CPhill

N!  =  N * N-1 * N -2 *...... *3 * 2 * 1

So.....for instance...

4!  = 4 * 3 * 2 * 1     = 24

And

5!  = 5 * 4 * 3 * 2 * 1 = 120

By definition......sqrt (-1)  = i   

So.....

You should have gotten    i + 7     as a result

Note......if this is a root of a quadratic, realize that not all quadratics have "real" roots that can plotted in the "real" plane

P.S. - If this one root....then 7 + i     would be another

What do we want to prove????

That EF  = [ BC + AD ] /2       ???

I assume you wavt to find the roots of this using a graph???....if so......here it is :

https://www.desmos.com/calculator/5tdc8m2jfk

The roots occur at x = -3 and x = 11

√[14^2 + 14^2 ]   =  √ [2 * 14^2]   =  √2 * √14^2   =  14√2   = about 19.8

We can use the tangent to solve this:

tan 27 = 185 / D    where D is the distance we are interested in  ......  rearrange as

D = 185 / tan 27   =  360 ft.   [to the nearest ten feet]

The bat costs $1.05   ....the ball costs 5 cents

Just multiply each entry in the matrix by the number.....example

3 [ 1   2  ]   =    [ 3   6  ]

   [ 6  10 ]         [18 30 ]

Using the Pythagorean Theorem, we can find the length of the diagonal(s) of the rectangle:

Diagonal length  = sqrt(6^2 + 8^2)  = sqrt (100) = 10

The circle's center will lie at the intersection of these diagonals and its radius will be (1/2) the length of a diagonal  = 5

So.....the area of the circle - the area of the rectangle  =  the part of the circle lying outside the rectangle ....

pi*(radius)^2   -  Length of rectangle * width of rectangle  =

pi (5)^2   - 6*8  =

25pi  - 48   = about 30.54 units^2

We need to find the proportionality constant, k. So we have...

D = kT    where D is the distance and T is the time

90 = K9       divide both sides by 9

10 =  k

So...in 5 hours, we have

D = 10*5     = 50 (kilometers)