CPhill

Note that the numerators are just the set of odd numbers starting with 1. The denominators are the set of perfect squares starting with 1.

The nth term is given by:

[2n - 1] / n²

If we want an "exact" answer, we have

√18 +√128 =

√(9*2) + √(64*2) =

3√(2) + 8√(2) =

11√2

Melody had "m" points on Monday afternoon......then, she answered several questions and got 25 more points. Her point total that evening was m + 25.

(However, because of the site administrator, by Tuesday morning, she had m - 1000 points.... )

-4x²y * -9x²y³  =

(-4)(-9) * (x²) (x2) * (y) (y³) =

36x⁴y⁴

Here's a rather odd method of determining this....but it works!!! It's called the  "Sieve of Eratosthenes"

First take the smaller given number and subtract it from the larger......so we have......

20 - 8   = 12   ........Now, does 12 divide both 8 and 20???  Nope.  Now, compare what we subtracted (12) and the result we obtained (8) and, again, subtract the smaller from the larger.

So we have    12 - 8   = 4........Now, does 4 divide 8 and 12?? Yep. And that's our GCF...!!!

Why does this work?? Because if a number divides two subtracted quantities, it also divides their sum. So 4 divides 8 and it also divides 8 + 12 = 20 !!!

Note, if we use this process on two numbers and we end up with a  "1," the numbers are relatively prime to each other. That makes sense......only one non-zero number divides two relatively prime numers....namely, 1 !!

factor 6x^2+11x-10 =

(3x - 2) (2x +5)

"Quotient" means "divide".....so we have

20/5 + 9 =

4 + 9  = 13

√(2.5)  = (2.5)^1/2  in exponential form.....

There are only three solutions to this problem......if he only needs a minimum of 6 notebooks.

He can buy no more than 2 of the $5 dollar notebooks. If he bought 3, he wouldn't have enough money for 3 more, even the cheaper ones !!!!

So, let the ordered pair x, y represent the number of $5 notebooks and the number of $2 notebooks, respectively. So we have:

(x, y) = (2, 4) ,  (1, 5),  (0, 6)......and as AT pointed out, buying 6 of the $2 ones would be the cheapest route.

-l1/3l - l-2/3l =

-1/3 - 2/3   =

-1