Answer:
(2)
Step-by-step explanation:
-3,2
-1,-1
slope is -1.5
Which expression is equivalent.
2 answers:
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Answer:
The sum of the first nine terms of the sequence is 74.44.
Step-by-step explanation:
Geometric sequence concepts:
The nth term of a geometric sequence is given by the following equation.
In which r is the common ratio.
This can be expanded for the nth term in the following way:
In which is the first term.
Or even:
The sum of the first n terms of a geometric sequence is given by:
Finding the common ratio:
Finding the first term:
Sum of the first nine terms:
The sum of the first nine terms of the sequence is 74.44.
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