XxAngelGirlxX

24,511 N would be the answer

From SOHCAHTOA, we conclude that sin A = BC/AC and cos A = AB/AC. We have BC/AC=2AB/AC, or BC=2AB. You want tan A, which is BC/AB by SOHCAHTOA. But you have BC=2AB, so BC/AB=2, which is your answer.

Call the  roots  m and  n

By Vieta's Theorem......

ax^2  + bc + c

Sum  of roots   = m + n  =  -b/a  =   3/2       square both sides   m^2 + 2mn + n^2  = 9/4   (1)

Product of  roots  = mn  =  c/a  =  27/2      and  2mn =  27    (2)

So......subbing   (2) into ( 1)   we have

m^2  +  27  + n^2  =  9/4

m^2 + n^2   =   9/4 - 27

m^2  + n^2   =  [9 - 108 ]  / 4   =   - 99 / 4

Let d be the number of dollars that Jeri finds.  Then solving the inequalities, you get d >= 200 and d < 575, so the answer is [200,575).

Two triangles are congruent if they have the same traced outline, possibly up to rotating and flipping. This is equivalent to having the same set of 3 side lengths.

Total 9

Every perfect square which is an odd number can be represented as the difference of two consecutive perfect squares. The odd numbers less than 100 (which is the square root of 10000) should be the answer. So, the answer is 50

Explanation:

Consider (x+1)^2 and x^2 be two consecutive perfect squares.

Difference of those two:

(x+1)^2 - x^2

= x^2 + 2x + 1 - x^2

= 2x + 1 = is an odd number and should also be a perfect square.

For example: consider an odd perfect square : 25

Which can be written as 2(12)+1here, x=12

25 can be written as (x+1)^2 - x^2

= (12+1)^2 - 12^2

= 13^2 - 12^2

= 169 - 144

= 25

I hope you understood.
 

Note that 1400 = 2^3 * 5^2 * 7.

A fraction (reduced to lowest terms) has a terminating expansion if and only if the only prime factors in the denominator are 2 and 5.

In the case of n/1400, we therefore need n to be divisible by 7.

Hence, there are floor(1000/7) = 142 possible values of n.

I hope this helps!

HOPE THIS HELPS!!

We first determine the largest positive integer value of n such that 3^n | 15!. We determine this by counting the number of factors of 3 in the product. There are 5 multiples of 3 in the product, and there is one extra factor of 3 in 9, so there are a total of 5 + 1 = 6 factors of 3 in the product of the first 15 integers. So, for all n between 1 and 6, inclusive, 3^n is a factor of 15!
so it is 6

The value of k is 1/2.

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