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2x+4y=8. xy=-8 is not necessary to solve this problem

A guest has answered it.  Thanks guest.   I hope you thank guest too.

I probably would not have answered it.  Your 'request' sounds really rude.

Anyway, that question is ancient...

What calculator?  I don't think it is on the web2.0 calc

AoPS have a strict policy that you are not to ask their questions on other sites.

Please respect the policies and possibly the copyrights of your educator.

You should be able to work it out from this pic.

Given:

Ratio of wallet & bags = 5:7

Wallet cost = $13.30 more than a bag

Total spenditure by company = $9.065

Total cost of wallet = 17/20 of total cost of bag

To find:- Cost of one wallet

Let cost of one bag is y 

Cost of wallet = $(13.30+y)
No of wallets         5

------------------ =  ------ = Let 5x/7x

No of bags            7

Total cost of bag = 7x * y

Total cost of wallet -(13.30+y) * 5x

Now Total cost of wallet = 17/20x Total cost of bag

                 (13.30+y) * 5x = 17/20 * 7y

                  (13.3+y) * 100 = 119y

                   1330 + 100y = 119y

                       1330 = (119-100)y

                         19y = 1330

                             y = 70

So Cost of one bag = $y = $70

Cost of one wallet = $(13.30 + y) = $(13.30 + 70)

                              = $83.30

The common difference of an arithmetic sequence is the difference of any two consecutive numbers. The nth term of a sequence, in this case the 27th term, is equal to, (the common difference multiplied by n-1) + the first number in the sequence. Since the common difference in this arithmetic sequence is 10-1=9 or 19-10 = 9, and the first term in the sequence is 1, the 27th term will be 9*(27-1) + 1 = 9*26+1 = 235 :)  

Oh fudge, I made a mistake in my explanation.   

On line 4, that should be "Let's add (6.4 m/sec2) • (t) to both sides."  

I did it right, I just said it wrong.  Why don't I find theses things before it's too late to edit....

_.

Let x be no of buttons Ryan had

Then

        No of Blue buttons = 3/7x * = 3x/7

=>    No of Green Buttons = x - 3x/7 = 4x/7 -(3)

Ryan gave away buttons = 2/5x * = 2x/5

Buttons Left = x - 2x/5 = 3x/5

Given away button = 2x/5

Blue given away = 80

Green give away = 2x/5 - 80 -(2)

Green button left = 2/3x(3x/5) = 2x/5 -(1)

Green Button Left + Given button Givrn away = Total Green Button 

So (1),(2),(3) we have 

2x/5 + 2x/5 - 8o = 4x/7

        4x/5 - 4x/7 = 80

          28x-20x/35 = 80

                     x = 10×35

                     x = 350

Total Buttons Ryan had = 350

Felipe drives his car at a velocity of 28 m/s. He applies the brake, which slows the vehicle down at a rate of 6.4 m/s2 and causes it to slow to a stop. How long does it take for the car to stop? Round your answer to the nearest tenth.     

What we want is for the velocity to equal 0 m/s.  

(Initial velocity) minus (acceleration times time) = 0  

28 ^m/_sec – [(6.4 ^m/_sec²) • (t sec)]  =  0    

Let's subtract (6.4 ^m/_sec²) • (t) from both sides.  

28 ^m/_sec  =  (6.4 ^m/_sec²) • (t)  

Divide both sides by (6.4 ^m/_sec²)     This is going to be tricky. 

                                                        I'm going to call sec² sec-sec so I can cancel one of them    

Dividing by a term is the same as multiplying by the inverse of that term.  

 28    meter         1    sec-sec 

–––  –––––   •   –––  ––––––  

  1      sec          6.4    meter  

Cancel units  

28   meter         1    sec-sec           28 sec 

––– –––––   •   ––– ––––––    =    ––––––           =   4.375 sec, rounds to  4.8 sec    

  1     sec          6.4   meter               6.4  

_.

oops, my eyes must have crossed, I typed a p instead of a q    

The above should be  

                               (x + 4)(x – 1)     q = –4  

                               (x + 5)(x – 2)     q = –10  

                               (x + 6)(x – 3)     q = –18  

                               (x + 7)(x – 4)     q = –28  

                               (x + 8)(x – 5)     q = –40  

The length of a rectangle is increasing at a rate of 4 inches per second while its width is decreasing at a rate of 3 inches per second. At what rate, in square inches per second, is the area of the rectangle changing when its length is 23 inches and its width is 18 inches?

We are not given a start point but I only care about the rates so where it starts, I mean at what size, doesn't matter.

