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2 years ago

What is the slope of the line containing the points (-6,1) and (5,3)

Mathematics

1 answer:

Alina [70]2 years ago

8 0

The slope of the line containing the points (-6, 1) and (5, 3) is $\frac{2}{11}$

Solution:

Given that we have to find the slope of the line containing the points (-6, 1) and (5, 3)

$\text{The slope of points } (x_1, y_1) \text{ and } (x_2, y_2) \text{ is given by: }$

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Here in this question,

$(x_1, y_1) = (-6, 1)\\\\(x_2, y_2) = (5, 3)$

Substitute the values in above mentioned formula,

$m = \frac{3-1}{5-(-6)}$

Simplify the above expression

$m = \frac{2}{5+6}\\\\m = \frac{2}{11}$

Thus the slope of the line containing the points (-6, 1) and (5, 3) is $\frac{2}{11}$

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What is the ratio in which the point P(3/4,5/12) decides the line segment joining points A(1/2,3/2) and B(2,-5)

timama [110]

Given:

The point $P\left(\dfrac{3}{4},\dfrac{5}{12}\right)$ divides the line segment joining points $A\left(\dfrac{1}{2},\dfrac{3}{2}\right)$ and $B(2,-5)$ .

To find:

The ratio in which he point P divides the segment AB.

Solution:

Section formula: If a point divides a segment in m:n, then the coordinates of that point are,

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Let point P divides the segment AB in m:n. Then by using the section formula, we get

$\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{m(2)+n(\dfrac{1}{2})}{m+n},\dfrac{m(-5)+n(\dfrac{3}{2})}{m+n}\right)$

$\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{2m+\dfrac{n}{2}}{m+n},\dfrac{-5m+\dfrac{3n}{2}}{m+n}\right)$

On comparing both sides, we get

$\dfrac{3}{4}=\dfrac{2m+\dfrac{n}{2}}{m+n}$

$\dfrac{3}{4}(m+n)=\dfrac{4m+n}{2}$

Multiply both sides by 4.

$3(m+n)=2(4m+n)$

$3m+3n=8m+2n$

$3n-2n=8m-3m$

$n=5m$

It can be written as

$\dfrac{1}{5}=\dfrac{m}{n}$

$1:5=m:n$

Therefore, the point P divides the line segment AB in 1:5.

6 0

3 years ago

HELP ME PLEASEE real quick just answer

nordsb [41]

B 1/2 because there is a 6/12 chance simpllify that and it's 1/2

6 0

2 years ago

PLEASE I NEED HELP QUICK:

nignag [31]

1/3 is 0.3333333 and you round it by the 3rd three, so it looks like 0.334

3 0

3 years ago

If the Ramirez family deposits $5000 in a savings account at 7.5% interest compounded continuously, how much will be in the acco

GenaCL600 [577]

Answer: The amount is $14794.39 and the interest is $9794.39

Step-by-step explanation: If you deposit $5000 into an account paying 7.5% annual interest compounded yearly , how much money will be in the account after 15 years?

To find amount we use formula:

A-P(1+r/n) n*t

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

P=$5000, r=7.5, n=1 and, t=15 years

After plugging the given information we have

A= $5000 (1+0.075/1)^1.15

A= 5000 *1.075^15

A=14794.39

To find interest we use formula A=P+I'

since A= 14794.39 and P=5000

we have: A=P+I 14794.39=5000+I

I= 14794.39 -5000

I=9794.39

8 0

2 years ago

Read 2 more answers

Whats the area of a circle with a diameter of 12 cm?

Vedmedyk [2.9K]

Answer:

113.1cm

Step-by-step explanation:

area= $\pi$ r²

r= half the diameter r=6

a= $\pi$ 6²

a= $\pi$ 36

a=113.1 cm

8 0

3 years ago