#20 #21 and #22 for 12 points you

20. AD = DC

21. AM = 9

22. x = 4 , RS = 3

Step-by-step explanation:

* Lets explain how to solve the problems

20)

- A mid-point is the point which divides a line segment into two equal

 parts in lengths

∵ D is the mid-point of AC

∴ D divides segment AC into two equal parts in lengths

∴ AD = DC

21)

- Line l is a segment bisector of AC at point M

∵ Segment l bisects AC at M

∴ M is the mid point of AC

∴ AM = MC

∵ AM = y + 6

∵ MC = 4y - 3

∴ 4y - 3 = y + 6

- Subtract y from both sides

∴ 3y - 3 = 6

- Add 3 to both sides

∴ 3y = 9

- Divide both sides by 3

∴ y = 3

- Substitute the value of y in AM to find its length

∴ AM = 3 + 6 = 9

∴ AM = 9

22)

- Points R, S, T are col-linear and S is between R and T

∴ RT = RS + ST

∵ RS = 2x - 5

∵ ST = 3x + 2

∵ RT = 17

- Substitute these value in the equation above

∴ 2x - 5 + 3x + 2 = 17

- Add like terms in the left hand side

∴ 5x - 3 = 17

- Add 3 to both sides

∴ 5x = 20

- Divide both sides by 5

∴ x = 4

* The value of x is 4

- Substitute the value of x in RS

∴ RS = 2(4) - 5 = 8 - 5 = 3

∴ The length of RS = 3

x = -2

y = 848

step-by-step explanation:

plug in the numbers

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step-by-step explanation: