prove or disprove:
a) any positive integer can be written as the sum of the squares of two integers
b) for every integer n, the number 3(n2 + 2n + 3) ? 2n2 is a perfect square

Step-by-step explanation:

a). Let

Now since is a square of an integer, its value is 0.

Therefore, ≥ 0, since x is an integer

where = 1,2,3,...

and x = 1

But as x = ,... cannot be integer

∴

              = 1.732      which is not an integer

Thus, any positive integer cannot be written as the sum of the squares of the two integers.

b). Let n be an integer

∴

On solving we get,

which is a perfect square

Hence proved.

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

5   1/4   miles per hour

step-by-step explanation:

15   3/4 / 3 = 5   1/4