ElectricPavlov

x= 35^o    Opposite angles of intersecting lines are equal.

Yes, I believe YOU are correct......the diagram is deceiving !

  If you abut the poles (i.e. right next to ecah other with no distance between)   , the cable goes from 50 m to 10 m (above the ground) then back to the top of the other pole .....   for a total of 80 m length.     SO the distance betwen the poles = 0

   (If you start to move the poles apart....the point that is 10 m above the ground will start to rise above 10 m . )

1/30    +    1/15      =   1/x        x is the minutes required when both working together.

1/30     +   2/30     = 1/x

3/30                    = 1/x

x = 10 minutes

https://web2.0calc.com/questions/need-help-with-a-problem-i-can-t-solve

I think your question is

x² + 4/5 x + ?         We need to 'complete the square'      take 1/2 of the x coefficient  (2/5) , square it , and add it to the equation

(x² + 4/5 x   + 4/25)     then it becomes

(x+2/5)^2

Anywhere the denominator = 0   there will be a hole

x=0    produces a denominator = 0      so that is one hole....

    now you try x= 10     and -10    to see if denominator = 0   ,    another hole

-b/2a    will be the x coordinate of the vertex of this bowl shaped parabola

= - -4/4 = 1      x = 1

put in x = 1 to find the y value of the vertex

=-2     vertex =   1,-2

it says   'a'  'b' and 'c' have no common factors other than one     NOT    'a' and 'b' have no common factors other than one

The line equation is   y = 2x - 4     everything in yellow is less than this  (but includes the line)  

           y <= 2x-4

         2x-y-4 >=0

If you draw a Venn diagram , you will find 10 students play both sports     out of 28 students     10/28 =   5/14