A. a survey of 110 teachers showed that 28 of them have a second job. b. a survey of 90 teachers showed that 27 of them have a second job. c. a survey of 70 teachers showed that 21 of them have a second job. d. a survey of 80 teachers showed that 32 of them have a second job. in math class, 4 students complete individual surveys to determine the percentage of high school teachers that have a second job. which two surveys show proportional results? a) a and b b) b and d c) a and d d) b and c

The answer is B and C im 100% correct 

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