Final answer:
After substituting 0.75 seconds into the given height function, the height of the object at that time is calculated to be 15 meters. The answer choices given in the question seem to be incorrect as they do not match the calculated value.
Step-by-step explanation:
The question is asking for the height of an object at a specific time given the quadratic equation H(t) = -16t^2 + 16t + 12, where t is the time in seconds and H(t) is the height in meters. To find the height after 0.75 seconds, we simply substitute 0.75 for t in the equation:
H(0.75) = -16(0.75)^2 + 16(0.75) + 12
Calculating this we get:
H(0.75) = -16(0.5625) + 12 + 12
H(0.75) = -9 + 12 + 12
H(0.75) = 3 + 12
H(0.75) = 15 meters
However, the answer choices provided in the question do not include 15 meters. There may be an error or typo in the provided choices.