ElectricPavlov

Vertex (3,2) form of a parabola

y = a(x-3)^2 + 2   sub in point 1,0 to calculate a

0 =a(1-3)^2 + 2        a =-1/2

y = -1/2 (x-3)^2 + 2       Now expand and put into form   ax^2 + bx + c    to get your final answer

8 = 20 (1-.5)^t      Where t = # of half lifes

t = 1.3219 half lifes

1.3219 x 1620 = 2141.5 yrs

Plug in the data to see which equation works

example    5 boxes   = 20.40

    second equation

         5* (3.6) = 18        18 does not = 20.40   so second equation is NOT the answer.....try the others to find the correct one

                                            always a good idea to try one of the other data sets when you think you have the right eqution as a check

112 = 7 * 2 * 2 *2 * 2

98 = 7 * 7 * 2

Slope, m,  of given line is -3/4       perpindicular is  - 1/m    =   4/3

A  and C have slopes of  4/3     ....   plug in 12,9   to see which equation it is.....

(6*12^0 + 10*12^1  +  4 * 12^2  + 1 * 12^3 )         -       ( 9*12^0   + 11*12^1  + 5* 12^2 )

Then convert the result  back to base₁₂

87 coins total

x = nickels

  then   87- x = quarters

value

5 x     +   25 (87-x)   = 1395            solve for 'x' = number of nickels   then quarters = 87-x

3x^2-18x+55                           divide first part  by 3

3 ( x^2-6x)   + 55                    'complete the square'

3 (x^2 -6x +9)    -9    + 55       simplify

3 ( x-3)² + 46      You can finish......

Draw a V enn diagaram and complete it to find 81 dogs in the school

a 2^r = 1      and   a 64^r = 4

2^r = 1/a                   (2^6)^r = 4/a

                                 (2^r)^6 = 4/a

                                   (1/a)^6 = 4/a

                                    1 = a^6 * 4/a  = 4a⁵ 

                                            a = (1/4)^1/5 = .757858283

then    a 64^r = 4

.757858283 *  64^r = 4   

     r = .4