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thanks!

x/y  = 2/5

5x = 2y

x = 2/5 y

(-x+3y) =   (-2/5y+3y) =   13/5 y            2x+y =  2(2/5y)+y = 9/5 y

13/5  :  9/5

13:9

The green line has a length of 2, the blue line has a length of 7, and the red line has a length of 15.

Since the green line is parallel to the blue line, the 2 right triangles shown above must be similar to each other.

That means the smaller red length is just \(\frac{2}{9}\cdot15 = \boxed{\frac{10}{3}}\), which is the answer.

Venn diagram below

  people who use only 1 facility =    23 + 21 + 14

x²  + my² = 4

x² /4  +  m y² /4  = 1

x²  / 4   +  y² / ( m^-1  *4)   = 1 

c^2 = a^2 - b^2         we want the FOCI to be  +-4  to be on the circle of radius 4  ( c is the focus)

4²   =   m^-1  *4    -    4

20 =     m^-1 *4

5 = m^-1

m =  .2

x^2 + .2 y^2  = 4            ( I think !)                 I also got - 1/3 ....but I do not think that is an ellipse conic section

See graph:

https://www.desmos.com/calculator/n8wecwwstr

Oh I just found out my mistake, so when I tried to find the equation of Foci, which was a^2 -b^2=c^2
all I did was a^2-b^2=c!

btw I got -1/3, 1/5

  y = 5x+8      substitute this into the other equation for y

5x+8 = -5x -22

10x = -30

x = -3         Now you have 'x' ....use this value in one of the equations to calculate the value of 'y'

1130 to 130 is   2 hrs

168 km / 2 hr =  84 km/hr

Similar triangles

2y-3 = 129       solve for 'y'

1/2  x +1 = 31       solve for 'x'

  Multiply first equation by 2 to get

10x-8y=6

-10x+7y=-4​        now add the two equations   (this eliminates 'x')

-y = 2

then y = 2     use this value in one of the equations to calculate the value of 'x'

*** edited ***

Area of triangular ends  *  'depth' = volume

Area of a right triangle = 1/2  leg1 * leg2        need to find leg 2  via pythagorean theorem

sqrt (20.5² -13.3² )=  leg2 = 15.6 mm

Area = 1/2  13.3 * 15.6 = 103.74 mm²

 Now multiply by depth of 16 mm              = 1659.84 mm³

Perimeter is all of the sides added (since this is a right triangle)

3 + 4 + 5 = 12 ft

Area of a triangle =   1/2 b * h

                             = 1/2 * 3 * 4 = ............    ft²

If I understand the syntax of your question correctly 

    P ( 56<= x <60 )       56 is one standard deviation below the mean     z - score = .1587

                                      60 is the mean so  z = .5000

                                             the area between     .5000 - .1587 = .3413         Not positive of this answer 

Cos 70 =  ? / 5      (adjacent/hypotenuse)

5 cos 70^o  = ? = ........... units   (use calculator)

Sam is one standard deviation above the mean with a score of 630

   this puts him at z-score  .8621        so  86.21 % got a lower score than Sam

https://web2.0calc.com/questions/find-the-value-of-b-a-if-the-graph-of-ax-by-3-passes

8 and 4

Angle bisector theorem for a triangle

11/SP = 15/36

SP = 26.4  units                     (if I did that correctly)

perimeter =   15 + 36 + 11  + 26.4 = ..............  units

x = 2y = 5

-2+ 10:4+5

8:9

This is a straightforward one ....the shaded area includes the line

       the equation of the line is y = 0

           the shaded area is everything less than or equal to  this       y<=0              

                                                                                      (1) y + (0)x  + 0  <= 0

Use the Quadratic Formula   with a = 3     b = -3       c= 1

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

\(x = {3 \pm \sqrt{(-3)^2-4(3)(1)} \over 2(3)}\)   to find the two values of 'x' = ............    and  ............

The shaded area is everything LESS THAN the line....does not include the line (because it is a dashed line)

   so find the equation of the line

Find two whole number coordinate points       0,7     6, - 5

   slope =  (7- -5) / (0-6) = -2

point slope of the line becomes    (y - -5) = -2(x-6)    rearrange

                                                            y = -2x +7       now remember we want everything LESS than the line

                                                                                     y < -2x+7     re-arrange into the form requested in the Q

                                                                                      -2x - y + 7 > 0

Guest was right for the first part, but the number of ways to pass through the point (2, 2, 2) is not \(\frac{6!}{2!2!2!}\), it's \((\frac{6!}{2!2!2!})^2 = 8100\), so the answer is \(\boxed{26550}\)

Thanks for the info guest.    It is always good to get interesting background information.

Jugoslav was still asked to prove it though. 

He couldn't just say. It is true because Ptolomy said so.

[12  +  2] / 2 = 7 mph - speed of the boat in still water.

Check: 7 - 5 = 2 mph - its speed upstream

             7 + 5=12 mph - its speed downstream.