If M is midpoint of line BK,
BM = 5x + 9, MK = 3x + 33 then what does x equal. What does BK equal.
5x+9=3x=33
5x-3x=33-9
2x=24
x=12
BK=2(5(12)+9)
=138
the first line should be "5x+9=3x-33"
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To find the value of x, we need to use the fact that M is the midpoint of line BK.
Using the midpoint formula, we know that the coordinates of the midpoint M is the average of the coordinates of the endpoints B and K. In this case, the coordinates of B are represented by BM and the coordinates of K are represented by MK.
The midpoint formula is:
M = (B + K) / 2
Substituting the given information, we have:
(5x + 9 + 3x + 33) / 2 = M
Simplifying the equation, we have:
(8x + 42) / 2 = M
Now, we can substitute M with the value given:
M = (8x + 42) / 2
Since M is the midpoint, it is equal to both BM and MK:
BM = (8x + 42) / 2
MK = (8x + 42) / 2
Now, we can substitute the given values of BM and MK into the equations:
BM = 5x + 9
MK = 3x + 33
Setting them equal to each other, we have:
5x + 9 = 3x + 33
Subtracting 3x from both sides and subtracting 9 from both sides, we get:
2x = 24
Dividing both sides by 2, we have:
x = 12
Therefore, x equals 12.
To find BK, we can substitute the value of x into either BM or MK:
BM = 5x + 9
BK = 5(12) + 9
BK = 60 + 9
BK = 69
Therefore, BK equals 69.