All categories

3 years ago

Find the coordinates of the midpoint of a line segment with the given endpoints (14,-8), (12,-1)

Mathematics

1 answer:

Flauer [41]3 years ago

4 0

Answer:

The coordinates of the midpoint of a line segment with the given endpoints (14,-8), (12,-1) are $\mathbf{(13,\frac{-9}{2})}$

Step-by-step explanation:

We need to find the coordinates of the midpoint of a line segment with the given endpoints (14,-8), (12,-1)

The midpoint of line segment can be found using formula:

$Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

We have $x_1=14, y_1=-8, x_2=12, y_2=-1$

Putting values and finding midpoint

$Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\Midpoint=(\frac{14+12}{2},\frac{-8-1}{2})\\Midpoint=(\frac{26}{2},\frac{-9}{2})\\Midpoint=(13,\frac{-9}{2})$

So, the coordinates of the midpoint of a line segment with the given endpoints (14,-8), (12,-1) are $\mathbf{(13,\frac{-9}{2})}$

You might be interested in

6) (after 2.3) Consider the infinite system of linear equations in two variables given by ax + by = 0 where (a, b) moves along t

Paraphin [41]

Answer:

Step-by-step explanation:

Given infinite system of linear equations is ax + by = 0

when (a,b) moves along unit circle in plane.

a) system having unique system (0, 0)

Since two of equation in thus system will be

$1.x+0.y=0\\x=0$

and

$0.x+1.y=0\\y=0$

It is clear that x = 0, y= 0 is the only solution

b) Linear independent solution in this system gives some set of solutions

$1.x+0.y=0\\\x=0$

and

$0.x+1.y=0\\y=0$

Vector form is

$\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] =I$

c) for this equation if add 0x +0y = 0 to system , Nothing will change

Because [0,0] satisfies that equation

d) If one of the equation is ax + by = 0.00001

where 0.00001 is small positive number

so, the system will be inconsistent

Therefore, the system will have no solution.

6 0

3 years ago

Consider the equations y = √x and y = x^2 - 1

lord [1]

<h3>Answer:</h3>

(x, y) ≈ (1.49021612010, 1.22074408461)

<h3>Explanation:</h3>

This is best solved graphically or by some other machine method. The approximate solution (x=1.49, y=1.221) can be iterated by any of several approaches to refine the values to the ones given above. The values above were obtained using Newton's method iteration.

_____

Setting the y-values equal and squaring both sides of the equation gives ...

... √x = x² -1

... x = (x² -1)² = x⁴ -2x² +1 . . . . . square both sides

... x⁴ -2x² -x +1 = 0 . . . . . polynomial equation in standard form.

By Descarte's rule of signs, we know there are two positive real roots to this equation. From the graph, we know the other two roots are complex. The second positive real root is extraneous, corresponding to the negative branch of the square root function.

8 0

3 years ago

URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! DUE IN LESS THAN 12 MINS

Anettt [7]

Answer:

28.26m^2 (aka. 28.26 meters squared)

Step-by-step explanation:

The area of a circle is A=pi*r^2 where r is the radius of the circle.

Since r=3, then A=pi*3^2=9pi=28.26

Therefore, the area of the merry-go-round is 28.26 square meters

6 0

2 years ago

If f(x) = 2x^3 - 14x^2 + 38x -26 and x-1 is a factor of f(x) find all of the zeros of f(x) algebraically.

Anestetic [448]

Answer:

Step-by-step explanation:

First confirm that x = 1 is one of the zeros.

f(1) = 2(1)^3 - 14(1)^2 + 38(1) - 26

f(1) = 2 - 14 + 38 - 26

f(1) = -12 + 38 = + 26

f(1) = 26 - 26

f(1) = 0

=========================

next perform a long division

x -1 || 2x^3 - 14x^2 + 38x - 26 || 2x^2 - 12x + 26

2x^3 - 2x^2

===========

-12x^2 + 28x

-12x^2 +12x

==========

26x -26

26x - 26

========

Now you can factor 2x^2 - 12x + 26

2(x^2 - 6x + 13)

The discriminate of the quadratic is negative. (36 - 4*1*13) = - 16

So you are going to get a complex result.

x = -(-6) +/- sqrt(-16)

=============

x = 3 +/- 2i

f(x) = 2*(x - 1)*(x - 3 + 2i)*(x - 3 - 2i)

The zeros are

3 +/- 2i

8 0

3 years ago

If a quantity increases by 25% and then decreases by 25%, will that result be the original quantity? Explain.

Helen [10]

It depends if its decreasing 25% of the original quantity or decreasing by 25% of the quanity that is after already increasing by 25%.

5 0

3 years ago