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2 years ago

A number divided by 4 equals 16. Find the number

Mathematics

1 answer:

Anna35 [415]2 years ago

5 0

64 o think because 16 times 4 equals 64

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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 .

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2 years ago

In Noels survey, 3 more people said they enjoyed volleyball than said they like soccer, and 5 more people enjoyed basketball tha

ExtremeBDS [4]

4 people liked soccer.

4 people liked tennis.

7 people like volleyball.

9 people like basketball.

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2 years ago

June is driving from Brookline, Massachusetts to Brooklyn, new york. The cities are 200 miles apart. Pretend June lives in a wor

I am Lyosha [343]

It took June 4 hours to get from Brookline to Brooklyn.

<h3><u>Time calculation</u></h3>

Given that June is driving from Brookline, Massachusetts to Brooklyn, New York, and the cities are 200 miles apart, and she can drive at a constant speed of 50mph the entire way, to determine the function that solves the time June takes to complete the route, the following calculation must be made:

C / Constant speed = T
200 / 50 = T
4 = T

So it took June 4 hours to get from Brookline to Brooklyn.

Learn more about time calculation in brainly.com/question/26707195

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1 year ago

Evaluate the expression when x=4 and y+-6.<br><br> x-5y

rosijanka [135]

Answer:-26

Step-by-step explanation:

4 0

2 years ago

Pls help me I give pick BRAINLIEST!!

mariarad [96]

Answer:

Step-by-step explanation:

56/7=8

8x3=24

6 0

2 years ago