The we of a father is 2 less than 7 times the age of his son. in 3 years, the sum of their ages will be 52. if the son’s present age is s years, which equation models this situation ?

Fathers age = F
F = S × 7 - 2

F + 3 + S + 3 = 52
F + S + 6 = 52
F + S = 46

Replace F in F + S, with our previous equation, so that we can only have one type of letter on any side at any given time

so in this case we have, (S × 7 - 2) + S = 46
We can remove the brackets, as they are not necessary in this case
S × 7 - 2 + S = 46
Remove -2 by adding 2 on both sides
S × 7 + S = 48
Simplify
S × 8 = 48
divide both sides by 8
S × 8/8 = 48/8
S = 6

F + S = 46
F + 6 = 46
F = 40

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

The answer is 1532.75