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a 2/3
b 1/6
c 2/9
d 1/3

Explanation:

There are 6 names in either circle A only, circle B only, or both circles (overlapped region)

The probability of getting someone in one of those circles, or both, is 6/9 = 2/3.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1