The flip-flop-alot company makes and sells flip-flops. they have one linear function that represents the cost of producing flip-flops and another linear function that models how much income they get from those flip-flops. describe the key features that would determine if these linear functions ever intersected.

Well if you start at zero for the cost and go to $10 which would represent the cost of one flip-flops and it goes up at a 10 to 1 ratio so your linear function for that would be f(x)= 10x 10 being the cost per production of flip-flops and x being the number of flip flops. then you would have the a $15 dollar sell rate or which would be a $5 extra rate. so then as you graph what would you get?

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