2 years ago

Who is good at algebra and is willing to help someone out with it-If so please help me I would really appreciate it

Mathematics

1 answer:

madam [21]2 years ago

6 0

Answer:

4y = -x + 9

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Mark orders food for a restaurant. He orders 5 times the number of pounds of chicken as he does beef, and he orders 4 times the

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180 pounds of chicken and 225 of beef

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2 years ago

Find the angle complementary to the angle 80°. A. 90° B. 180° C. 10° D. 100°

Alex_Xolod [135]

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C is the correct answer

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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

Kaylis [27]

$\Rightarrow$

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 .