CPhill

\(f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}} \)

From the bottom  

x cannot =  0

1 + 1/x =  [x + 1] / x

1 /  ( [ x + 1] / x) =   x / [x + 1]

x cannot be -1

1 + x / [x + 1]  =    [ 2x + 1 ]  / [ x + 1]

1 / [ (2x + 1) / (x + 1) ] =    (x + 1) / (2x + 1)

x cannot be  -1/2

sum =  0  -  1  - 1/2 =   -3/2

https://web2.0calc.com/questions/triangle_41241

If the area is 100, the side  = sqrt 100  = 10

Dilation by a scale  factor of 44 produces a perimeter of  (4 * 10)  * 44  =   1760

                      P

             5                  8

Q      5.5            M        5.5                R

Law of Cosines

Two Equations

5^2  = 5.5^2 + PM^2  - 2 ( 5.5 * PM)  cos PMQ

8^2  = 5.5^2  + PM^2  - 2 (5.5 * PM) cos  PMR

cos PMR  = -cos PMQ

So

5^2  = 5.5^2 + PM^2  - 2 (5.5 * PM) cos PMQ

8^2  = 5.5^2 + PM^2 + 2(5.5* PM) cos PMQ       add these

89  = 60.5 + 2PM^2

(89 -60.5) / 2  = PM^2

PM^2  = 14.25

PM =sqrt [14.25 ] ≈ 3.775

The rectangle s a square with a side of   10sqrt 2 / sqrt 2  =10

The area   10^2  = 100

x^2 + (k -9)x + 16

We have either

x^2 + 8x + 16 = ( x + 4)^2   or

x^2 -8x + 16  = ( x- 4)^2

k - 9    must be = to 8   or -8

k - 9 = 8        k - 9  = -8

k = 17            k = 1

Sum of possible k's   =  17 + 1  =  18

For the second term

C(n,1) (- a)  = -12

n! / (n-1)! * a  = 12                {   n!  /(n -1)!  =  (n) }

n * a  =  12

a = 12/n    →   a^2  =  144/n^2

For the third term

 C (n,2) (-a)^2  = 54

n! / [ (n -2)! (2!) ] * a^2  = 54             { n! / (n -2)!  =  (n)(n -1) }

(n)(n-1) * 144/n^2 = 108

(n^2 - n) / n^2  =  108 / 144 =  3 / 4

1n^2 - n  = (3/4)n^2

(1/4)n^2 - n  =  0

n (1/4 * n - 1)  = 0

n = 0   reject

n  = 4  accept

Since the expansion  terms  alternate signs,  then  

a  =  -12/n  =  -12/4  = -3

The binomial is  (1 -3x)^4

c =  C(4, 3) * (-3)^3   =    4 *  -27  =    -108

https://web2.0calc.com/questions/geometry_12483

2W   + 4A =  4.50      →   6W + 12A  = 13.50     (1)

3W  + 5A  =  7.50     →   -6W - 10A  = -15.00    (2)

Add (1), (2)

2A  =  -1.50

A = -.75     which is  impossible

No solution

https://web2.0calc.com/questions/geometry-question_42617