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Wait, I'm confused. Can you write the question properly please and not in Latex. I don't get the second part so I can't help you.

angle CBE  =  90   -70  = 20°

tan 20   =  CE  / 1  =  CE

So  ED  =  1 - CE  =  1  - tan 20

And  angle FBA  =  90  - 20  - 45  =   25°

tan 25  =  AF/ 1  =  AF

So  FD  = 1  - AF  = 1 - tan 25

And....by the Pythagorean Theorem

FE  =  sqrt  [ ( 1 - tan 20)^2   + ( 1 - tan 25)^2  ] 

So....the perimeter of FED  = 

ED + FD  + FE   =    (1 - tan 20) +( 1 - tan 25)  +   sqrt  [ ( 1 - tan 20)^2   + ( 1 - tan 25)^2  ]  =   

2 units !!!

Nothing shows up, kasuer1463  .....

That's OK....this isn't too hard once we  get the hang of  it.....!!!!

(x -3)^2

x^2  -  9  =  (  x + 3) ( x - 3)

(x + 3)^3

List all  the  different factors of  theses polynomials = 

(x  - 3)  ,  ( x + 3)

Take the  highest powers found on  each

(x -3) ^2     and  (  x + 3)^3

LCM =      (x - 3)^2  *  ( x + 3)^3

Let  the  normal speed  =  S

And  distance / rate  = time....so

Time Up  +  Time Down =   6...so....

96 / ( S  -16)    + 96 / (S + 8)   =    6                 divide  through by 6

16/ (S - 16)  + 16/ ( S + 8)   =  1

[16 ( S + 8)  +  16 ( S -16)  ]  /  [ (S -16) ( S + 8)  ] =   1

[ 32S   - 128  ]   =   (S  -16) ( S + 8)

32S  -  128  =   S^2  - 8S   -  128

32S  =  S^2 - 8S

40S  = S^2

S^2  - 40S  =   0

S ( S -40)  =  0

S - 40  =  0 

S = 40  km/h

We can use fraction decomposition, 

$A(x-3)(x+4)+B(x+1)(x+4)+C(x+1)(x-3)=2x+1$

Setting $x$ as $-1$, we get

$A(-4)(3)=-1$

$A=1/12$
 

setting $x$ as $3$, 

we get 

B(4)(7)=7

$B=1/4$
 

Setting x=-4

C(-3)(-7)=-7

$C=-1/3$
$1/12+1/4-1/3=0$

Thank you CPhil and Guest! I get it now :)

We can rearrange the the first expression as 

$-x^2+1$

we can factor a $-1$

$-1(x^2-1)$

$-(x+1)(x-1)$

the second expression is 

$(x-1)(x-1)(x-1)$

that means

$(x-1)^2*-(x+1)$

i am really unsure about the finding the least common multiple, because I am really rusty with that part, but the factoring part is definitely correct 

1  - x^2     = ( x - 1)  ( x + 1)   =    -( 1 - x) (x + 1)  =  -( x + 1) ( x  -1)

Take the  highest power on each  unique  factor between both  polynomials

highest power of  ( x -1)  =  3  =  ( x  -1)^3

highest power of  - (x + 1)  = 1  =   [- (x + 1) ]^1  =  -(x + 1)

LCM  =   -(x + 1) ( x - 1)^3

Hello guest!

We use vietas formula for the sum of roots, this formula states

$r_1+r_2=-b/a$

in this quadratic 

$a=2$

$b=7$

$c=-4$

the sum of the roots is $-b/a$ so that means it is equal to 

$-7/2$

a + b  =  9 (a  - b)

a + b =  9a - 9b

-8a  = - 10b

b = 8/10 a   =  4/5 a      (1)

And

a^2 - b^2   =   81      (sub in (1)  for b )

a^2 - [ (4/5)a ] ^2   = 81

a^2  - (16/25)a^2  = 81

(9/25)a^2  = 81

a^2 =  81 * ( 25/9)       take the positive  root

a = 9 * (5 / 3 )  =    15

b =  (4/5)a =  12

Half of  the side of  the square =  sqrt (12^2  - 9.6^2)   =  7.2 m

So the side of the  square   =  7.2 * 2  =  14.4 m =   the base of the triangle

So......the area of  the square = (14.4)^2   =  207.36 m^2

The  area of the triangle =   (1/2) ( 14.4) (9.6)   =  69.12m^2

The trapezoid   has  bases of   14.4 m  and 10 m    and  a  height of   25.4 -14.4  =  11 m

So its area =   (1/2) (11) ( 14.4 + 10) =   (1/2) (11)  (24.4)  =  134.2 m^2

So....the total area =  (134.2  + 69.12 + 207.36) m^2  =   410.68m^2

Let   the  number  of chairs in each row =   C

So

3C +  2  +  13   =    8C     simplify

3C  +  15   = 8C      subtract 3C from both sides

15 =  5C                 divide both sides  by  5

15/5 = C   =  3   chairs in each  row

Proof

3(3)  + 2 =   11

If she gets   13  more  she  has  24

And  8(3)  =  24

g^4  + 12g^2 + 9  - 10g^2   + 8   =

g^4  + 2g^2  +  17   =                 {complete the square on g }

g^4  + 2g^2  +  1  +  17    -  1   =

(g^2 + 1)^2   +   16

q   = 16

P =  2 (W + L)

L  = 8W

So

216  = 2 ( 8W  +  W)

216  = 2 (9W)

216  =18W

216 /18  =  W  =  12 cm

Strictly a graphical solution.....I found "a"  =  4.2

I belive they play each other in 10 games.

See Cphil's answer

75 yards

∑ [ 3^-n(-2 + 3n), n, 1, ∞] ==It converges to 5/4 ==1.25

The sum of the digits of a two-digit nunber is 7. When you reverse the digits of the original number the new number is 27 more than the orginal number. What is the value of the original number?   

There aren't many ways to total 7 under the terms of the problem, to wit, 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, 7+0  

I would have tried them all if I had to, but I got it on the second try.  The original number is 25. 

_.

I think this is the Answer:

So the first one is Harry, so the first choice has one option (1)

The second one has 4 options because Harry was already chosen  (4)

The third one has 3 options because 2 of them were already chosen (3)

The fourth one has 2 options because 3 of them were already chosen (2)

And one of them will be the last one; there is one option. (1)

So, 1*4*3*2*1=24

Angle AYX = 135 degrees.