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The equation simplifies to:

\((x-1)(x-2)(x-3) \dots (x-100) = 0\)

There are 100 solutions, namely x = 1 to x = 100.

\(f(x) = f(f(x))\)

\(x^2 - 2x = (x^2-2x)^2 - 2(x^2-2x)\)

Let \(x^2 - 2x = y.\)

\(y = y^2 - 2y\)

\(0 = y^2 - 3y\)

\(y = 0, 3\)

Now plug x back in.

\(x^2 - 2x = 0\)

\(\boxed{x = 0, 2}\)

\(x^2 - 2x = 3\)

\(\boxed{x = 3, -1}\)

Triangle  AOB  is similar to triangle COD

Then   since  base  CD  =  38/25   of  base   AB,  then the  height  of  COD  = (38/25)  that of  triangle AOB

Then  there are  38 + 25  =    63 equal parts  to  the height of the trapezoid  ...... and 63/2  = 31..5  equal parts on each side of the  midline

And  since the  height of AOB  contains 25  of  these equal parts......then  the height of triangle YOX  must = 31.5  - 25  = 6.5  of the equal parts

And triangles YOX  and COD  are similar

So

base  of  YOX  / base  of  COD     =     6.5  / 38   =    13/76

So  XY  = (13/76) CD  =    (13/76) ( 38) =  13 / 2    =  6.5  in

\(f(g(x)) = f(x-3)\)

\(f(x-3) = (x-3)^2 + 1 = \boxed{x^2 - 6x + 10}\)

Because AB and CD are parallel, 40 degrees.

Because BC and AD are parallel, 59 degrees.

Finally, z = 180 - x - y = 180 - 40 - 59 = 81 degrees.

The formula for circular acceleration is \(a = \frac{v^2}{r} = \frac{53 (\frac{m}{s})^2}{422 m} = 6.656 \frac{m}{s^2}\).

Therefore, the force is \(F = ma = (695 kg)(6.656 \frac{m}{s^2}) = \boxed{4625 N}\)

The shape is a parallelogram, as one set of sides is parallel and the other set of sides have the same length.

So, x = 180 - 48 = 134 degrees.

The rock hits the surface when the height is 0, or when \(-t^2 + 8t + 10 = 0\)

\(t^2 - 8t - 10 = 0 \)

Use the quadratic formula: t = -1.099 and 9.099. Time can't be negative, so the answer is t = 9.099.

This  is  a  hexagon.......

Sum  of  interior angles  =   (n  - 2)  ( 180)    where  n  = the number of  sides

So

(6 - 2)  *  180   =  

4 *  180   = 

720°

Thx, Cubey !!!!

Here's another  approach

In  the form    ax^2  +  bx  + c......the  x  value that  minimizes the function is given  by  - b / (2a)

So   b  = - 20         a  =  5

- b / (2a)  =    -(-20)   /  (2*5) =     20  / 10  =  2

Put this back into the  function to  find the the  min

5(2)^2  -20(2)  +  1357   =

20 - 40  +  1357    =

1337

The number of 10-digit binary numbers that end with 2 ones is \(2^7=128\), since the first digit must be 1, the last 2 digits must be 1, and the middle 7 digits can be either 1 or 0.

The number of 10 digit binary numbers that start with 2 ones is \(2^8 = 256\), since the first 2 digits must be 1 and the other 8 digits can be either 1 or 0.

If you add the 2 numbers together, you get \(128+256 = 384\), but that is not the answer because the number of 10-digit binary numbers satisfying both conditions is overcounted and needs to be subtracted.

The number of 10-digit binary numbers that satisfy both conditions is \(2^6 = 64\), since the first 2 and the last 2 digits must be equal to 1 and the middle 6 digits can be equal to either 1 or 0. 

Therefore, the answer is \(384-64=\boxed{320}\)

The diagonals bisect  each other....so....

AO  = OC .....so....

3x  - 4  =   8

3x  =  8  +  4

3x  =  12

x  =  12 /  3   =   4

thx a lot

1.8 m  =   180 cm

432 kg   =  432,000  g

Mass   =  Density  *   Volume

432,000 g  =  2.5 g/ cm^3  *  Volume

(432,000) / (2.5)  cm^3  =  172800 cm^3  =  Volume  of real  thing

The scale  factor  of the model  to the real thing  is    15 / 180 =  1/12

Volume of model  =   

Volume of real thing  *   scale factor^3   =

172800  *  ( 1/12)^3   =  100 cm^3

Let the intersection of AC and BD be O.

z = 180 - 96 - 40 = 44 degrees.

Edit: It appears that most of my answer has been deleted, sorry about that.

There are 180 degrees in a triangle.

Use triangle ABC

So 180 - 40 - 44 - 52 = 44

z = 44

Complete the square.

\(5x^2 - 20x + 1357 = 5(x-2)^2 + 1337\).

So, the minimum value is 1337.

CD for that question was 30, in this its 38

TOTAL AREA TO BE PAINTED

     2 x 10 x 20  +   2 x10x 16 = 720 ft²

720 ft² / 400 ft² /gal = 1.8 gal       you will need to purchase 2 gallons

Note

(3x  + 1)  ( 3x  + 1)  =   9x^2  +  6x   +   1

THX, Alan  !!!!!

\(\frac{7+x}{17+x} = \frac{3}{5}\)

\(5(7+x) = 3(17+x)\)

\(35 + 5x = 51 + 3x\)

\(2x = 16\)

\(\boxed{x=8}\)

The vertex of f(x) is given as  (1,-2)

   the vertex of f(x+8) will be shifted 8 units to the LEFT to  ( -7,-2 )    

The only way to put it in the calculator is to convert it entirely to inches. 

5 ' 10'' = 5(12) + 10 = 70 inches.

Then you would put that in the calculator.