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soldier1979 [14.2K]
3 years ago
13

State the Lagrange Theorem, and find the order of all possible subgroups of a group of order 5. The same question of a group of

order 6.
Mathematics
1 answer:
oksian1 [2.3K]3 years ago
4 0

Answer:

  Lagrange Theorem

Step-by-step explanation:

The Lagrange Theorem:

Let G be a finite group and T be a subgroup of G. Then the order of T divides the Order of group G.

This can be written as:

If T \subset G, then, o(T)|o(G).

Possible Subgroups

Now, we are given a group with order 5. We have to find all possible subgroups.

So, the possible subgroup are: groups with order 1, group with order 5

We are given a group with order 6.

Possible subgroups are: group of order 1, group of order 2, group of order 3 and group of order 4.

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3241004551 [841]

From the setup of the problem, the "length of the top of the bookcase, measured along the attic ceiling" will be the hypotenuse of a right triangle, the length "AB". We have both the angle between AB and AC and the length of AC (3.24 meters), so we can use trigonometric identities.

The cosine of the 40 degree angle between AB and AC is equivalent to the length of AC divided by the length of AB. Equivalently, we have:

cos(40) = \frac{3.24}{h}

where "h", the hypotenuse, is the length we want. Rearranging the formula to solve for h we have that

$h = \frac{3.24}{cos(40)}$

which is 4.2295... meters. Converting to centimeters (multiplying by 100) we have that h = 422.95... centimeters, or if we round the value, h = 423 centimeters.

6 0
2 years ago
Solve the equation by clearing the decimals: 0.8x -0.3 = 0.7x + 0.2
Mashutka [201]

Answer:

x = 5

Step-by-step explanation:

0.8x - 0.3 - 0.7x = 0.2

0.8x - 0.7x = 0.2 + 0.3

0.1x = 0.2 + 0.3

0.1x = 0.5

5 0
3 years ago
Communicate mathematical ideas why might you want to use the commutative property to change the order of the integers in the fol
Kruka [31]

I might want to use the commutative property to change the order of the integers in the following sum before adding the given expression

"-80 + (-173)+(-20)"

As commutative property states that " Changing the order of addends does not change the sum" which means if we add 'a' to 'b' or 'b' to 'a', we will get the same answer.

Therefore, here if we add '-80' to '-173' or '-173' to '-80' , or if we add '-173' to '-20' or '-20' to '-173' , we will get the same answer.

Therefore, we might use commutative property to change the order the of integers in the following sum.

7 0
2 years ago
Find the volume of each prism
o-na [289]
Volume of a prism=LWH
V=12 3/8 * 10*5
V=12.375 * 50
V=618.75
The volume of the prism is 618.75yd³
4 0
3 years ago
Find x. Please help!!!
solong [7]

Answer:

85

Step-by-step explanation:

In this type of problem, x is always the average of the two angle measures of the arcs. In this case, (100+70)/2=85 degrees. Hope this helps!

5 0
3 years ago
Read 2 more answers
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