#12 find the value of x. #13 find the value of the variable.

  12.  x = 5

  13.  z = 2√21

Step-by-step explanation:

For any given pair of intersecting secants, the product of the distances to the near and far circle intersections is a constant. When those intersection points are both the same (as for a tangent), the same is still true: the product is the square of the length of the tangent segment.

12. (x-2)((x-2) +(x+4)) = 4(4+5)

  (x -2)(2x +2) = 36

  x^2 -x -2 = 18 . . . . . . . divide by 2 and eliminate parentheses

  (x -5)(x +4) = 0 . . . . . . subtract 18 and factor

  x = 5 . . . . . . . . . . . . . . by the zero product rule, the only solution with x > 2

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13. 6(6+8) = z^2

  z = √84 . . . . . . . . take the square root

  z = 2√21 . . . . . . . simplify

it would take 7/10 of an hour too fill the pool.

step-by-step explanation:

the answer is 13/48

step-by-step explanation: