Answer:
We are known that Katya and her friends stand in a circle and both neighbors are of same gender this means that the person on the right and the person on the left of anyone in the circle will be of same gender either a girl or a boy.
We are given that there are five boys, we could have considered the circle to be only composed of boys but we are given there is a girl Katya within it and it is also mentioned that 'Katya and her friends' that means there can be more girls in the circle.
Now when we draw a circle on a page and mark points K for Katya and boys B1 and B2 on right and on the left of Katya we will get to know that after each boy there has to be a space vacant because on that space a girl should be positioned only then we will meet the criteria of both gender's same on the neighbor side of each person.
Also we will mark boys B1,B2,B3,B4,B5 as five boys and leave space vacant for girls and with those vacant spaces we get to know there will be 4 vacant spaces and one is Katya herself.
Therefore there will be a total of five girls in the circle one is Katya and other four.
First, we draw our line.
|------------------------------------------------------------------------------------|
a e
Next, break up this line into segments using the information.
|----------------------|----------------------|--------------------|------------------|
a b c d e
The entire line is 29.
ab + bc + cd + de = ae
ab + bc + cd + de = 29
You also know that
bd = bc + cd
Due to midpoint theorem,
ab = bc
cd = de
Then,
2ab + 2cd = 29
The equations we will use are
bd = bc + cd eq1
2bc + 2cd = 29 eq2
Dividing both sides of the equation in eq2 yields
bc + cd = 14.5
bd = bc + cd
bd = 14.5
The answer is <span>y= (x-3)^2 + 9
I hope this helps</span>
