Question

Standing on a lighthouse platform that is 76 feet above the ground, an observer sees a hot-air balloon 100 feet above him. On a number line, let 0 represent the position of the obsenver, and let the hot-air balloon's position be on the positive side of 0. Which number sentence correctly compares the distances between the observer's position and the ground and the observer's position and the hot air balloon?

A. 75>-300
B. |75|=|-3
C -75>730)
D |-75|

Answer 1

The correct number sentence that compares the distances between the observer's position and the ground and the observer's position and the hot air balloon is |-75|. The absolute value of -75 represents the distance between the observer's position and the ground, which is 75 feet. The distance between the observer's position and the hot air balloon is 24 feet.

Step-by-step explanation:

The correct number sentence that compares the distances between the observer's position and the ground and the observer's position and the hot air balloon is:

|-75|

The absolute value of -75 represents the distance between the observer's position and the ground, which is 75 feet. The observer is 76 feet above the ground, so the distance between the observer's position and the balloon can be found by subtracting the height of the balloon from the height of the observer:

76 - 100 = -24 feet.

Since the balloon is below the observer, the distance is negative. Taking the absolute value of -24 gives us 24, which represents the distance between the observer's position and the hot air balloon.