Please help as soon as possible
This is grade 12 math vectors

48*sqrt(2)

Let me know if there was anything you didn't understand

Step-by-step explanation:

To find the distance between any two points on a normal 2D graph you would  use the pythagorean theorem.  Well, if you have a 3D graph  you do something similar, where instead of just two dimensions it is 3.  so you take the sum of the length squared, width squared and height squared and they equal this 3D hypotenuse.

So, AB is the distance between A and B.    so you take the x distance, y distance and z distance to find the height, length and width.  The two points are (4, 0, 0) and (6, 3, 5).

Startign witht he x coordinates the difference is 2, since there are 2 between 4and 6.

y then is the difference between 0 and 3, so just 3

z then of course is 5.

so now to find AB you do that 3D pythagorean theorem.

AB = sqrt(2^2 + 3^2 + 5^2)  = sqrt(36) = 6

BC is the distance between points (6,3, 5) and (2,3,5) so now the x distance is 4, y is 0 and z is 0.  so then BC = sqrt(4^2 + 0^2 + 0^2) = 4

Finally BD is sqrt(0^2 + 2^2 + 2^2) = sqrt(8)

Then just multiply all those together 6*4*sqrt(8) = 24*sqrt(8) = 48*sqrt(2)  i simplified sqrt(8) into sqrt(4*2) = sqrt(4) * sqrt(2) = 2*sqrt(2).  Simplifying is just the standard thing you are supposed to do.

the first one, all those points on the line just make a strait line.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be