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I guess just hanging around here, coding, playing with puzzles...

being an only child sucks. :(

Our equation will be--

30000 * 8.0 * 105 

=(25200000) * 105 

=(2.52 * 10^5) · 105

The answer will be  $2.52 * 10^10

Hope this helped!

Let

x=first number

x+6=second number

(x + 6)^2 - x^2  = 132  

x2 + 12x + 36 - x^2- 132 = 0   

12x + 36 = 132 

12x = 96 

x = 8    and    x + 6 = 14

Therefore, the numbers will be 8 and 14.

Hope this helped!

Thanks so much, jfan! That's impressive!

Name the quadratic you try to find as :

\(x^2+ax+b\)

Next we define the roots as:

x1 and x2

By vietas formulas:

x1 + x2 = -a

x1 * x2 = b

Since we know that the roots are one more than the last two coefficients respectively, we have:

x1 = a + 1

x2 = b+ 1

Substituting back in, we get:

a + 1 + (b+1) = -a

a+b + 2 = -a

2a = -b-2

a = -b/2 - 1

(a+1) * (b+1) = b

(-b/2 -1 + 1) * (b+1) = b

(-b/2) * (b+1) = b

(-b2/2 - b/2) = b

b2/2 + b/2 = -b

Dividing by b on both sides, we get:

b/2 + 1/2 = -1

b/2 = -3/2

b = -3

plugging back into our first equation, we get:

(a + 1) + (-3 + 1) = -a

a + 1 -2 = -a

a -1 = -a

2a = 1

a = (1/2)

our two roots are 1/2 and -3

Thanks!!!

You multiply 1 by 0 first and then get 4(1) which is 4

Anytime 

Thank you!

Nice, Chris!!!!

Thank you!

Hint:

The numbers which add to give -3 HAVE TO BE positive and negative.

identify the centere and radius. then sketch the graph

1. x^2+y^2-4x-14=0

Cmplete the square on x   and  we have that

(x^2  -4x  + 4)  + y^2  =  14  + 4

(x - 2)^2  + (y - 0)^2  = 18

The center  is  ( 2, 0)

The radius  =  √18

Nice, CPhill!

We know that the position of the vice president must be chosen by one of two already chosen.

For president, we have 15 possible opted, for the second position, vice president -

For secretary, we only have 14 options, since one was chosen for president, for the position vice president

For treasurer, we will have 13 options, and finally, 2 possible options for vice president, either the treasurer or the secretary,

The number of ways in which the committee can be chosen will be---

15*14*13*2=5460

Here's a couple  :

1. If the  ends of a diameter  are  11,-6)  and (1,14)   then the  midpoint  is the  center of the circle

So   we  have that     [ (11 + 1) / 2  , (14 - 6)/2 ]  =  [ 12/2, 8/2 ]  = (6, 4)  is the  center

And  the  radius^2 can be computed as    [ ( 1 -6)^2  + (14 -4)^2 ] =   [ 5^2  + 10^2]  = 125

So...the  equation of the  circle  is

( x - 6)^2  + (y - 4)^2  =125

x^2  - 12x + 36  + y^2  - 8y  + 16   =   125

x^2  + y^2  - 12x  - 8y  - 73    = 0

This is 4.

Since 1+1+1+1+0=4.

Nice, Chris!!!

(a)   longer than 11 inches

[ 11 - 10]

________  =      1/4  = .25

      4

The  percentage associaed with this z score  is   .5987

So approx   1 - .5987  =  .4013  ≈  40.13%   fish are longer than 11 inches

(b)  shorter than 8 inches

[ 8 - 10]

_______  = -1/2  = -.50

      4

The percentage associated with this z score is  .3085

So.....the   number of  fish  out of 400  that  are shorter than 8 inches =

400 (.3085)  ≈   123