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2 years ago

Find a formula for the sum of the first n even integers : 2 + 4 + 6 + ... + 2n.

Mathematics

1 answer:

Sedbober [7]2 years ago

7 0

Let S be the sum,

S = 2 + 4 + 6 + ... + 2 (n - 2) + 2 (n - 1) + 2n

Reverse the order of terms:

S = 2n + 2 (n - 1) + 2 (n - 2) + ... + 6 + 4 + 2

Add up terms in the same positions, so that twice the sum is

2S = (2n + 2) + (2n + 2) + (2n + 2) + ... + (2n + 2)

2S = n (2n + 2)

Divide both sides by 2 to solve for S :

S = n (n + 1)

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What two numbers have a product of 34 and a sum of 19?

agasfer [191]

Answer:

2 and 17

Step-by-step explanation:

its easy to just think of what 34 is divisible by ...you can divide 34 by 2 and find out that 17 x 2 is 34 and when you add them together its 19

6 0

3 years ago

a car rent is $240 per week plus $1.00 per mile. Find the rental cost for a two week trip of 500 miles for a group of three peop

tankabanditka [31]

Answer:

I'm not sure if you mean each person has a car for 2 weeks and travels 500 miles each but if so the rental cost is $2,940.

If it is just one car for all 3 people the rental cost is $980

Step-by-step explanation:

renatl cost = r

weeks = w

miles = m

the equation would be r = $240w + $1m

and if there are 3 people you mulitply the answer by 3

5 0

3 years ago

Which of the following is the equation of a line parallel to the line y=-x+1 passing through the point (4,1)

Softa [21]

Y=-x+b

plug in x = 4 and y = 1 to find b

1 = -4 + b and we know that if you add 5 and -4 you get 1. So ...

5 = b so if we plug that in

y= -x + 5

which is the same as y + x = 5, So it would be A

6 0

4 years ago

Express the following in standard form.

salantis [7]

To write in standard form, we have to move the decimal point in

3.42

over 3 places to the left since our exponent is 10 3

This gives us our answer of

0.00342

Hope this helps.

6 0

3 years ago

Shaneya purchased a membership to play basketball at her local gym. The membership costs $450 for the year, plus she pays $10 to

olga55 [171]

Answer:

Step-by-step explanation:

So start with the total 1,000

then take the 1,000 and minus it by the 450 year so then you can see how much money you have left for the times that she can go to the gym to play.

1,000 - 450 = 550

Now you 550 dollars because basic math. Then you divide the number you got which the number you got was 550 so 550÷10 you divide it by 10 because the rent is 10 each time.

550 ÷ 10 = 55

Now you get 55 so that means she can got to the gym 55 times before she goes over 1,000 dollars!

Hoped this helped. Don't forget a middle school person did this so I bet you could have too!

6 0

3 years ago