Kylie and Matt are driving out of town, leaving from the same house in different cars. Matt drives at a rate of 40 miles per hour. Matt drives 50 miles before Kylie beings traveling. Kylie drives at a rate of 50 miles per hour. Part A:
Y = 40x + 50
Y = 50x
Graph the system in the coordinate plane and label each line with the driver it represents.

Part B: Describe a situation in which Kylie and Matt are traveling but are never the same distance from the starting point at the same time. Write a system of equations to model the situation. How many solutions does the system have? Explain your reasoning.

The answer is 63.!

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