Will give brainliest! 2017 amc 12a problem 24 quadrilateral is inscribed in circle and has side lengths , and . let and be points on such that and . let be the intersection of line and the line through parallel to . let be the intersection of line and the line through parallel to . let be the point on circle other than that lies on line . what is ? show all work!

  XF·XG = 17

Step-by-step explanation:

Drawing a cyclic quadrilateral from side lengths is interesting enough. I have no idea how to compute the desired value, but my geometry program says it is 17.

In the attached, XF is line segment m, approximately 7.63 in length. XG is line segment n, approximately 2.23 in length. The product is the number "o", shown at the end of the red arrow.

is inscribed in circle " />

yes

Step-by-step explanation:

XF*XG = 17

No solution

Step-by-step explanation:

Because the absolute value of each number is non negative

|a| ≥ 0 for all real numbers

These are 3 questions and 3 answers.

Part 1.] Indicate the general rule for the arithmetic sequence with A3 = - 4 and A8 = - 29

option C. An = 6 + (n-1)(-5)

Solution:

1) A3 is the third term
2) A8 is the eigth term
3) The formula for arithmetic sequences is: An = Ao + (n - 1)d

where n is the number of term and d is the difference between two consecutive terms.

=>

4) A8 = Ao + (8 - 1)d = - 29 => Ao + 7d = - 29  [equation 1]

5) A3 = Ao + (3 - 1)d = - 4 => Ao + 2d = - 4 [equation 2]

6) Subtract equation 2 from equation 1 => 7d - 2d = - 29 - (-4) =>

5d = - 29 + 4
5d = - 25
d = - 25/5 = - 5

7) Find Ao using equation 2:

 Ao + 2d = - 4 =>
 Ao = - 4 - 2d = - 4 - 2(- 5) = - 4 + 10 = 6

8) General rule: An = 6 + (n - 1) (-5)  

Part 2.] Which of the following is the general term for the sequence m, -m, m, -m, . . .?

option a. m (-1)^ (n-1).

Justification:

the sign of the coefficient changes for each term.

when n = 1, the sign is positive: (-1)^ (1-1) = 1
when n = 2, the sign is  negative: (-1)^ (2-1) = - 1
when n = 3, the sign is positive: (-1)^ (3-1) = 2

And so on. So, m (-1)^ (n-1) does the work.

Part 3.] Indicate a general rule for the nth term of the sequence when A1 = 5 and r = √3

option C. An = (5)(√3)^(n-1)

Explanation:

This is a geometric sequence with A1 = 5 and r = √3

The terms of the geometric sequence are:

A1 = 5
A2 = A1 * √3 = 5√3
A3 = A2 * √3 = 5(√3)(√3) = 5(3) = 15
A4 = A3 * √3 = 15√3

So, the general expression is An = 5 * (√3)^(n-1), which is the option C.