So I am going to say that at  time 0 the length is 23inches  and the width=18 inches

When t=0   L=23,  w=18

\(\frac{dw}{dt}=3\\ so\quad w=3t+18\\ and\\ \frac{dl}{dt}=4\\ so \quad l=4t+23\\ A=wl \\ A= (3t+18)(4t+23)\\ A=12t^2+(69+72)t+(18*23)\\ A=12t^2+141t+(18*23)\\ \frac{dA}{dt}=24t+141\\ when \;\;t=0\\ \frac{dA}{dt}=141\;\;inch/sec\)

LaTex:

\frac{dw}{dt}=3\\
so\quad w=3t+18\\
and\\
\frac{dl}{dt}=4\\
so \quad l=4t+23\\
A=wl \\
A= (3t+18)(4t+23)\\
A=12t^2+(69+72)t+(18*23)\\
A=12t^2+141t+(18*23)\\
\frac{dA}{dt}=24t+141\\
when \;\;t=0\\
\frac{dA}{dt}=141\;\;inch/sec

As the first term is 1, the smallest common difference between the terms is 1 because the terms are all integers.

This series would go 1, 2, 3... 89, 90, 91 ... and so on. 

\(91 \cdot (1 - \frac{4}{7}) = 91 \cdot \frac{3}{7} = 39\)

Thus, Tom had 39 cards left. 

or

6 to the 10th power X 67

10=14 (base 6)

67= 36+31 = 36+5*6+1 = 251 (base 6)

6 to the 10th power X 67 = 251 * 10^14 (base 6) =  2.51 * 10^20   (base 6)  

I am going to assume we are looking nly for real solutions.

sqrt(6y + 2)/sqrt(2y + 2) = 5/2

\(\displaystyle \frac{\sqrt{(6y + 2)}}{\sqrt{(2y + 2)}} = \frac{5}{2}\\ \)

First you need to recognize that  2y+2 must be > 0

y > -1

square both sides

\(\displaystyle \frac{(6y + 2)}{(2y + 2)}= \frac{25}{4}\\ \)

Can you take it from there?

The question is asking you to answer this.

For what x value is f(x) = g(x)

Does that help?

Hi Straight,

Thanks but I am trying to get people to present their own questions properly.

If they cannot be bothered to present their question properly it usually would mean they are also too lazy to learn from any answer given.

x^2 + px + q = 0 has one negative solution and one positive solution.  If p = 3, then what are all the possible values of q?    

In other words         x² +3x + q = 0   

                               (x + 4)(x – 1)     p = –4  

                               (x + 5)(x – 2)     p = –10  

                               (x + 6)(x – 3)     p = –18  

                               (x + 7)(x – 4)     p = –28  

                               (x + 8)(x – 5)     p = –40  

I must not understand the question, because this could go on forever and  

you couldn't write down all of them if you keep writing until the end of time.  

_.

The ninth and tenth terms of an arithmetic sequence are 1/4 and -1/3, respectively. What is the second term?   

Let's use a common denominator so all we have to worry about are the top numbers.    

Try 12 as the common denominator, which would be 3/12 and –4/12    

So it looks like the change from any term to the next term is –7/12.  

Let's work backwards, 10^th term, 9^th term, and keep adding 7/12 (since we're going backwards) 

10    -    –4/12     add 7/12 to this to get the 9^th term  

  9    -      3/12     add 7/12 to this to get the 8^th term  

  8    -    10/12  

  7    -    17/12  

  6    -    24/12  

  5    -    31/12  

  4    -    38/12  

  3    -    45/12  

  2    -    52/12     unless I've bungled terribly, 52/12 is the 2^nd term, or 4⁴/₁₂  which reduces to  4¹/₃  

_.

2p + 187 = 507

2p = 320

p = 160

caitlin = 347

hope this helps because i dont understand the qustion

this is 4,051,233,792

5.55 moola. I know dat may sound steep but it's one of those special blends. See, I'm not well. Things have been rough for me. I only get a .25 of a moola from every 4th person that walks by. I got .45 moola already. I need ta know how many people will have to pass by before I can get a drink...UUURRR I mean coffee?"

You need 5.55 moola for a drink coffee. 

You already have 0.45 moola, so you need 5.10 more moola.  

At 0.25 moola per pop, you need (5.10 / 0.25) = 20.4 pops.  

Since your pops come in quanta of 4 peeps, and not fractions, you need 21 pops.  

(21 pops) x (4 peeps per pop)  =  84 more peeps must pass by  

_.

Would be 70280 (not 2009!) , but that's still wrong.

Straight