Sven is trying to find the maximum amount of time he can spend practicing the five scales of piano music he is supposed to be working on. he has 70 minutes to practice piano and would like to spend at least 55 minutes playing songs instead of practicing scales. so, sven sets up the following inequality, where t is the number of minutes he spends on each scale, and solves it. 70 − 5t ≤ 55 −5t ≤ −15 t ≥ 3 sven has concluded that he should spend 3 minutes or more on each scale. is this correct? if not, what mistake did he make? then solve for the correct answer.

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

/-/////////looks tough ‍♂️