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lesya692 [45]
3 years ago
12

1 (15 Points]. Prove the following statement: is divisible by 3 if only if it is a sum of three consecutive integers. be ddvisbk

Mathematics
1 answer:
Alinara [238K]3 years ago
4 0

Answer:

<em>First.</em> Let us prove that the sum of three consecutive integers is divisible by 3.

Three consecutive integers can be written as k, k+1, k+2. Then, if we denote their sum as n:

n = k+(k+1)+(k+2) = 3k+3 = 3(k+1).

So, n can be written as 3 times another integer, thus n is divisible by 3.

<em>Second. </em>Let us prove that any number divisible by 3 can be written as the sum of three consecutive integers.

Assume that n is divisible by 3. The above proof suggest that we write it as

n=3(k+1)=3k+3=k + k + k +1+2 = k + (k+1) + (k+2).

As k, k+1, k+2 are three consecutive integers, we have completed our goal.

Step-by-step explanation:

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after a school election,Jamie had 3/8 of the votes Richard the only other candidate had 75 votes how many people voted for jaime
dalvyx [7]
Jamie and Richard are the only contestants of the election.

Jamie got 3/8 of the total votes.

Richard got = 1 - 3/8 = (8-3)/8 = 5/8 of total votes

Number of votes Richard got = 75

So 5/8 of total votes = 75

Total votes = 75 ÷ 5/8 = 75 × 8/5 = 120

Jamie got = 120 - 75 = 45 Votes
8 0
4 years ago
In triangle abc, ab=90 in, bc=80 in, and angle b measures 50°. what is the approximate perimeter of the triangle?
Arlecino [84]
You need to use the Law of Cosines:
AC² = AB² + BC² - 2·AB·BC·cos(b)
       
Therefore, you get:

AC = √(90² + 80² - 2·90·80·cos(50)
      =√5243.86
      = 72.4 in

Now you can sum up all the sides in order to find the perimeter:

AB + BC + AC = 90 + 80 + 72.4 = 242.4 in

The correct answer is A) 242.4 in

8 0
4 years ago
(5b2+3b)+(b2-2b) in standard form
den301095 [7]

Answer:

6b+b^2 (b to the 2nd power)

Step-by-step explanation:

8b+b^2-2b (b to the 2nd power)

(8b-2b)+b^2

6b+b^2

Hopefully this helps :)

3 0
3 years ago
Read 2 more answers
A collection of 33 coins having dimes quarters and nickels, there are 3 times more nickels then dimes and half the amount of dim
zloy xaker [14]

Answer:

Each coins are quarters of <u>6</u>, nickels of <u>18</u> and the dimes of <u>9</u>.

Step-by-step explanation:

<u><em>There is a mistake in question.</em></u>

The question must be:

A collection of 33 coins having dimes quarters and nickels, <u>there are 3 times as many nickels as quarters, and one-half as many dimes as nickels</u>, all of the coins equal $3.30 how many coins of each kind are there?

Now, to find the number coins of each.

Let the quarters be x.

Nickels be 3x.

And the dimes be \frac{3x}{2}.

So, the total collection of coins are:

x+3x+\frac{3x}{2} =33.

On adding the fractions we get:

\frac{2x+6x+3x}{2} =33

\frac{11x}{2} =33

Multiplying both sides by 2 we get:

11x=66

Dividing both sides by 11 we get:

x=6.

Thus, quarters = 6.

Nickels = 3x=3\times 6=18.

Dimes = \frac{3x}{2} =\frac{3\times 6}{2} =\frac{18}{2}=9 .

Therefore, each coins are quarters of 6, nickels of 18 and the dimes of 9.

3 0
3 years ago
PLEASE HELP ILL GIVE BRAINLIST
sdas [7]

Answer:

Its hard to explain but essentially the zero in the 10 and 100 place cancels out the decimal essentially

8 0
3 years ago
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