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Not sure if this is correct but, if every 5th person gets a free hat and every 7th person gets a free shirt than we multiply 7 by 5 for the lcd and 7*5=35 and 632/35=18.05=18 so the answer is 18.

The graph is a circle with radius sqrt(28), so the area is 28*pi.

I believe you have read the answer on that site incorrectly.  

That site does not claim the answer to be 40

Hi DragonLord,

Welcome to the Web2.0calc  forum

I would help you but I am not good with conics.

If you do not get a timely answer you could try asking Heureka, Omi, or Geno direct.

Others may also be able to help though. 

Thank you so much for your time into doing these problems, but an explanation would be delightful. As much as I like answers, the explanations are more amusing. I would love one if someone doesn't mind.

The maximum value is 16/3, which you get when x = y = 4/sqrt(3).

How about smartmouthfool?

But I will think on it if you want.

You have definitely made a total fool of yourself. Not just a partial one. 

ok I get it. PartialMathematician, PartialFool....

But it still does not fit for you.

Maybe

PartialMathematiciansmoron but PartialMathematician may not want to be linked to you for ever.

PartialMathematiciansidiot.

PartialMathematiciansfool.      That one is not too bad. 

PartialMsFool                          Maybe that one.  Yea that seems ok.

PartialMsTotalFool

Actually the fool in a yesteryear King's court was the only person who could get away with criticising the King, whether he was a idiot or not.  He usually kept his head, in a literal sense, when others did not.  So maybe being PM's fool might appeal to you. Everyone else on the forum will either know or not care where the name comes from but you can live in a make believe world thinking you are a witty intelligent fool.

A quadratic equation can have exactly one solution if it is a perfect square.

(2x + 7)(x - 5)  =  -43 + jx

2x² - 10x + 7x - 35  =  -43 + jx                                   [multiply out]

 2x² - 3x - 35  =  -43 + jx                                            [simplify]

2x² - 3x - jx - 35 + 43  =  0                                         [subtract -43 + jx from both sides]

 2x² - (3 + j)x + 8  =  0                                               [factor and simplify]

2[ x² - ( (3 + j)/2 )x + 4 ]  =  0                                     [factor out the 2]

x² - ( (3 + j)/2 )x + 4   =  0                                          [divide both sides by 2]

Now:  x² - 4x + 4  =  (x - 2)²  =  0     and     x² + 4x + 4  =  (x + 2)²​  =  0      will have one real solution each.

So:  either  (3 + j)/2   =  4     or      (3 + j)/2   =  -4

Solving:       3 + j  =  8          or         3 + j  =  -8

                          j  =  5         or               j  =  -11

I think this is a computer coding assignment. Because there are 900,000 numbers to be checked !! Even if you were to narrow it down to just the multiples of 1009, you would still have almost 900 numbers to check !!.

They have to sell enough to cover the set up fee ($ 75) plus the cost of the shirts ( $ 3/ea)

Break even #    will b found   as  'x'

$ 18 x  = $ 75 + $ 3x       Solve for x the number of shirts that must be sold     75 + 3x is the cost in $

The possible values of j are 7 and -2.

bro chillll. This is a math forum right? 

Let the two numbers be x and y.

The square of x+y is x^2+2xy+y^2 and that is 144

The sum of x^2 and y^2 is 180. 

So you can get from substituting the second equation to the first and you get

180+2xy=144

So 2xy= -36

xy= - 18

And x+y = 12 or -12

because 12^2 or -12^2 is 144.

(x-y)^2 is x^2-2xy+y^2 which is 180 +36 or 216

So x-y equals 6sqrt6, or -6sqrt6. 

Adding and dividing be 2

gives x = 6 + 3sqrt6 and y= 6 - 3sqrt6

And your done

By: GF

A car and truck are 540 miles apart. The two vehicles start driving toward Each other at the same time. The car drives at a speed of 65 miles per hour, and the truck travels at a speed of 55 miles per hour. At which point will they both meet.

250000 in standard form? 

A typical calculator doesn't display exponents, so if the number of digits in the number exceeds the capacity of the calculator display, then instead of showing 2.5 • 10⁵ it would show as 2.5 e5.  The "e" meaning that that's the exponent of ten.  

_.

Thank you; but for the first one i got 6. Can you tell me how you got 4?

You mean "at what TIME will they meet"

Let the time it takes for them to meet =T hours

65T   +   55T =540, solve for T

T =4.5 hours when they will meet after their start time.

Thanks, but I could look in the back of the book for the bare answer. 

The help that I really need is to know how the answer is calculated / derived.

4 ways

Change1: 3/4

Change2: 9/16

Change3: 27/64

Change4: 81/256

Change5/ 243/1024

...............................

Change n:  3^n/4^n

(B)

thank u so much!

Omi67:

There are 19 "sevens" between 10 - 99.

17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 87, 97 =19 "Sevens"

There are 300 "sevens" between 1 and 999.

1. p = 4/3

2. The distance between the foci is 4*sqrt(2).

Guest, do you seriously know how you are talking to. If you really had some appreciation for learning, maybe you'd see our answerers in a better light. It's not the answers that matter, it's the process.

Actually, the correct answer is 40 according to AOPS: https://artofproblemsolving.com/wiki/index.php/1985_AJHSME_Problems/Problem_24

38 

I did it as follows: 

                                                    11

                                               12      14

                                            15     10     13 

Each side adds up to 38