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Lerok [7]
3 years ago
5

What is the value of X?

Mathematics
1 answer:
balandron [24]3 years ago
3 0
The problem can be solved using the Power of a Point, which states that:

EC \cdot ED=EB \cdot EA.

Substituting

EC=x+4; ED=x+5; EB=x+1; EA=x+12, 

we have the equation

(x+4) \cdot (x+5)=(x+1) \cdot (x+12).

Expanding both sides we get, 

x^2+9x+20=x^2+13x+12.

Subtracting x^2 from both sides, we have
                           
9x+20=13x+12. 
 
Collecting x's and the numbers on two different sides, we have:

4x=8, which finally yields x=2.



Answer: x=2
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13. The midpoint divides the segment into two equal parts. That is

BC = (1/2)·AC = (1/2)·(8x -20)

BC = 4x -10

Since you are told the other half is 3x -1, the two halves being equal tells you

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The problem statement is not clear as to the desired form of the answer—whether it is to be in terms of x, or a number.

14. Same deal as the previous problem. The halves of the bisected segment are equal, giving you an equation that can be solved for x.

... CG = GD

... 5x -1 = 7x -13

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... 38 = 2x . . . . . . . . . . . . . . . . add 43-6x

... x = 19

Since R is the midpoint of QS, RS will be half the length of QS. The length of RS is 2x -4 = 2(19) - 4 = 34. Then the length of QS is 2·34 = 68.

QS = 68

_____

To help check our work, we can find the lengths of the other segments in the diagram. ST = 4x - 1 = 75; RT = 8x - 43 = 109. So, we have ...

... QR : RS : ST = 34 : 34 : 75 . . . with QS = 68 and RT = 109.

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