Question

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Answer 1

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 observer, 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. |76| > |-100|
B. |76| = |-100|
C. |-76| > |100|
D. |-76| < |100|

Answer 2

I hope you're ok with a vertical number line, but it makes more sense since we're talking about vertical distances

anyway, notice how 0 is the point where the person is standing. the ground is 76 feet below the platform, so the ground would be represented by -76

the hot air balloon is 100 feet above the platform, so it would be represented by positive 100

now, since its talking about distances, we take the absolute value of both quantities

|100| and |-76|. now compare them - which one is larger? remember, we're talking about absolute value.