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The  circumference  of  each  circle will be  36 cm

So...in one  circle

C = 2 pi  * r

36   =  2pi * r

36  /( 2pi)  = r

18  /pi   =  r

So....the combined areas  of the  2 circles  = 

2 * pi  r^2   =

2 * pi  * ( 18/pi)^2   =

2 *  pi *  324 / pi^2  =

648  / pi      cm^2         { ≈  206.26 cm^2   }

FOUR ways to keep the four  TRUES   separated in the line up of 10 questions

 |     |     |     |     |     |     |     |     |     |   

T         T          T         T                          This is one way.....then you can shift the line of trues to the right 3 more times    total   4 ways

Nice, EP   !!!!!!!

Thanks CPhill

From the picture below yo can see that the shaded area will be 12 semicircles of diameter 2    (radius 1)

    12 semi circles = 6 circles of radius 1

        6   * pi (r^2)   = 6 pi

144 degrees....here is a picture to explain:

Very nice, FMP    !!!!!!

1. \(a+b+c=-3\)

2. \(a+3b+c=9\)

3. \(a+b+3c=-19\)

Subsrtacting equation number 1 from equation number 2 we get

\(b=6\)

Substracting equation number 1 from equation number 3 we get

\(c=-8\)

Then putting \(b\) and \(c\) into equation 1

we get

\(a=-1\)

so

\(abc=-1\times-8\times6=\)48

h^-1 (5)   means  that

5 =   ( 1 + y)  / ( 2 - 2y)

5 ( 2 - 2y)   =  1 +  y      simplify

10  -  10y   =   1 + y

10 - 1   =   10y +  y

9  =  11y

y  = 9 / 11    =   h^-1 (5)

Here is a  very similar problem that should  help .....

https://web2.0calc.com/questions/geometry-help_102

There are 4 slots for math books    12 ways to place them   (4 P 2)

    for each of those 12 placements the other books can be arranged  4 * 3 * 2 * 1 = 24 ways

24 * 12 = 288 ways

3x + y + xy = 115

(x + 1)(y + 3) - 3 = 115

(x + 1)(y + 3) = 118

Can you take it from here?

=^._.^=

Sorry, Ninchux.....!!!!!

You gotta' be fast around here....LOL!!!!

(14/x)/(2/5x)

(14/x)*(5x/2)

(70x)/(2x)

35

=^._.^=

14 / x    /   2/(5x)=

14 / x   *  5x / 2 =

70 /2 = 35

By Vieta

The  sum of the  roots  =  a + b =  9/2

The product of the  roots =  ab  =  2/2  =  1

And note that

1/ ( a - 1)    +  1  /( b - 1)   =   

b -1   +  a  - 1

_____________   =

(a - 1)  ( b - 1)

   a + b  - 2

____________  =

ab  - a - b  + 1

( a + b)  - 2

_______________    =

ab  - (a + b) + 1

   9/2   - 2

__________   =

1 - (9/2) + 1

     5/2

_______   =

    -5/2

-1

First  p (q(x) =

   (2x^3 +1)^2    = 4x^6 + 4x^3 + 1

       then add r(x)

                   4x^6      + 7x^4      + 4x^3 -5x^3      - 6x    -2  +1 =

                    4x^6     + 7x^4     - x^3   - 6x   -1

a1 = x

a2 = x + r

a3 = x + 2r

a4 = x + 3r

a5 = x + 4r

(x + r)/(x + 3r) = a2/a3

I don't think it's possible to figured out (x + 4r)/(x + 2r).

=^._.^=

i made it seem so much harder than it actually was oml im so dumb haha thank you for breaking it down for me!!!

CPhill, you just beat me on time by a minute

Note that     x^2  + 6x  -27   = ( x - 3) ( x + 9)

So  the  first term  actually  reduces to     x + 9

This wil "cancel"  with the denominator of the  other  term....so.....you are left with

3x

Good job   !!!!!

The smallest possible value of x + y + z is 120.

I will get you started.....

1. 250/2 = 125 FT

2. 125/2 =62.5 FT

3. 62.5/2 =31.25

Just continue this pattern 3 more times I belive in u :))