Help please, I’m not sure

Which of the following equations represents the perpendicular bisector of WX graphed below?

kotykmax [81]

The coordinates of the 2 given points are W(-5, 2), and X(5, -4).

First, we find the midpoint M using the midpoint formula:

$\displaystyle{ M_{WX}= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )= (\frac{-5+5}{2}, \frac{2+(-4)}{2} )=(0, -1).$

Nex, we find the slope of the line containing M, perpendicular to WX. We know that if m and n are the slopes of 2 parallel lines, then mn=-1.

The slope of WX is $\displaystyle{ m= \frac{y_2-y_1}{x_2-x_1}= \frac{2-(-4)}{-5-5}= \frac{6}{-10}= -\frac{3}{5}$ .

Thus, the slope n of the perpendicular line is $\displaystyle{ \frac{5}{3}$ .

The equation of the line with slope $\displaystyle{ n= \frac{5}{3}$ containing the point M(0, -1) is given by:

$\displaystyle{ y-(-1)=\frac{5}{3}(x-0)$

$\displaystyle{ y+1= \frac{5}{3}x$

$\displaystyle{ 3y+3=5x$

$\displaystyle{ 5x-3y-3=0$

Answer: 5x-3y-3=0

8 0

3 years ago

please factor completely !Thank yoy

Vilka [71]

You can download the app photo math and that will help you

8 0

3 years ago

A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x,

tatiyna

Answer:

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3

7 0

3 years ago

When I double my number add 4 and then subtract my number and subtract three I get my number plus one what is my number?

Lady bird [3.3K]

2 because once you double it, it becomes 4. Once you add 4, you get 8. When you subtract your number, which is 2, you get 6. Then when you subtract 3, you get 3. 3 is your number (2) plus 1

5 0

2 years ago

Expand & simplify 5 ( p + 6 ) − 5 ( p − 2 )

HACTEHA [7]

Answer: 0p + 40

Step-by-step explanation:

5p + 30 - 5p + 10

0p + 40

8 0

2 years ago