What number comes next?
2,7,8,3,12,9

14. 

The first, third and fifth number are even numbers. 2, 8, 12

And the second, forth and sixth numbers are odd numbers. 7, 3, 9 

1. y = c + 2x

c1= 2 (and subsequent c= next number in the series) and x is in reducing order:

2 + 2x3 = 8

8 + 2x2 = 12

12 + 2x1 = 14 

2.  u = a (+-) 2(v).   

a1=7 (and subsequent a= next number in the series) and v is in increasing order.

7 - 2x2 = 3

3 + 2x3 = 9

9 - 2x4 = 1 

the subsequent number is an even number, so it should be 14

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