Answer:
1. (5x - 2) + (2x - 2) + x =
2. m<J =
3. m<K =
4. m<L =
Step-by-step explanation:
Generally, the sum of angles in a triangle = .
So that;
m<J + m<K + m<L =
(5x - 2) + (2x - 2) + x =
5x + 2x + x -2 -2 =
8x - 4 =
8x = + 4
8x = 184
x =
x =
Thus,
m<J = (5x - 2)
= 5(23) - 2
=
m<K = (2x -2)
= 2(23) - 2
=
m<L = x
=
Answer:
7.75%
Step-by-step explanation:
7%
7.75%
Answer:
6*8=48 groups with elements of order 7
Step-by-step explanation:
For this case the first step is discompose the number 168 in factors like this:
And for this case we can use the Sylow theorems, given by:
Let G a group of order where p is a prime number, with
and p not divide m then:
1)
2) All sylow p subgroups are conjugate in G
3) Any p subgroup of G is contained in a Sylow p subgroup
4) n(G) =1 mod p
Using these theorems we can see that 7 = 1 (mod7)
By the theorem we can't have on one Sylow 7 subgroup so then we need to have 8 of them.
Every each 2 subgroups intersect in a subgroup with a order that divides 7. And analyzing the intersection we can see that we can have 6 of these subgroups.
So then based on the information we can have 6*8=48 groups with elements of order 7 in G of size 168