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It takes each of them 4 hours alone

1/ (1/4 + 1/4 + 1/4) =  4/3 hr if they all work on it

.19

.302

0.31

0.340  = .34

6.000 026

6.000 777

A   3- 4 - 5 triangle is a right triangle totalling 12    multiply by 6

    18 24 30   totaling 72 inches perimeter       area = 1/2 b h = 1/2 18*24  in²

Suppose you invest $150 a month for 8 years into an account earning 9% compounded monthly. After 8 years, you leave the money, without making additional deposits, in the account for another 29 years. How much will you have in the end?

What are you on about guest.

That is a direct extract copy from one of my recent answers.

You are one very lazy rude person!

Initially

a + b = 480      or   b = 480-a

then

(a-2/5a)  + (b + 2/5 a  ) 3/7    =    (b+2/5 a) 4/7       (b+2/5a) is the amount b has after a gives him 2/5....then he gives back 3/7 leaving b with 4/7

3/7 b + 6/35 a      +   3/5 a    =    4/7 b + 8/35 a

19/35 a = 1/7 b                now sub in the red equation

19/35 a = 1/7 (480-a)

24/35 a  = 480/7

a = 100 dollars at first

The total 'x' distance of the drive goes from x = 0    to  x = 32      for 'x' distance 32   

the part of the drive where you can hear the radio goes from x = 11.35   to  19.64     for x distance  8.29 

percentage of distance you can hear the station is then       8.29/32 = 25.9%

You COULD find the distance between the starting and end points    and then the points of intersection...BUT that is a much more difficult method than is necessary...    

distance formula   d^2 = (x1-x2)^2  + (y1-y2) ^2    (recognize this as modified pythagorean theorem)    .....   so for the two intersection points you would have to calculate the 'y' coordinates (you have the x's)

    for A to B      d^2 =  (0-32)^2  + ( 31-0)^2      resulting in d =  44.55 miles

  I would use a quadratic formula calculator like this one:

https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php

                       P(A)              P(B)              P(C)

                         1/3               1/3                1/3

P(green)           6/10             3/9                3/9

                       _________________________

Poverall            1/5               1/9                1/9             P = 1/5 + 1/9 + 1/9 = 19/45

Like so:

Here is a good start

Area = 2a+2b

tan 20 = 2/b      and       sin20=2/(a+b)

solve simultaneously then substitute

As follows:

AB = 12

∠B = 180 - 2x

∠y = 180 - x

(180 - 2x) + (180 - x) + 48 = 180

x = 76

∠B = 28º

FG = 6 + √525

You are very welcome.  

The area of overlap is 13/8.

AB = 18.

1, 3, 4, 5, 6 =5! ==120 permutations as follows:

(13456, 13465, 13546, 13564, 13645, 13654, 14356, 14365, 14536, 14563, 14635, 14653, 15346, 15364, 15436, 15463, 15634, 15643, 16345, 16354, 16435, 16453, 16534, 16543, 31456, 31465, 31546, 31564, 31645, 31654, 34156, 34165, 34516, 34561, 34615, 34651, 35146, 35164, 35416, 35461, 35614, 35641, 36145, 36154, 36415, 36451, 36514, 36541, 41356, 41365, 41536, 41563, 41635, 41653, 43156, 43165, 43516, 43561, 43615, 43651, 45136, 45163, 45316, 45361, 45613, 45631, 46135, 46153, 46315, 46351, 46513, 46531, 51346, 51364, 51436, 51463, 51634, 51643, 53146, 53164, 53416, 53461, 53614, 53641, 54136, 54163, 54316, 54361, 54613, 54631, 56134, 56143, 56314, 56341, 56413, 56431, 61345, 61354, 61435, 61453, 61534, 61543, 63145, 63154, 63415, 63451, 63514, 63541, 64135, 64153, 64315, 64351, 64513, 64531, 65134, 65143, 65314, 65341, 65413, 65431)

Total Sum ==5,066,616

Thanks, I was able to get an answer.

Correct too!

I really appreciate it. The answer was

 6 3 9

 1 8 7

 1 1 2 

Thanks for the help, it helped me understand how to solve it.

Thanks!!

Refer to this answer:

ok, your first step is fine

Solve the system of equations

5x-2y=16

15x-7y=51

Enter answer as ordered pair (x,y).

This is what I did:

-3(5x-2y=16)

-15x+6y=-48

15x-7y=51

so far so good  :)

   I am going to sid track for a bit

        You know that   24 = 2 dozen

        and you know that    7 = 21/3

        these are completely unrelated facts but from this knowledge I can say   24+7 = 2 dozen + 21/3

        Think very hard about what I have done.  I added the left sides and that will = the sum of the right side.

So

you have

-15x+6y=-48

15x-7y=51

these are 2 independent facts

Add the left sides and that will equal the sum of the right sides

-15x+15x+6y+-7y = -48+51

-1y=3

y=-3

Now you know that y=-3 just sub it into one of the original equations to get x

5x-2y=16

5x-2*-3=16

5x+6=16

5x=10

x=2

so I have x=2 and y = -3

I have substituted them into both original equations to check and they work just fine.

Your second question you have asked is almost identical.   Just easier.

An equilateral triangle has an altitude length of 27 feet. Determine the area of the triangle.  

Would it help if you realized that the altitude creates a right triangle with 60^o opposite that side?  

tan(60) = 27 / adjacent               That adjacent side is half the base of the triangle.