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∠DAH = ∠BAC

x = (144 + 124) / 2

This is also incorrect.

Actually, there are two triangles.

Crossing chords of a circle

x (x-11)  = (x-8)(x-5)

x^2 - 11x = x^2 -13x+40      solve for x

2x = 40

x = 20

Find the rate     (1 + r)¹⁰  = 2      (after ten years the investement doubled)      

                                      solve for   r = .071773

(1 + .071773)ⁿ = 4       after 'n' years the investement is 4 times original 

                                         solve for n = 20 years    (makes sense....it doubled in ten years)

FV = 5000 (1+ .071773)³⁰ = $ .........    at the end of 30 years

The two other angles at A   equal   (61+31)/2 = 46

    Angle x   + one of these = straight line = 180

       x + 46 = 180     

        x = 134 ^o

Is it the LCM(5, 8) = 40 passes?

I'm not sure what that means

This is wrong.

Graph below:

\\\\

There are 405 possible sequences of passes.

(c - 1)/(6 - 3) = (c - 5)/(6 - 5)

==> (c - 10)/3 = (c - 5)/1

==> c - 10 = 3(c - 5)

==> c - 10 = 3c - 15

==> 2c = 5

==> c = 5/2

Using geometric probability, the probability is pi/9.

I'm reading the question as the "ceilings" of the square roots of 3 to 83. If that is correct, then this is what I got:

Sum =(2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10) = 542

Thanks Heureka,

I would have done this with a probability contour map.     

We can use algebra s=speed and l=length (500+l)/s=20, (1900-l)/s=30 we have that s=48 and l=460 by Adding the equations in order to solve for the first variable. Then we plug this value into the other equations in order to solve for the remaining variables. 

so we have the \(\text{speed}=48,\text{ and }\boxed{\text{length of the train}=460m}\)

Yes I know  

It is good that it has made you think though   

And I should mention, I got the same answer, just I didn't know how to correctly do it.

honestly, I didn't either, I just kind of slightly ignored it. I also did the problem, but my explanation defiitely was not clear at all. I need to work on that. :)

we do 5.70*25.5=145.35(total price) and we can use algebra x+y=25.5(weight) and (2.20)x+(7.30)y=145.35 we have x+y=25.5 and we subtract y from both sides to get x=25.5-y then we substitute x with 25.5-y in (2.2)x+(7.3)y=145.35 which becomes 2.2(−y+25.5)+(7.3)y=145.35. We simplify both sides of the equation to get 5.1y+56.1=145.35 and subtract 56.1 to get 5.1y=89.25 so we get that y=17.5 and x=22.5-17.5=8 

and we have \(\boxed{x=8}\text{ and } \boxed{y=17.5}\)

given line  (re-arranged to  y = mx + b form )      y =   -2/3x + 2/3      slope =  -2/3

   parallel slope is the same   - 2/3

       y = -2/3 x + b    sub in the given point

       0 = -2/3 (2) + b          b = 4/3

your line is now    y = -2/3 x + 4/3       now, re-arrrange to the form requested

                  y + 2/3 x  = 4/3

                 3y + 2x = 4

You are welcome, 

I am glad you could understand it :)

I wish I understood what the a b c stuff in the question was about....

Yay free points

Not locked yet

Um a fraction is a numerical quantity that is not a whole number 

EXAMPLE: 1/3,5/7, 4 5/7, 86/21