ElectricPavlov

( 8 + 2\(\sqrt[1/4]{4}\)  + 4 \(\sqrt[1/4]{2}\) + \(\sqrt[1/4]{8}\) )  /  7

Arrangel first line into y = mx + b form   where m = slope

y = -3x +8           m = - 3       perpindicular slope = - 1/m = 1/3

arrange second equation into y=mx + b form    (I'll change the 'b' in the question to 'z' to avoid confusion)

- 2x + z y = - 9

y =  2/z  x  - 9 / z         slope    2/z = 1/3       then z = 6     (this is the   'b ' you are looking for )

2x^2 + 2y^2 + 4x + 12y + 6 = 0    divide thru by 2

x^2  + 2x       + y^2 + 6y   =    -6      complete the square for x and y

(x+1)^2         +  (y+3)^2    = - 6  +1 + 9

(x+1)^2         +  (y+2)^2    =   4                        

this is a circle equation of the form     (x-h)^2   + (y-k)^2   = r ^2        center = (h,k) = ( -1,-2)    radius = 2

10 x 9 x 8     x 10   = 7200            1 /7200 chance to win jackpot

Confusingly written question !

When Mark  gave half of her (?)  pencils to James, he then had 12 fewer pencils than he had...

    if Mark gives away 1/2 and has 12 less....then Mark had 24 to start .

The cone will now hav a circumference of    pi * 30  -   pi*30 (144/360) = 56.549 units

    this will be a diameter of     56.549/pi   = 18        radius of  9  units

the side length will still be 15  units

sin of 1/2 of the vertex =  opp / hyp = 9/15   

   arcsin (9/15 ) = 36.87 degrees                              2 x 36.87 = 73.74 degrees            

The domain is all 'x' except the value of x that causes the denominator to be equal to zero

(-inf,4) U (4, + inf)

.25 (4) +1.0(x)= .5(4+x)       solve for x gallons of pure

All you need to do is this:

140 = 12.5( 0.2^t -1) + 20t            can you solve this for 't' ?

There will be a 3 x^3   term in the final expansion, so this cannot be reduced to " Ax^2 + Bx^2 + Cx + D " form.....    is your question correct?