Answer:

Step-by-step explanation:
Multiply out
in order to find out which expression it is equivalent to.
1) Since the whole quantity is squared, write it out as
.

2) Multiply binomials by using the FOIL method. Multiply the terms that are listed first in each binomial, then the ones that are listed outermost when looking at both binomials, then innermost, and finally the last terms listed in each binomial. Simplify and combine like terms.


3)
, so
must be
. Thus,
is equivalent to -1. Knowing this, simplify and combine like terms.


Thus, it is equivalent to
.
Answer:
Angle BEA
Step-by-step explanation:
They share the same straight line and their degrees add to 180
The midpoint of (x1,y1) and (x2,y2) is

just average them
(4,1) and (-2,4)
the midpoint is

(1,-1.5)
Answer:


Step-by-step explanation:
First we define two generic vectors in our
space:


By definition we know that Euclidean norm on an 2-dimensional Euclidean space
is:

Also we know that the inner product in
space is defined as:

So as first condition we have that both two vectors have Euclidian Norm 1, that is:

and

As second condition we have that:


Which is the same:

Replacing the second condition on the first condition we have:

Since
we have two posible solutions,
or
. If we choose
, we can choose next the other solution for
.
Remembering,

The two vectors we are looking for are:

This is always ''interesting'' If you see an absolute value, you always need to deal with when it is zero:
(x-4)=0 ===> x=4,
so that now you have to plot 2 functions!
For x<= 4: what's inside the absolute value (x-4) is negative, right?, then let's make it +, by multiplying by -1:
|x-4| = -(x-4)=4-x
Then:
for x<=4, y = -x+4-7 = -x-3
for x=>4, (x-4) is positive, so no changes:
y= x-4-7 = x-11,
Now plot both lines. Pick up some x that are 4 or less, for y = -x-3, and some points that are 4 or greater, for y=x-11
In fact, only two points are necessary to draw a line, right? So if you want to go full speed, choose:
x=4 and x= 3 for y=-x-3
And just x=5 for y=x-11
The reason is that the absolute value is continuous, so x=4 works for both:
x=4===> y=-4-3 = -7
x==4 ====> y = 4-11=-7!
abs() usually have a cusp int he point where it is =0
Hope it helps, despite being this long!