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Julli [10]
3 years ago
8

Find the value of x and y

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
3 0

Answer:

x = 63 , y = 27

Step-by-step explanation:

x+ 117 make a straight line so they equal 180 degrees.

x+117 = 180

Subtract 117 from each side

x+117-117= 180-117

x =63

x and y are complementary, which means they add to 90

x+y = 90

63+y = 90

Subtract 63 from each side

63-63+y = 90-63

y = 27

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Three cars are driving on a racetrack. The mean speed of the three cars is 100 miles per hour. Car X drives 101 miles per hour a
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Read 2 more answers
Let H and K be subgroups of a group G, and let g be an element of G. The set <img src="https://tex.z-dn.net/?f=%5Cmath%20HgK%20%
34kurt

Answer:

Yes, double cosets partition G.

Step-by-step explanation:

We are going to define a <em>relation</em> over the elements of G.

Let x,y\in G. We say that x\sim y if, and only if, y\in HxK, or, equivalently, if y=hxk, for some h\in H, k\in K.

This defines an <em>equivalence relation over </em><em>G</em>, that is, this relation is <em>reflexive, symmetric and transitive:</em>

  • Reflexivity: (x\sim x for all x\in G.) Note that we can write x=exe, where e is the <em>identity element</em>, so e\in H,K and then x\in HxK. Therefore, x\sim x.
  • Symmetry: (If x\sim y then y\sim x.) If x\sim y then y=hxk for some h\in H and k\in K. Multiplying by the inverses of h and k we get that x=h^{-1}yk^{-1} and is known that h^{-1}\in H and k^{-1}\in K. This means that x\in HyK or, equivalently, y\sim x.
  • Transitivity: (If x\sim y and y\sim z, then x\sim z.) If x\sim y and y\sim z, then there exists h_1,h_2\in H and k_1,k_2\in K such that y=h_1xk_1 and z=h_2yk_2. Then, \\ z=h_2yk_2=h_2(h_1xk_1)k_2=(h_2h_1)x(k_1k_2)=h_3xk_3 where h_3=h_2h_1\in H and k_3=k_1k_2\in K. Consequently, z\sim x.

Now that we prove that the relation "\sim" is an equivalence over G, we use the fact that the <em>different equivalence classes partition </em><em>G.</em><em> </em>Since the equivalence classes are defined by [x]=\{y\in G\colon x\sim y\} =\{y\in G \colon y=hgk\ \text{for some } h\in H, k\in K \}=HxK, then we're done.

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3 years ago
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