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8 minutes is incorrect.

Let the purchase price of each bicycle =P
6P x 1.25 =7.5P - profit on sale of 6 bicycles.
4P x 0.75 =3P - loss on sale of 4 bicycles
7.5P + 3P =10P+2000
10.5P - 10P = 2000
P = 2000/.5
P =4000 rands - price of a single bicycle.
4000 x 10 =40,000 total price of 10 bicycles.
[4000 x 6] x 1.25 =30,000 gross take on sale of 6 bicyles.
[4000 x 4] x 0.75 =12,000 gross take on sale of 4 bicyles.
30,000 + 12,000 = 42,000 gross take on sale of 10 bicycles.
42,000 - 40,000 =2,000 net profit on sale of 10 bicyles.

You are welcome as long as you are not cheating your homework

Ok thanks!

\(11m^3\) simplified is \(\frac{11m}{m^-2}\)  so 11*reciprocal 1/m^2 which is equal to m^2*11m= \(11m^3\)

Ok sweet how about this one with the same directions. 

11m^-5/m^-7

That is SOOOOOO EZ            \(\frac{happynumber}{happiness}\)

6^-6= 1/6^6 because a negative exponent gives you the reciprocal to the exponent power and t^5 is multiplying it so t^5*1/6^6 is equivalent to \(\frac{t^5}{6^6}\)

How does that work though i need to understand it.

For which positive integer values of k does kx² + 20x + k = 0  have rational solutions? Express your answers separated by commas and in increasing order.

Hello Guest!

 \(kx^2+20x+k=0 \)

 \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ a=c=k\\ b=20\\ x = {-20 \pm \sqrt{20^2-4k^2} \over 2k}\\ x = {-20 \pm \sqrt{400-4k^2} \over 2k}\)

 \(x = {-20 \pm 2\sqrt{100-k^2}\over2k}\)

\(k=\{1,2,3,4,5,6,7,8,9,10\}\)

  !

Isn't it 4 times?

isn't it just (t^5)/(6^6)?

*1 and 12 are incorrect it is 8  minutes

Guest, it's obviously not 70. Use your brain. And if you math teacher says 70 is the answer then he/she's obviously incompetent.

Let's say x is the time in hours.

Since it would take 20 more minutes, so we have 20/60 = 1/3.

TRIP____________speed______time___________distance
Actual___________40________x______________40x
Hypothetical_____30_______x+30/40_________30(x+1/3)

So the distances are equal so

40x = 30(x+ 1/3) 

40x = 30x + 10

10x = 10

x = 1

Now let's plug x in. x * 40 = 40 so 40 miles.

Checking...

40 mph for 40 miles means 1 hour, 30 mph for 40 miles means 1 1/3 hour, and 1 hour is 60 minutes, 1 1/3 hour is 80, 80-60 = 20.

Boom.

Guest, use your brain.

If you don't understand anything feel free to ask.

r  is  (32)^1/2   --->   r^1/3  =  [ (32)^1/2 ]^1/3 =  (32)^1/6

When you find theta, you use  tan^-1( 4 / -4 )  =  tan^-1( -1 )

One of the values of  tan^-1( -1 )  is  -45^o  or  -pi/4  -- however --

     for this problem, since the number is 

    -4 + 4i -- which is in the second quadrant, you need to use either: 

if you are using degrees:  -45^o + 180^o  =  135^o

or, if you are using radians:  - pi/4 + pi  =  3pi/4.

12 minutes is incorrect.

Actually, it would take 12 minutes.

I guess it's 81 

70 is not correct. But it would be really helpful if everyone showed their work.