3 years ago

Potted plant:18.69 Discount rate: 8.25%

Mathematics

1 answer:

ale4655 [162]3 years ago

3 0

What is the question for me to answer

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a rectangular prism measures 3 in by 8 in by 9 in. what is the side length of a cube with the same volume?

Novay_Z [31]

Answer:

6 in.

Step-by-step explanation:

Rectangular prism

V = lwh l = 8 W = 3 h = 9

= 8(3)(9)

= 216

Cube

$V = s^{3}$ where s = length of side

216 = $s^{3}$

$s = \sqrt[3]{216}$ = 6

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3 years ago

What is the measure of tje fourth angle of the quadrilateral

grin007 [14]

37 would be the answer.....

5 0

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 .