ElectricPavlov

x+y = 12     or     y = 12-x

1/x - 1/y = 2/9       sub in the red equation

1/x  - 1/ (12-x) = 2/9     now solve for 'x'       then y = 12-x

https://web2.0calc.com/questions/june-cleaver-needs-2-000-in-7-years-time-so-she-can#r1

You already posted this....... check the earlier post....don't be lazy!

Area of a rectangle = length * width

a) width = area / length =   (2x^2-x-1) / (2x+1)

b) non-permissable values would be values that result in a denominator of 0      2x+1 = 0     x  cannot equal -1/2

c) Length cannot be LESS than zero either,   soooo    2x+1 cannot be less than 0

          2x+1 < 0

            x < -1/2     x cannot be less than -1/2

Looka at the graph.....look at the line x = 2     find where it intercepts the graph at y = -2     this is f(2)

The vertex of the parabola will be shifted 3 units to the LEFT  to   -1,-1

9 % annual interest  compounded monthly is   .09/12 = .0075 %   periodic interest

7 years is  7 * 12 = 84 periods

2000 is future value

2000 = d * ( 1+.0075)⁸⁴        where d = initial deposit amount

d = 1067.69 dollars initial deposit

a ( x^2 -x-6)         no matter what value 'a' is, the zeroes are still going to be 3   and -2

                                  so we know one leg of the triangle is +3

triangle area = 1/2 b * h

                          1/2  3 * h = 12

                              shows the other leg (the y-axis intercept) needs ot be | 8 |

 |a (-6) | = 8

   a = - 1 1/3   or    + 1 1/3          

so

a  = + 1 1/3    ( since the parabola opens upward)

Find slope     (rise/run) = 4 / 1 = 4

point slope form      y -9 = 4 ( x-4)   re-arrange

                                y-9 = 4x - 16

                                         4x -y = 7

TRY number THREE:

1200 possibles     1 / 1200 chance to match that exactly

1 / 10 chance to match only superball     10 out of 1200

1 / 120 chance to match all 3 whites       10 out of 1200            

3 ways to match 2 out of three whites      3 out of 1200              you could hit the superball too     ( + 3/1200* 1/10 ?)

1 + 10 + 10 + 3   / 1200 =    24/1200      1/50 chance of a wining ticket       so far....but I do not know how to compensate for the red note above