Write two or three rational numbers with emmet's time in each denominator. si the rational number always a terminating decimal? .justify your answer. emmet's time is 20 minutes

So I guess we want 2 or 3 rational numbers with 20 in the denenaotre

a rational number is a number that can be written in form a/b where a and b are integers and b≠0

so

1/20 and 3/20 and 7/20 are 3 rational numbers with emmet's time in the denomenator

so far, they are terminating decimals because
1/20=0.05, terminates
3/20=0.15, terminates
7/20=0.35, terminates

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