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have you taken trigonometry yet?

This might be quite impossible if you havent learned it yet.

thank you so much! that is a very beatiful solution I will make sure in the future to use the same strategy!

Sorry, kiddo!. I used dimes instead of quarters!.

yes i used to play roblox when I was a little kid! what is yoru username? XD

So basically he means that you have to use elimination.

Dont actually solve for A B C just get it where you have one equation and it is a + b + c = ?

Here's the solution ....

Note that we should have this equation

9x + 17y  =  541           which we can manipulate as follows

9x  =     541  - 17y

x  =        541  - 17y

             ________

                     9

x  =  541   -  (18 - 1)y

       _____________

                   9

x  =  541 + y                18y

       _______     -        ____

             9                      9

x  =  540  + 1 +  y                18y

        ___________   -         ____

                   9                         9

x =  540           1 + y             18y

      ___   +       _____  -       ___

        9                  9                 9

Note that the first and last terms will always be divisible by 9

And.....the middle term will be divisible by 9  when y  =  8, 17  or 26

So   we have the following possibilities for x

x  =  541 - 17(8)        =      45

        _________   

               9

x =   541 - 17*17    =    28

        __________

                9

x =   541  -   17*26      =   11

        ____________

                  9

Note   if y =  35,we get the next multiple of 9...but  x  = -6 if this is so....    so....these are the only possible solutions

So....the solutions  (x, y)   = ( 11,26)  (28, 17)  (45, 8)

Just add these coordinates and you will get your answer, CU

PS i like your profile pic :D

nikels are 5 cents

quarters are 25 cents

so make equation

5x + 25y = 85

Notice how quarters can only amount to 25, 50, and 75 cents. This means there can only be (1, 2, 3) quarters.

So plug 1, 2, and 3 in the equation for y and find the answers!

Sorry I posted again I was confused by the explanation... I dont understand why it works.

It is locked now I couldnt reply to the answer today.

You posted the same question about 4 weeks ago. See here for the answers:

https://web2.0calc.com/questions/money-problem_5

@Logic you may have counted wrong... or you may have missed the square underneath the overhanging cube.

Here, Logic  :   https://web2.0calc.com/questions/geometry_64537

(c)         x^2

          ______

            1  -  x

Unfortunately....other than a graph, we will need to use some Calculus to find the range..this is a little involved, but not that difficult....hence.....the graph might be the best way to go :

https://www.desmos.com/calculator/vdr0itmcy5

The graph shows that the range is  (-inf, 4]   and [ 0, inf )

Draw this out if you are having trouble visualizing

PAD is an equilateral triangle with a length of 6, this means that the hexagon base is 6 inches long in total.

If you divide the hexagon into 6 equilateral triangles, then each has a side length of 3 by dividing 6 in half knowing the hexagon's height.

So the sum of the edges of the HEXAGON is 18

The sum of the edges on the pyramid is 36

So the answer is 54

(b)         3x + 1

             ______

               x + 8

We  have     a   same degree polynomial  / same degree polynomial......this means that we will have a horizontal asymptote    at   y   =    ratio of  the coefficients on x  in the numerator/denominator  

So....the horizontal asymptote occurs  at     y  =  3 / 1  =  3

So...the range will be   (-infinity, 3)   and  (3, infinity )

Check the graph, here :   https://www.desmos.com/calculator/umaqjrwwtr

The lines y = (5/12)x and y = (4/3)x are drawn in the coordinate plane. Find the slope of the line that bisects the acute angle between these lines.

Here's one way, Logic.....but I don't know if it's the most elegant

Construct a circle centered at the origin with a radius of 1

The  equation  is

x^2 + y^2  = 1

We can find the x coordinate  of the intersection of the first line and this circle,thusly :

x^2  + [ (5/12)x ]^2  = 1

x^2 + (25/144)x^2   =1

[144 + 25] / 144  x^2  = 1

[169] /144 x^2  =1

x^2 = 144/169

x = 12/13

And y = (5/12)(12/13) = 5/13

So   ( 12/13, 5/13 )  is on the circle

Likewise...we can find the intersection of this circle with the  second line :

x^2  +[ (4/3)x\^2  =1

x^2  + (16/9)x^2  = 1

[9 + 16 ] / 9 * x^2  =1

25/9 x^2  =1

x^2  = 9/25

x = 3/5

And y = (4/3)(3/5)  = 4/5

So  (3/5, 4/5)  is on the circle

And a chord can be drawn on this circle with endpoints   ( 12/13, 5/13)  and (3/5, 4/5 )

And the midpoint of this chord is

  (  [12/13 + 3/5]  / 2,  [ 5/13 + 4/5 ] / 2 )  =

(99/130 , 77/130  )

And  the line drawn  from the origin to this point is the line we seek and it will have the slope

[77/130]  / [99/130]  =    77/99   =  7/9

First, draw a diagram. Label the information that has been presented to you in the problem, then male the steps and moves.

Drawing an altitude from the top of the base to the bottom, we should cleverly use the six units and eight units. By the Pythagorean Theorem, the diagonal length is ten inches. Now, take half of the diagonal, which is five, and point it towards the corner. Here, we should see a 5-12-13 triangle, and thus the height is twelve inches. The volume of the pyramid is \(\frac{B*h}{3}=\frac{48*12}{3}=48*4=\boxed{192}\) squared units(units squared).