Given the trinomial, what is the value of the coefficient 'b' in the factored form?

2x2 + 14xy − 36y2 = 2(x + by)(x − 2y)

b=

2x2 + 14xy -36y2 = (2x+2By)(x - 2y) 
2x2 + 14xy -36y2  = 2x2 -4xy +2Bxy -4By2 
2x2 + 14xy -36y2  = 2x2 + (2B-4)xy -4By2 
since the coefficient of y2 is equal so 
-4B = -36 
B = 9 
if you want to make sure subs in coeeficient of xy by B=9 
and you'll get 14 so the answer is right 
B=9 

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