From point A, draw a line segment at an angle to the given line, and about the same length. The exact length is not important. Set the compasses on A, and set its width to a bit less than one fifth of the length of the new line. Step the compasses along the line, marking off 5 arcs. Label the last one C. With the compasses' width set to CB, draw an arc from A just below it. With the compasses' width set to AC, draw an arc from B crossing the one drawn in step 4. This intersection is point D. Draw a line from D to B. Using the same compasses' width as used to step along AC, step the compasses from D along DB making 4 new arcs across the line. Draw lines between the corresponding points along AC and DB. Done. The lines divide the given line segment AB in to 5 congruent parts.
![2x(4-x)^{-1/2}-3(4-x)^{1/2}=(4-x)^{-1/2}\bigg(2x-3(4-x)\bigg)](https://tex.z-dn.net/?f=2x%284-x%29%5E%7B-1%2F2%7D-3%284-x%29%5E%7B1%2F2%7D%3D%284-x%29%5E%7B-1%2F2%7D%5Cbigg%282x-3%284-x%29%5Cbigg%29)
We effectively rewrite the equation as
![\dfrac{5x-12}{(4-x)^{1/2}}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B5x-12%7D%7B%284-x%29%5E%7B1%2F2%7D%7D%3D0)
In order for the LHS to be defined, we need to restrict
, or
. Now, the LHS will vanish when the numerator is 0, which happens for
![5x-12=0\implies5x=12\implies x=\dfrac{12}5](https://tex.z-dn.net/?f=5x-12%3D0%5Cimplies5x%3D12%5Cimplies%20x%3D%5Cdfrac%7B12%7D5)
This value is indeed smaller than 4, so the solution is
.
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Answer:
45
Step-by-step explanation:
3 and 5 both go into 45 and 45 is the smallest for it