All Answers 357330 Answers

One possibility is as follows:

(of course, I've made up arbitrary rankings for the 10% table above; you would need to replace these with your actual rankings).

Look more carefully!!

792*14 = 11088

792*15 = 11880

Happy birthday Hectictar. I hope you are having the best day ever!   

Where is the pic??

This is almost identical to the one I just did so have a go at it yourself :)

I've never heard the term multiplicity used like this before but i am assuming this is what you are after:

$y=a(x-7)^2(x+5)^3 \\through\;\;(6,2662)\\ 2662=a(6-7)^2*(6+5)^3\\ 2662=a(-1)^2*(11)^3\\ 2662=a*1331\\ a=2\\ y=2(x-7)^2(x+5)^3$

You would use this formula to calculate the monthly payment:

PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}

PMT=15,995 x 0.089/12{[1 + 0.089/12]^(5*12) / [1 + 0.089/12]^(5*12) - 1}

PMT =15,995 x 0.00741666{[1+0.00741666]^60 /[1.00741666]^60 - 1} 

PMT =118.62958333[ 1.557929826865] / [0.557929826865]

PMT =   118.62958333   x        2.792340096995.............

PMT =$331.25 The monthly payment for this loan.

Hi Hectictar, happy birthday.....i was actually at a bakery to buy your cake but then CPhill told me he already bought you one...so i thought to buy you gifts from all of us...your beloved forum....

here they are....hope you like them!

Hope you have a blasting day......happy birthday !

Lat the original number =a. Then we have:

1/a + 1 = 7/3

(1 + a) / a =7/3     cross multiply

3 + 3a =7a              subtract 3a from both sides

3 = 7a - 3a

3 = 4a                      divide both sides by 4

a = 3/4 - The original number

Thanks, X².....your method is easiest.....

Here's an algebraic solution.....

The x coordinate of the vertex  is    -b/ [ 2a]....so we have

-b/ [2a]  = -6

b = 12a

And we know that

a(-6)^2  + 12a(-6)  + c   =  -14

36a  -72a + c   = -14

c = 36a - 14

And since 17  is a root.......we have that

a(17)^2  + 12a (17)  +  [ 36a - 14 ] =  0

289 a + 204a  + 36a  = 14

529a  =  14

a  = 14/529

b = 12a  = 168/529

c = 36 a - 14  = -6902/529

So.......our function is

f (x)  =  (14/529)x^2  +  (168/529)x - 6902/529

Set this to 0   and multiply through by 529 and we have that

14x^2   + 168x  - 6902  =  0      divide through by 14

x^2  + 12x - 493  = 0   and this factors as

(x - 17) (x + 29)  = 0

Setting the two linear factors to 0 and solving for x gives the two roots  x = 17  and x = -29

Just as X²  found......!!!!!

At first, I was unsure how to go about this problem. However, I think I have found a pretty easy way to find the "solution."

First of all, let's consider some properties about quadratics when graphing. One thing we know is that there exists an axis of symmetry. This means that if the quadratic were reflected over the axis of symmetry, then the same graph would result. Since this is true, this means that the roots are equidistant from that axis of symmetry. If this does not make any sense, then maybe this rough sketch of a parabola will help you out!

Let's find the distance between (-6,0) and (17,0). All you have to do is subtract the x-coordinates. It happens to be 23. This means that the other root is 23 units in the other direction. -6-23=-29. This means that (-29,0) is where the other zero is located.

Happy Birthday Hectictar!

Cphill and Mr. BB  are spot on. You are an asset and bright light on the forum. I too believe that you are this to everyone who knows you and for many others who do not.

Let's go through the process again, shall we?

Let x represent one of the numbers. Then 15-x is the other number. Knowing this, the equation becomes $x(15-x)=63$.

This means that no quadratic equation with real solutions can have property aforementioned, which is a sum of 15 and a product of 63.

Therefore, x=0 is the solution to the equation.

Happy Birthday. I wouldn't have known.

Nobody knows.......most of our answers on here are only rough guesses......

Thank you very much. I understand it now.

Look at the right side

   1 / (x - 1)  + 1

Note that we can write 1  as    (x - 1) / (x -1)

And  we have

1 / (x -1)  + (x -1) / (x - 1)     so we have a common denominator

So we have

[   1   + ( x - 1) ]  / ( x - 1)  =

[ 1  +  x  - 1 ] / ( x - 1)  =

x / (x - 1)  = the left side

Happy birthday indeed. You are one of the brightest lights on this forum!! Many, many returns.

Wow! You baked that cake so fast you ought to work at a bakery!!!

It tastes super good too!!

Thank you, I really really appreciate it!!! 

The inside is yellow too! Yummy!!! 

The distance that the bus travels each minute is  42/60 miles.....and it has a 15 minute head start

So....in 15 minutes....the distance that your mother will have to close to catch the bus is     

(15) * 42/60  miles  

The distance that your mother travels each minute is 72/60 miles

So......the time it will take to catch the bus is given by

( 72/60 - 42/60) T  = 15 * 42 / 60

(30/60)T = 15* 42 .60      multiply through by 60

30T   =  15*42   divide both sides by 30

T = (1/2) 42

T  = 21  minutes

So.....15 minutes after 7:18 AM is 7:33AM....and 21 minutes after this is 7:54 AM....and this is when she will overtake the bus

Your explanation is just fine, Gh0sty.....!!!!

This might be a horrible explanation, but I'll try. 

First, we know that the ratio is 3:5. 

You can also think of this ratio as 3x:5x.

3x+5x=8x. Make this equation: 8x = 72(total). 

x=9. 

3x would be the part that represents the pink marbles, so plug in 9 for x.

3(9)=27.

There are 27 pink marbles.

According to the order of operations, you have to solve multiplication first before you do addition or subtraction. In your math question, the first step should be 2*8*2=32,and then 9+32-12=29. 29 is the final answer.