Using a loyalty card at the local gas station store, ella gets a free soda after buying 5 sodas at the regular price of 89¢. same-sized sodas at the local fast food restaurant are 79¢ each. how do the two deals compare if ella buys 6 sodas?

a ella saves 50¢ by purchasing her sodas at the fast food restaurant

b ella saves 60¢ by purchasing her sodas at the fast food restaurant

c ella saves 29¢ by purchasing her sodas at the gas station using the loyalty card

d ella saves 31¢ by purchasing her sodas at the gas station using the loyalty card

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