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principal has given $75

Total cost of trip = $386

price of a pie = $5

5p + 75 ≥ 386

Basically, t is all the divisors of 24. 

There is more than 1 answer.

3) Note that because a year has 1 exta day, you will need to wait 7 years.

But, on 2012 (leap year), we have 2 extra days, so it is \(2009 + 7 - 1 = \color{brown}\boxed{2015}\) 

Thank you!

So it would be all the divisors of 24, which is 1, 24, 2, 12, 3, 8, 4, and 6, so the answer would be 8?

2) \(1989 = 3^2 \times 13 \times 17 \), so \(\color{brown}\boxed{3}\) prime divisors. 

0x7=7

1) \({19 \over t} + {5 \over t} = {24 \over t}\). 

For t to work, it must be a divisor of 24.

Hello ambermoe!

\((-3)^{-3}=\dfrac{1}{(-3)^3}=\color{blue}-\dfrac{1}{27}\)

  !

A square sand box has an area of 75 square feet .

Estimate the length of one of the sides of the sand box  

          8 squared is 64  

          9 squared is 81 

So the answer is between 8 and 9. 

Refine this further.  Check halfway between them. 

8.5 is easy to square.  8.5² = 72.25 

So the answer is between 8.5 and 9   That's what they call an "estimate"  

_.

is 71 a prime n.o    

Yes  

If you doubt this answer, refute it by providing an example of  

any number that will divide into 71 evenly, except 1 of course.  

_.

The formal definition of 1/0 is undefined.  Seriously. 

_.

thanks its right

thank you

For your other equation you need to do some manipulation first:

results in

If it works, it works. Thank you so much :D

You can do the following  (notice the x=x at the end):

 to get:

I've no idea why this works!!

8.66

\(\phantom{=\quad}\dfrac{x^2+2x^4+3x^6+\cdots+1005x^{2010}}{2x+4x^3+6x^5+\cdots+2010x^{2009}}\)

Factor  x  out of all the terms in the numerator and factor  2  out of all the terms in the denominator to get:

\({=\quad}\dfrac{x(x+2x^3+3x^5+\cdots+1005x^{2009})}{2(x+2x^3+3x^5+\cdots+1005x^{2009})}\)

Now we can cancel out the common factor from the numerator and denominator to get:

\({=\quad}\dfrac{x}{2}\)

gdfngkdfngkj

The difference between  √N  and  10  is less than 2. So the following two inequalities must both be true:

√N - 10  <  2     and      10 - √N  <  2

Looking at the first inequality:

√N - 10  <  2

√N  <  12

N  <  144          ( and   N > 0 )

Looking at the second inequlaity:

10 - √N  <  2

-√N  <  -8

√N  >  8

N  >  64          ( and   N > 0 )

So  N  must be a positive integer in the interval  (64, 144)

That is  79  integers.

nevermind i got it! the answer is 7 for anyone interested :D

x + 1/x = 5.