after midnight and T is the temperature in degrees Fahrenheit?(1 point) Responses (5, 5.8) (5, 5.8) (7,3) open paren 7 comma 3 close paren (4, 18.4) (4, 18.4) (−1, 14.2)
We know that the temperature at midnight was 12.8°F and it fell 1.4°F each hour for six hours. So, after h hours, the temperature can be determined using the equation:
T = 12.8 - 1.4h
Now let's substitute the given solutions into the equation and see which ones are viable:
1. T = 5.8 and h = 5
T = 12.8 - 1.4(5)
T = 12.8 - 7
T = 5.8
This solution is viable.
2. T = 3 and h = 7
T = 12.8 - 1.4(7)
T = 12.8 - 9.8
T = 3
This solution is viable.
3. T = 18.4 and h = 4
T = 12.8 - 1.4(4)
T = 12.8 - 5.6
T = 7.2
This solution is not viable.
4. T = 14.2 and h = -1
T = 12.8 - 1.4(-1)
T = 12.8 + 1.4
T = 14.2
This solution is viable.
Therefore, the viable solutions are: (5, 5.8), (7, 3), and (-1, 14.2).