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4 years ago

A line segment has the endpoints x (-4,2) and y (2,11). which coordinates perpendicular to xy?

Mathematics

1 answer:

Lelechka [254]4 years ago

5 0

(–1, 6.5)

Step-by-step explanation:

Given XY is a line segment with coordinates (–4, 2) and y(2, 11) respectively.

To find the coordinates perpendicular to XY.

A Perpendicular bisector is a line segment which intersects the line segment at its midpoint.

Hence, using midpoint formula we can find perpendicular co-ordinates.

Mid-point = $\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here, $x_{1}=-4, x_{2}=2, y_{1}=2, y_{2}=11$

Mid-point = $\left(\frac{-4+2}{2}, \frac{2+11}{2}\right)$

= $\left(\frac{-2}{2}, \frac{13}{2}\right)$

= (–1, 6.5)

Hence, the coordinates perpendicular to XY is (–1, 6.5).

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Consider this right triangle with given measures what is the unknown length

DIA [1.3K]

Answer:

b = 9

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

b² + 12² = 15²

b² + 144 = 225 ( subtract 144 from both sides )

b² = 81 ( take the square root of both sides )

b = $\sqrt{81}$ = 9

4 0

3 years ago

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[30 POINTS] Please help!!!

Len [333]

Answer:

Part 1) $y=1.5x+5$

Part 2) $y=-(2/3)x-(11/3)$

Part 3) $y=0.25x+2.75$

Part 4) $y=-2x+5$

Part 5) $y=0.5x-1$

Part 6) The graph in the attached figure

Step-by-step explanation:

Part 1) we have

$m=3/2=1.5$

$point(-2,2)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-2=1.5(x+2)$

$y=1.5x+3+2$

$y=1.5x+5$

Part 2) we know that

If two lines are perpendicular

then

the product of their slopes is equal to minus one

$m1*m2=-1$

the slope of the line 1 is equal to

$m1=1.5$

Find the slope m2

$1.5*m2=-1$

$m2=-2/3$

Find the equation of the line 2

we have

$m2=-2/3$

$point(-7,1)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-1=(-2/3)(x+7)$

$y=-(2/3)x-(14/3)+1$

$y=-(2/3)x-(11/3)$

Part 3) we have

$m=1/4=0.25$

$point(1,3)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-3=0.25(x-1)$

$y=0.25x-0.25+3$

$y=0.25x+2.75$

Part 4) we have

$m=-2$

$b=5$ -----> y-intercept

we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

substitute the values

$y=-2x+5$

Part 5) we have that

The slope of the line 4 is equal to $-2$

the slope of the line perpendicular to the line 4 is equal to

$-2*m=-1\\m=(1/2)=0.5$

therefore

in this problem we have

$m=0.5$

$point(-2,-2)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y+2=0.5(x+2)$

$y=0.5x+1-2$

$y=0.5x-1$

Part 6)

using a graphing tool

see the attached figure

3 0

3 years ago

Kalon and his friend Marna own a chimney sweep service company. Working together, they can clean a chimney in 1 5/7 hours. If it

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The amount of work done by Kalon in an hour is equal to 1/4. This is based on his time to finish the job. Letting x be the number of hours Marna can finish the job alone will let her finish 1/x of the job in an hour. If their rates are added together and multiplied by the number of hours they worked together, the product should be one whole job.
(1/4 + 1/x)(1 5/7) = 1
The value of x is 3. Therefore, it will take 3 hours for Marna to clean the chimney alone.

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3 years ago

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Which of the following is less

miv72 [106K]

I think it B 2/3 mile

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4 years ago

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The radius of a circle is changing at the rate of 1/π inches per second. At what rate, in square inches per second, is the circl

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Answer:

10 square inches per second.

Step-by-step explanation:

The radius of the circle is given by the equation:

r(t) = (1/π in/s)*t

Where time in seconds.

Remember that the area of a circle of radius R is written as:

A = π*R^2

Then the area of our circle will be:

A(t) = π*( (1/π in/s)*t)^2 = π*(1/π in/s)^2*(t)^2

Now we want to find the rate of change (the first derivation of the area) when the radius is equal to 5 inches.

Then the first thing we need to do is find the value of t such that the radius is equal to 5 inches.

r(t) = 5 in = (1/ in/s)*t

5in*(π s/in) = t

5*π s = t

So the radius will be equal to 5 inches after 5*π seconds, let's remember that.

Now let's find the first derivate of A(t)

dA(t)/dt = A'(t) = 2*(π*(1/π in/s)^2*t = (2*π*t)*(1/π in/s)^2

Now we need to evaluate this in the time such that the radius is equal to 5 inches, we will get:

A'(5*π s) = (2*π*5*π s)*((1/π in/s)^2

= (10*π^2 s)*(1/π^2 in^2/s^2) = 10 in^2/s

The rate of change is 10 square inches per second.

4 0

3 years ago