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Katyanochek1 [597]
2 years ago
11

Please Help! Its due in 2 hours!

Mathematics
1 answer:
WITCHER [35]2 years ago
6 0

Answer:

x=40

Step-by-step explanation:

<h3> firstly 180 -110 = 70 (sumnof angle of a straight line ) </h3><h3>180 -110 = 70 (sumnof angle of a straight line ) also the triangle is an isocelels triangle of which the two sides have equal angle </h3><h3>180 -110 = 70 (sumnof angle of a straight line ) also the triangle is an isocelels triangle of which the two sides have equal angle there fore 70 +70 +x= 180 </h3><h3>180 -110 = 70 (sumnof angle of a straight line ) also the triangle is an isocelels triangle of which the two sides have equal angle there fore 70 +70 +x= 180 140+x=180 sum of angles of a triangle </h3><h3>180 -110 = 70 (sumnof angle of a straight line ) also the triangle is an isocelels triangle of which the two sides have equal angle there fore 70 +70 +x= 180 140+x=180 sum of angles of a triangle x=180 -140 = 40 </h3>

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Prove that H c G is a normal subgroup if and only if every left coset is a right coset, i.e., aH = Ha for all a e G
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\Rightarrow

Suppose first that H\subset G is a normal subgroup. Then by definition we must have for all a\in H, xax^{-1} \in H for every x\in G. Let a\in G and choose (ab)\in aH (b\in H). By hypothesis we have aba^{-1} =abbb^{-1}a^{-1}=(ab)b(ab)^{-1} \in H, i.e. aba^{-1}=c for some c\in H, thus ab=ca \in Ha. So we have aH\subset Ha. You can prove Ha\subset aH in the same way.

\Leftarrow

Suppose aH=Ha for all a\in G. Let h\in H, we have to prove  aha^{-1} \in H for every a\in G. So, let a\in G. We have that ha^{-1} =a^{-1}h' for some h'\in H (by the hypothesis). hence we have aha^{-1}=h' \in H. Because a was chosen arbitrarily  we have the desired .

 

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The landscape artist who designed New York City’s
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The landscape artist who designed New York City’s Central Park believed that providing scenic settings accessible to all would not only benefit the public’s physical and mental health <u>and also foster a sense of democracy. </u> (Option D: but also foster a sense of democracy).

<h3>What is sentence correction?</h3>

Sentence correction or sentence improvement is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.

Now,

  • When 'not only' is used, 'but also' must come after it. When utilizing a correlative conjunction like "not only," "but also," the goal should be parallelism, meaning that the words that come after both sides of the conjunction should be from the same part of speech.
  • Here, using 'and' after 'not only...' distorts the structure of the sentence.

Hence, Option D is the right response, i.e., The landscape artist who designed New York City’s Central Park believed that providing scenic settings accessible to all would not only benefit the public’s physical and mental health <u>and also foster a sense of democracy. </u> (Option D: but also foster a sense of democracy).

To learn more about sentence correction, refer to the link: brainly.com/question/14632568

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