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ArbitrLikvidat [17]
2 years ago
10

For which k is it true that the sum of k consecutive integers is always divisible by k?

Mathematics
1 answer:
nevsk [136]2 years ago
5 0

Answer:

Step-by-step explanation:

We have two consecutive even integers:

a and b.

We know that we can write a even integer as:

a = 2*n

where n is an integer.

Then the consecutive integer to a, b, will be:

b = 2*n + 2.

Then the sum of a and b is:

a + b = 2n + 2n + 2 = 4*n + 2 = 2*(2n + 1) = k.

The next two consecutive integers greater than b will be:

c = 2n + 4

d = 2n + 6

then:

c + d = (2n + 4) + (2n + 6) = 4n + 10 = k + 4.

I hope i helped:D

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On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80). Wh
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The x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J is  (85, 105).

Given

On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80).

<h3>Coordinates</h3>

The coordinates point any point can be found by using the following formula.

\rm X=\dfrac{m}{m+n}(x_2-x_1)+x_1\\\\ Y=\dfrac{m}{m+n}(y_2-y_1)+y_1

The x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J is;

\rm X=\dfrac{m}{m+n}(x_2-x_1)+x_1\\\\ X = \dfrac{3}{3+5}(-40-160)+160\\\\ X = 3 \times (-25)+160\\\\\X = -75+160\\\\ X = 85\\\\\ Y=\dfrac{m}{m+n}(y_2-y_1)+y_1\\\\ Y=\dfrac{3}{3+5}(80-120)+120\\\\Y =- 3\times 5 +`120\\\\Y=-15+120\\\\Y=105

Hence, the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J is  (85, 105).

To know more about co-ordinates click the link given below.

brainly.com/question/13847533

5 0
2 years ago
I NEED HELP ASAP PLEASE
Molodets [167]

Answer:

The answer is B

Step-by-step explanation:

You add up all the numbers which should be 600 and divide by the total amount numbers used.

600/15=40.

5 0
3 years ago
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