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2 years ago

3, 9, 15, ... Find the 45th term.

Mathematics

2 answers:

Lelechka [254]2 years ago

8 0

First the nth term which is 6n-3
So 6x45-3 is your answer

cestrela7 [59]2 years ago

3 0

Answer:

The answer is 273

Step-by-step explanation:

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Isabella has twice as much money invested at 4% as she has invested at 3%, and she has $500 more invested at 5% than she has at

adell [148]

Invested at 3% = x
invested at 4% = 2x
invested at 5% = x+500

0.03x + 0.04(2x) + 0.05(x+500) = 2025
0.03x + 0.08x +0.05x +25 = 2025
0.16x = 2000
x= 12,500
4% = 2x = 12,500 * 2 = $25,000

3 0

2 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 .

5 0

2 years ago

Gary had a 40% discount for car speakers. The sale price of the speakers was $96.25. What was the original price of the speakers

Ostrovityanka [42]

Answer:

Step-by-step explanation:

If the price after the discount is subtracted is $96.25 then this is what you do

u times 0.40 x 96.25 which is 38.5 so since you are wanting to know what the price was before the discount you would add 38.5 to 96.25 and when you do that your answer is 134.75

but if you are just trying to get the discount from 96.25 you subtract 38.5 from 96.25

5 0

2 years ago

The height of a tree, y, is related to the length of its shadow, x, by the equation y = kx. If a tree's height is 24 feet and it

Marta_Voda [28]

Answer:

The value of k is 8/3

Step-by-step explanation:

To find this, start with the base equation and input the values. Then solve for k.

y = kx

24 = k9

24/9 = k