the table shows the height, in meters, of an object that is dropped as time passes until the object hits the…

the table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. falling object\n| time (sec), $x$ | 0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | 4.6 |\n| height (m), $h$ | 100 | 98.8 | 95.1 | 89.0 | 80.4 | 69.4 | 55.9 | 40.0 | 21.6 | 0 |\na line of best fit for the data is represented by $h=-21.962x + 114.655$. which statement compares the line of best fit with the actual data given by the table?\n○ according to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.\n○ according to the line of best fit, the object was dropped from a lower height.\n○ the line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds.\n○ the line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.

the table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. falling object\n| time (sec), $x$ | 0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | 4.6 |\n| height (m), $h$ | 100 | 98.8 | 95.1 | 89.0 | 80.4 | 69.4 | 55.9 | 40.0 | 21.6 | 0 |\na line of best fit for the data is represented by $h=-21.962x + 114.655$. which statement compares the line of best fit with the actual data given by the table?\n○ according to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.\n○ according to the line of best fit, the object was dropped from a lower height.\n○ the line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds.\n○ the line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.

Answer

Explanation:

Step1: Find when the object hits the ground according to the line - of - best - fit.

Set (h = 0) in (h=-21.962x + 114.655). Then (0=-21.962x + 114.655), so (21.962x=114.655), and (x=\frac{114.655}{21.962}\approx5.22) seconds. The actual time the object hits the ground is (4.6) seconds. The difference is (5.22 - 4.6=0.62\approx0.6) seconds.

Step2: Check the initial height according to the line - of - best - fit.

When (x = 0), (h=-21.962\times0 + 114.655 = 114.655) meters. The actual initial height is (100) meters, so the object was dropped from a higher height according to the line - of - best - fit.

Step3: Check the height at (x = 3.5) seconds.

Substitute (x = 3.5) into (h=-21.962x + 114.655). (h=-21.962\times3.5+114.655=-76.867 + 114.655 = 37.788\neq40) meters.

Step4: Check the general height difference.

The line - of - best - fit does not predict a height of 4 meters greater than the actual height for any time in the table.

Answer:

According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.