White shapes and blacks shapes are used in a game. some of the shapes are circles. all other are squares. the ratio of the number of white shapes to the number of black shapes is 3: 7. the ratio of the number of white circles to the number of white squares is 4: 5. the ratio of the number of black circles to the number of black squares is 2: 5. work out what fraction of all the shapes are circles?

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

Two because two of one thing is two.

$22. if larry's profit were to minimize by one for every hour his store were to be closed, we would subtract 30 by 8.