. A sailboat with a sick passenger abroad is following a parabolic path given by the equation y=〖-x〗^2+6x+7. The boat’s captain sent out a distress signal. A speedboat is trying to catch the sailboat to provide medical aid and is on a path given by the linear equation y= x+7. Besides the y-intercept (starting location) where do the paths of the two boats cross (show all the appropriate work and give answer in coordinate pair notation)?
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Where’s the following prism

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

These are the multiples of 15 but what you are probably asking or what are the factors of 15