Item 10 a cheetah that is running 90 feet per second is 120 feet behind an antelope that is running 60 feet per second. how long will it take the cheetah to catch up to the antelope?

4 second
To answer this question you need to know the difference between the cheetah and the antelope speed.
It would be: 90 feet/s- 60feet/s= 30 feet/s

That means the distance between the cheetah and the antelope will shorten 30 feet every second. After that divide the distance with the speed difference:
120 feet / ( 30feet/s )= 4 second

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12