Answer:
12
Step-by-step explanation:
3! = 6
2! = 2
6 * 2 = 12
Answer: The numerical length of
is 20 units.
Step-by-step explanation:
Given: Point T is on line segment
.
i.e.
(i)
Since , it is given that ST=2x+6,TU=4, and SU=4x
Substitute these values in (i), we get

Now, the numerical length of 
Hence, the numerical length of
is 20 units.
Answer:
See below
Step-by-step explanation:
3. What are two ways that a vector can be represented?
Considering a vector
in some vector space
we have

This is the component form. I don't like that way. It is probably used in high school, but
is preferable because the inner product on
is defined to be

You can also write it using linear form such as 
4.
For this question, I think you meant
vectors


Once

Considering that the dot product is

and the norm of
is 
and the norm of
is 
Thus,


Answer: (3.5,-2)
Step-by-step explanation:
To solve this problem, all we have to do is plug in y=-2 into either equations from step one to find the coordinate. To make sure we have the right x-coordinate, let's plug in y for both equations.
4x-7y=28 [plug in y=-2]
4x-7(-2)=28 [multiply]
4x+14=28 [subtract both sides by 14]
4x=14 [divide both sides by 4]
x=3.5
------------------------------------------------------------------------------------------------------------
6x-5y=31 [plug in y=-2]
6x-5(-2)=31 [multiply]
6x+10=31 [subtract both sides by 10]
6x=21 [divide both sides by 6]
x=3.5
Now, we know the solution to the system is (3.5,-2).
X is the hypotenuse of an isosceles triangle. The length of the sides are the difference of the inner and outer squares divided by 2. Which means that the sides of the triangle is 1.5 inches. Using that information, the length of X can be deduced to be 2.12 inches using Pythagoras theorem