Centralizers and conjugacy. Let G be a group. For any element a EG, the centralizer Ca of a is the set of all elements which commute with a: Ca = {x € G: xa = ax} = {x € G:a= xax1}. (1) Show that Ca is a subgroup of G. (2) Show that xax-1 = yay-1 if and only if xCa =yCa. (3) Show that the conjugates of a are in bijective correspondence with the left cosets of Ca. Thus if G is finite, the conjugacy class [a] has [G: Ca] elements, and the size of the conjugacy class divides the order of the group. (4) Let p be prime and let G be a group of order pa for some a > 1. Recall that the center of G is C(G) = {a EG: ax = xa for all x EG}. Show that C(G) + {e}. (Hint: Use problem

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!

is should be y = 5x

step-by-step explanation:

correct me if im wrong

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc