ElectricPavlov

Yikes !   

The radius is shown as '2'....I think...    the diameter = 2 * radius = 4  units 

For an absolute answer , I think I need more info.....

See image below :

Using the vertical line test.....if a vertical line passes through the graph only ONE time ( no matter where the vertical line is placed)  the graph is a function 

a) no

b) no

c) no 

d) yes      this is the graph of    f(x) = | x - d |    where 'd' is the distance from the origin to the vertex 

x^2+4mx+m = 2x - 6 has exactly one real root means the discriminant of the quadratic = 0 

Put in quadratic form 

x^2 + ( 4m-2) x + m+ 6  = 0 

discriminant = b^2 - 4 ac = 0 

                     = (4m-2)^2 - 4 (1)(m+6) 

                     =  16m^2  - 16m + 4   - 4m - 24 

                     =  16 m^2 - 20 m - 20                          Use quadratic formula with a = 16    b = -20   c = -20 

                                                                                          to find the positive valueof m = 5/8 + sqrt(105) / 8     ( or  m =  1.90587 ) 

Using distance formula, the distance^2 from a,b to each of the points on the circle is the same ....

    to 2,0 and 7,1 :

           (a-2)^2 + (b-0)^2  = (a-7)^2 + (b-1)^2       simplify to 

10a+2b = 46

    to  2,0 and 3,5 

           ( a-2)^2  + ( b-0)^2  = (a-3)^2 + (b-5)^2    simplify to 

2a +10b = 30 

    Now you have two equations relating two unknowns....solve for a and b 

Multiply top equation by -5 to get 

-50a - 10 b = -230    and add it to the second equation to get 

-48a = -200 

a = 4.167.      use this value of 'a' in one of the equatins to find  b = 2.167           

45 mem * 60 min =   2700 mem min required to paint the wall 

2700 mem min / 12 mem =  225 minutes for 12 members to paint the same wall

the integers are    n     n+1    n+2   .....   n+6     and summed they equal    7 ( n+6) 

7n + 21 = 7 (n+6)      <==== this can't be true....no answer ....no solution.

y = your money 

b = brother's money 

y - 5  = b + 5            <===== given    this is    y = b + 10  

y+10 = 2 ( b-10)       <====  given      sub in   'y = b+10 '

b+10   + 10   = 2b - 20    Solve for 'b' by adding twent to both sides and subtracting 'b' from both sides 

$ 30 = b                         ( and you have $ 40) 

5x / (x+2)  = 6       <=====given    multiply both sides by (x+2) 

5x = 6x + 12          subtract 12 from both sides

5x-12 = 6x              subtract 5x from both sides 

-12 = x