Sam found a tie he liked at two different stories. at store a, the tie was originally priced at $49.50 and was on sale for 25% off. at store b, the tie was originally priced at $53.00 and was on sale for 30%. after the discount, will the tie cost less at store a or store b? how much will it cost?

Store A : 25% off means u r paying 75% 75% of 49.50...
              0.75(49.50) = 37.125 rounds to 37.13

store B : 30% off means u r paying 70%70% of 53
              0.70(53) = 37.10

so the tie will cost less at store Bit will cost 37.10

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