Mary solved this problem. robert bought 5 packages of rubber bands. he paid $0.69 for each package. how much did robert pay for the rubber bands? mary thought the answer was $345. is mary's answer reasonable? a. yes, mary's answer is reasonable. b. no, mary's answer should be closer to $34. c. no, mary's answer should be closer to $0.34. d. no, mary's answer should be closer to $3.40

Robert paid a total of 5($0.69), or $3.45, for the bands.  So May was right on in thinking that the amount paid by Robert was $3.45.

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