A lot of money because then they get even more back
Answer:
Step-by-step explanation:
We are given that G be a finite group with
have two elements of order two.
We have to prove that <x,y> is either abelian or isomorphic to a dihedral group.
<x,y> means the group generated by two elements of order 2.
We know that
is a cyclic group and number of elements of order 2 is always odd in number and generated by one element .So , given group is not isomorphic to ![Z_n](https://tex.z-dn.net/?f=Z_n)
But we are given that two elements of order 2 in given group
Therefore, group G can be
or dihedral group
Because the groups generated by two elements of order 2 are
and dihedral group.
We know that
is abelian group of order 4 and every element of
is of order 2 except identity element and generated by 2 elements of order 2 and dihedral group can be also generated by two elements of order 2
Hence, <x,y> is isomorphic to
or
.
The equation of the given circle is :
![(x - 2) {}^{2} + (y - ( - 2)) {}^{2} = 9](https://tex.z-dn.net/?f=%28x%20-%20%202%29%20%20%7B%7D%5E%7B2%7D%20%2B%20%28y%20-%20%28%20-%202%29%29%20%7B%7D%5E%7B2%7D%20%20%3D%209)
So the value in the blanks will be :