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2 years ago

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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BartSMP [9]

Answer:

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Step-by-step explanation:

Let be "s" the length in meters of the short piece and "l" the lenght in meters of the long piece.

Set up a system of equations:

$\left \{ {{s+l=57} \atop {s=l-23}} \right.$

Apply the Substitution Method to solve the system. Substitute the second equation into the first equation and solve for "l":

$(l-23)+l=57\\\\2l=80\\\\l=\frac{80}{2}\\\\l=40$

Susbstitute the value of "l" into the second equation in order to find the value of "s". This is:

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3 years ago

F(x) = 4x^2 + 3x - 11<br> f(-3)

Mnenie [13.5K]

Just plus in x for -3
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3 0

3 years ago

Consider m = y2 - y1/ x2 - x1 . Which x1 and x2-values would determine that the line is vertical? Justify your answer

Y_Kistochka [10]

Answer:

$x_2=x_1$

Step-by-step explanation:

We were given the slope formula;

$m=\frac{y_2-y_1}{x_2-x_1}$

This line is vertical if the denominator is zero.

That is when $x_2-x-1=0$

This implies that;

$x_2=x_1$

Justification;

When $x_2=x_1$ , then, the line passes through;

$(x_1,y_1)$ and $(x_1,y_2)$

The slope now become

$m=\frac{y_2-y_1}{x_1-x_1}=\frac{y_2-y_1}{0}$

The equation of the line is

$y-y_1=\frac{y_2-y_1}{0}(x-x_1)$

This implies that;

$0(y-y_1)=(y_2-y_1)(x-x_1)$

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$0=(x-x_1)$

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3 0

3 years ago

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Kay [80]

Answer:

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Step-by-step explanation:

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3 years ago

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elena55 [62]

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