Final answer:
The Fahrenheit and Celsius scales have the same numerical value at -40 degrees. The Fahrenheit and Kelvin scales, however, can never have the same numerical value because the Kelvin scale is an absolute scale starting at absolute zero, where temperatures are only positive.
Step-by-step explanation:
To find the temperature at which the Fahrenheit and Celsius scales have the same numerical value, we need to look at the points where the two scales intersect. The formula to convert Fahrenheit to Celsius is C = (F - 32) × 5/9. By setting F = C and solving the equation F = (F - 32) × 5/9, we find that the temperature at which they are equal is -40 degrees. Therefore, -40°F equals -40°C.
As for the relationship between the Fahrenheit and Kelvin scales, they can never have the same numerical value because the Kelvin scale is an absolute temperature scale that starts at absolute zero (0 K), which is the theoretical lowest temperature possible. Absolute zero equates to approximately -459.67°F, and since Kelvin does not have negative values, the Fahrenheit and Kelvin scales cannot intersect at the same numerical value.