3 years ago

Using the math panel write the distance from 20 to zero as an absolute value

Mathematics

1 answer:

Ronch [10]3 years ago

8 0

There a app called photo math

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It takes 16pounds of seed to completely plant a 3-acre field. How many acres can be planted per pound of seed?

tiny-mole [99]

Answer:

16x3=48

Step-by-step explanation:

4 0

3 years ago

I need help with this

Ksenya-84 [330]

Answer:

6.7-(-2.5)=9.2 6.7+(-2.5)=4.2 Neither

2.5 + 6.7 6.7 - 2.5 2.5 - 6.7

-2.5 + 6.7 -2.5 - 6.7

-6.7 + 2.5

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3 years ago

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 .