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2 years ago

Find the slope of the line (-3,-3) (1,1)

Mathematics

2 answers:

Volgvan2 years ago

5 0

Answer: The slope is m = 1

Step-by-step explanation:

-To find the slope, you need the slope formula:

$m=\frac{y2-y1}{x2-x1}$ where you have $(x1,y1)$ and $(x2,y2)$ on the equation.

-Next, you put the two points to the equation:

$m=\frac{1+3}{1+3}$

-And then you solve the equation:

$m=\frac{1+3}{1+3}$

$m=\frac{1+3}{1+3} = \frac{4}{4}=1$

$m=1$

Lelechka [254]2 years ago

3 0

The answer to your question is that your slope is m=1

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13. The least common multiple of two non-zero integers a and b is the unique positive integer m such that (i) m is a common mult

Vlad [161]

Answer:

[a,b] divides n

Step-by-step explanation:

Let us denote the least common multiple of a and b [a,b]=m.

We want to prove that m divides n, where n is a multiple of a and b.

We suppose m does not divide n, then by the Division Theorem, there exists q and r integers such that:

(1) ... n=mq+r, where 0<r<m

As n is a multiple of a and b, there exists s and t integers such that:

sa=n and tb=n

Same thing happens to m as it is the least common multiple, there exists u and v such that:

ua=m and vb=m

So (1) has the following form:

n=mq+r ⇒ sa=uaq+r ⇒sa-uaq=r⇒(s-uq)a=r and

n=mq+r ⇒ tb=vbq+r ⇒ tb-vbq=r⇒ (t-vq)b=r

So r is a multiple of a and b, but r<m which is a contradiction as, m is the least common multiple of a and b. So this concludes the proof.

So this means that $\frac{ab}{m}$ is and integer.

As m= vb, then $\frac{m}{b}$ is an integer, lets say $\frac{m}{b}$ =v; and as m=ua, then $\frac{m}{a}$ =u.

So $\frac{ab}{m}$ v= $\frac{ab}{m}$ $\frac{m}{b}$ =a, so $\frac{ab}{m}$ divides a; on the other hand, $\frac{ab}{m}$ u= $\frac{ab}{m}$ $\frac{m}{a}$ =b, so $\frac{ab}{m}$ divides b. From this we can conclude that $\frac{ab}{m}$ is a common divisor of a and b.

4 0

3 years ago

What is the slope of the line?<br> y=54x−13π

Grace [21]

If the equation is in the form of y = mx + C, where m and C are real numbers, the slope (which means gradient) of the line is the coefficient of x (I.e. the number to the left of x in simple language), which is m.

In this case, m = 54 and C = -13pie. Both are real numbers, which means that this equation satisfies the form of y = mx + C

m is the coefficient of x, which is 54. 54 is the gradient of this line, which means that for every 54 y-axis units the line increases, the line increases 1 x-axis unit.

Hope this helps! :)

4 0

2 years ago

The sum of four consecutive negative integers is -26. what are the integers

Naily [24]

X + (x + 1) + (x + 2) + (x + 3) = -26

Even though it says negative, the same rules apply.

4x + 6 = -26
4x = -32
x = -8

-8, -7, -6, -5

Hope this helps!

8 0

2 years ago

What basic math skills should I know for grade 9 math

UkoKoshka [18]

Most likely rates, percents and ratios at a higher level. Also, multiplication and division of fractions at a higher level.

4 0

2 years ago

Read 2 more answers

A cricular arena is lit by 5 lights equally spaced around the perimeter of the arena. What is the measure of each angle formed b

Kitty [74]

Answer:

108°

Step-by-step explanation:

Suppose that circle with center A is a circular arena. Points B, C, D, E and F are 5 lights. These 5 points form regular pentagon (because these 5 lights are equally spaced around the perimeter of the arena).

The sum of all interior angles of pentagon can be calculated using following formula

$(n-2)\cdot 180^{\circ},\\ \\(5-2)\cdot 180^{\circ}=3\cdot 180^{\circ}=540^{\circ}$

All interior angles in regular pentagon are of equal measure, so

$\dfrac{540^{\circ}}{5}=108^{\circ}$

Thus, the measure of each angle formed by the lights on the perimeter is 108°.

7 0

3 years ago