CPhill

The  roots of (x -2) (x + 2)  are  2. -2

sum of these roots = B/A  = 0

product of the roots =  1/A

-4 = 1/A

A = -1/4

A + B  =  -1/4

x + y  = 10

y = 10 -x

x^2 + (10 -x)^2  = 32 + 2x(10-x)

x^2 + x^2 -20x + 100 = 32 + 20x -2x^2

4x^2 -40x + 68 = 0

x^2 -10x + 17  = 0

x^2 -10x  =  -17

x^2 -10x + 25  = -17 + 25

(x -5)^2  = 8

x -5 = +/- sqrt (8) = +/- 2sqrt 2

x = 5 +  2sqrt2      or      x =  5 - 2sqrt 2

y = 10 -x   =    5 -2sqrt 2    or   5 + 2sqrt 2

(x,y)  = (5 + 2sqrt 2 , 5-2sqrt 2)   or ( 5- 2sqrt 2, 5 + 2sqrt 2)

Let a,b be the sides

2 ( a + b)  = 40

a + b    = 20

b = 20  - a

a^2 + b^2  = (10 sqrt 2)^2

a^2  + (20 - a)^2  = 200

a^2 + a^2 -40a + 400 = 200

2a^2 -40a + 200  = 0

a^2 -20a + 100 =  0

(a - 10*2  = 0

a =10

b =20 -10  =10

Area =  a*b =  10 * 10   =  100

Half as many members will take  twice as long = 20 min

S1 = a1 = 1/5

S2  = 2a1 + d

1/10 = 2/5 +  d

1/10 - 2/5 = d

d  =  -3/10

sum of the first n terms of an  arithmetic sequence  =

(n)*a1 +  (n)(n-1)/2 *d

S15  =  (15 ) (1/5)  + (15)(14)/2 * (-3/10)  =   3 - 63/2  = -57/2  = - 28.5

\( \frac{4}{1 - \sqrt[3]{3}} + \sqrt[3]{9} \)

Note that   1 - 3   can  be written as  ( 1 - 3^(1/3)) ( 1 + 3^(1/3) + 3^(2/3))

Multiply num/den  of the first fraction by the expression in re and  we  get

4 (1 + 3^(1/3)  + 3^(2/3) )

_____________________ =   -2 ( 1 + 3^(1/3) + 3^(2/3) )  =   -2 - 2*3^(1/3) -2*3^(2/3)

          1 - 3

And   9^(1/3)  =   3^(2/3)

So we have

-2 -2*3^(1/3) - 2 *3^(2/3) + 3^(2/3)  =

-2 - 2*3^(1/3) - 3^(2/3) 

OA =  OB /  5  =  30 / 5   =   6

alpha = the measure of one of the interior angles  = 

(15 - 2) *180  / 15   =     156°

Simplify as

ab  - 9a - 5b

Take the product  of the two coefficients on a, b  =  (-9) (-5)  = 45

(This is the number that goes in the blank)

Add this

ab - 9a - 5b + 45       factor as

(a - 5) ( b  - 9)

∛-8  = -2   which is rational

l floor ( -2) l  = l -2 l  = 2

-pi  is irrational

(ceiling (-pi) )^2  =  (-3)^2  =  9

√50  is irrationa;

( ceiling (√50) )^2  = (8)^2  = 64

9/2 is rational

l floor (9/2) l  =  l 4 l  =  4

2 + 9 + 64 + 4  =   79