geno3141

Start with:  x(2x - 7)  =  3

Solve:          2x² -7x  =  3

              2x² - 7x - 3  =  0   

Use the quadratic formula with a = 2, b = -7, and c = -3:

      x  =  [7 +/- sqrt(73) ] / 4

From this answer, pick out m, n, and p and use these values to get the answer.

Final Amount  =  Initial Amount · (1 + yearly perecentage)^{number of years}

                 72000  =  24000(1 + 0.13)ⁿ

                 72000  =  24000(1.13)ⁿ                              simplify

                         3  =  1.13ⁿ                                           divide both sides by 24000 

                  log(3)  =  log(1.13ⁿ)                                    find the log of both sides

                  log(3)  =  n·log(1.13)                                  property of logs

 log(3) / log(1.13)  =  n                                                 divide both sides by log(1.13)

                         n  =  9.0 years                                     calculator time!

Let  X  be the original number.

Subtract that number from 1   --->   1 - X

Multiply this result by 4:          --->   4(1 - X)

Add half the difference when 6 is subtracted from 10 times the original number:

                                               --->   4(1 - X) + ½(10X - 6)

Final result:                            --->   4 - 4X + 5X - 3   =   X + 1

a)  Let  X = 3:  --->   X + 1  =  4

b)  To find the original number from the answer:  Subtract 1.

My guess is that the maximum will occur when all the variables (except for n) is zero.

This would mean that n = 10 and the maximum value of abs(a - n) = 10.

Each line segment from a red point that goes to either a green point or a blue point has endpoints of different colors.

There are 7 segments from each red point and there are 5 red points, for a total of 35 segments.

Each line segment from a green point that goes to either a red point or a blue point has endpoints of different colors.

There are 8 segments from each green point and there are 4 green points, for a total of 32 segments.

Each line segment from a blue point that goes to either a green point or a red point has endpoints of different colors.

There are 9 segments from each blue point and there are 5 blue points, for a total of 27 segments.

Adding these together, we get 35 + 32+ 27 = 94 segments.

However, we have counted each segment twice, so we need to divide that answer by 2:  47 segments.

Neil's roots were 1 and 6 --->  (x - 1)(x - 6)  =  0   --->   x² - 7x + 6  =  0   --->   c = 6

Chris' roots were -1 and -4   --->   (x + 1)(x + 4)  =  0   --->   x² + 5x + 4  =  0   --->   b = 5

x² + 5x + 6  =  0   --->   (x + 3)(x + 2)  =  0   --->   x = -3   or   x = -2

Yes.

Call the width:  W

Call the length:  L               The length is twice the width:  L = 2W

Call the height:  H              The length is 3 less than the height:  L = H - 3   --->   H = L + 3   --->    H  =  2W + 3

The total surface area = 100.

The total surface ares  =  2LW + 2LH + 2Wh  =  100 

     --->   LW + LH + WH  =  50

Substituting:

     --->   2W·W + 2W·(2W + 3) + W·(2W + 3)  =  50

     --->            2W² + 4W² + 6W + 2W² + 3W  =  50

     --->                                     8W² + 9W - 50  =  0

     --->                                  (8W + 25)(W - 2)  =  0

     --->     W = 2     or     W = -25/8   (impossible)

     --->     W = 2     and     L = 4     and    H = 7

The form is:  LLNNNLL

where "L" represents "letter" and N represents "number".

Replace each L with 26 and each L with 10, and multiply the numbers together.

The can win in these various ways:

 WWW =

WWLW =

WLWW =

LWWW =

WWLLW =

WLWLW =

WLLWW =

LWWLW =

LWLWW =

LLWWW =

In each of the above replace each "W" with 2/3 and each "L" with 1/3, and multiply the numbers together.

Then add these 9 values together to get the final answer.