Pls help will give crown to best answer!!

Write an equation of the perpendicular bisector of the segment with the endpoints (8,10) and ( -4,2).

ale4655 [162]

Answer:

The required equation is:

$y = -\frac{3}{2}x+9$

Step-by-step explanation:

To find the equation of a line, the slope and y-intercept is required.

The slope can be found by finding the slope of given line segment. A the perpendicular bisector of a line is perpendicular to the given line, the product of their slopes will be -1 and it will pass through the mid-point of given line segment.

Given points are:

$(x_1,y_1) = (8,10)\\(x_2,y_2) = (-4,2)$

We will find the slope of given line segment first

$m = \frac{y_2-y_1}{x_2-x_1}\\= \frac{2-10}{-4-8}\\=\frac{-8}{-12}\\=\frac{2}{3}$

Let m_1 be the slope of perpendicular bisector then,

$m.m_1 = -1\\\frac{2}{3}.m_1 = -1\\m_1 = \frac{-3}{2}$

Now the mid-point

$(x,y) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\= (\frac{8-4}{2} , \frac{10+2}{2})\\=(\frac{4}{2}, \frac{12}{2})\\=(2,6)$

We have to find equation of a line with slope -3/2 passing through (2,6)

The equation of line in slope-intercept form is given by:

$y = m_1x+b$

Putting the value of slope

$y= -\frac{3}{2}x+b$

Putting the point (2,6) to find the y-intercept

$6 = -\frac{3}{2}(2)+b\\6 = -3+b\\b = 6+3 =9$

The equation is:

$y = -\frac{3}{2}x+9$

7 0

3 years ago

I need to know the answer to those two equations

sladkih [1.3K]

6(3x-5)-7x=25
18x-30-7x=25
11x=55
x=11
-2(5+6m)+16=-90
-10-12m+16=-90
-12m+6=-90
-12m=-96
m=8

3 0

3 years ago

Help me plsssssss i need it now

Scrat [10]

Answer:

x= 4

Step-by-step explanation:

The two triangles are similar so the ratios of both should be the same. Triangle DEF is 15 times bigger than triangle ABC so 60 divided by 15 is 4. Moral of the story 4 equals X

5 0

3 years ago

When 5655 is divided by a positive two digit intreger "N" the remainder is 11, when 5879 is divided by the same intreger N the r

Temka [501]

Answer:

8

Step-by-step explanation:

Hi,

When we divide 5655 by N, we get remainder of 11, which means that 5655-11 is a multiple of N.

5655 - 11 = 5644 is a multiple of N.

Similarly, 5879-14 should be a multiple of N.

5879 - 14 = 5865 is a multiple of N.

Because 5644 and 5865 are both multiples of N, their difference must be a multiple of N.

5865 − 5644 = 221 then 221 is a multiple of N.

We have three number of which N can be a multiple of, however we choose to factorize the smallest possible number amongst these three, which is 221. (This is only for simplification of the solution, smaller the number, less the factors)

221 : 1, 13, 17, 221.

There are only two two - digit factors: 13 and 17.

We divide 5865 and 5644 by both numbers.

$\frac{5865}{13} = 451.15 \\\frac{5865}{17} = 345 \\\frac{5644}{13} = 434.15 \\\frac{5644}{17} = 332\\$