At most, Alana can spend $40 on carnival tickets. Ride tickets cost $4 each, and food tickets cost $2 each. Alana buys at least 16 tickets. The system of inequalities represents the number of ride tickets, r, and the number of food tickets, f, she buys. r + f ≥ 16
4r + 2f ≤ 40What is the maximum number of ride tickets she can buy?

The maximum number of ride tickets is 4

Step-by-step explanation:

r = number of ride tickets

f = number of food tickets

r + f ≥ 16

4r + 2f ≤ 40

Using these as equations

f = 16  -r

Using this in the second equation

4r+ 2 (16 -r) = 40

4r +32 -2r = 40

2r +32 = 40

2r = 8

r = 4

The maximum number of ride tickets is 4

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