Complete the function table and write the function rule.

To finish the table lets see what the differences are between the input (x) and the output (Y)

when input is 32 the output is 20, 32-20 = 12
when input is 14 the output is 2, 14-2 = 12

since the top 2 have the same result, the output is the input minus 12 
 now that we know that we can finish the table:

when the input is ? the output is -6, so the input = -6 +12 = 6
check: 6-12 = -6 true

when the input is -10, we subtract 12 to get -22 for the output
 so the missing input is 6 and the missing output is -22

 the function rule would be Y=x-12

The correct answer here is c

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