CPhill

In order:

1

4

2

3

x^2 - 4   =   (x - 2) ( x + 2)

x^2  + 25   =    (x - 5i) (x + 5i)

Looks like you're correct Angel

See the graph , here :  

https://www.desmos.com/calculator/lsth7dplge

Haven't seen one like this before.....!!!

Since AB : BD  =  1 : 5   so...from A to D  there are  1 + 5 = 6 parts

And since AC : CD  = 7 : 11   and we can divide each 6th part into 7 + 11 = 18 more parts

So.....from A to D there are   6 * 18  =   108  equal parts

So  AB  =   [108 / 6] * 1  = 18  units

And BD  =  [108 / 6] * 5  = 90 units

And AC =  [ 108/ 18] * 7  = 42 units

And CD  =  [ 108 / 18] * 11 =   66 units

AB  = 18        

BC =  AC - AB =  42 - 18  =  24 units

CD  =  66 units

A           B            C                D

     18    +    24     +        66            =       108   

So   AB :   BC : CD    =    18 : 24 : 66  =    3 : 4 : 11

Area of circle is

49  =  pi * r^2

49 / pi = r^2           take the square root of both sides

7 / √pi  =   radius

The diameter is twice this  =   14/ √pi  =  the diagonal of the square

And the diagonal of a square = √2 * side length

So.....we have that

14 / √pi  =  √2 * side length        [divide both sides by √2 ]

14 /  √ [ 2  pi ]  =   side length ≈   5.585 cm 

The points $(-3,2)$ and $(-2,3)$ lie on a circle whose center is on the $x$-axis. What is the radius of the circle?

If the center lies on the x axis, let the center be (x, 0)

So....the distance from the center to either point will be the same...so

( -3 - x)^2 + (2 - 0)^2  =  (-2 - x)^2 + ( 3 - 0)^2

x^2 + 6x + 9  + 4  =  x^2 + 4x + 4 + 9

6x + 13  = 4x + 13

2x  = 0

x = 0

So...the center is at the origin  ....so the radius is

√ (-3)^2 + (2)^2  ]  =

√ [9 + 4]

√13

cos ( θ + 3pi/2)  = sin θ 

We can use this identity to prove this

cos (A + B)  =  cosA*cosB - sinA*sinB

So we have

cosθ *cos 3pi/2  -  sinθ * sin(3pi/2) 

cosθ (0)  -  sinθ (-1)  

0   + sinθ  

sinθ

Distance  =

√ [   (subtract the x coordinates)^2  + (subtract the y coordinates)^2 ]  =

√  ( - 5 - 5)^2 +  (  5 -  - 5)^2 ]  =

√  (-10)^2  +  ( 10)^2 ]  =

√  [ 100  + 100]  =

√  [100 * 2 ]  =

√ 100 * √2

10√2  units

If 

 l scale factor  l  >  1     expansion 

l scale factor l  <  1   contraction

−5     expansion

−1/4   contraction

3.5    expansion

6/7     contraction

x = 1 is a root ....so....

f(x)  divided by (x−1)  has a remainder of 0     and

(x−1)  is a factor of  f(x)

x4−4x3−22x2+4x+21    we can write this as

x^4 - 4x^3  - 21x^2  - x^2 + 4x + 21

x^2 ( x^2 - 4x - 21)  -  1 ( x^2 - 4x - 21 )

( x^2 - 1) (x^2 - 4x - 21)

(x + 1) ( x - 1) (x - 7)(x + 3)

The zeroes  are     -1, 1, 7, -3