Look at it this way:
-- Since the two groups have the ratio of 4 to 7, then the first group has 4 parts
and the other group has 7 parts.
-- If the first group has 4 parts and the other group has 7 parts, then they have
11 parts all together.
-- Those 11 parts are all parts of 33. There must be ( 33 / 11 ) = 3 items in each part.
Now you can go back to the groups . . .
-- The first group has 4 parts.
With 3 items in each part, that's (4 x 3) = 12 items.
-- The other group has 7 parts.
With 3 items in each part, that's (7 x 3) = 21 items.
The answer is 0
The formula is
n!/ r!(n-r)!
4!/ 9!(4-9)!
<h3>
Answer: -2</h3>
===============================================
Explanation:
We use the remainder theorem. This is the idea where if we divide P(x) over (x-k), then the remainder is P(k).
Comparing x+1 to x-k shows that k = -1
It might help to rewrite x+1 as x-(-1) to get it into the form x-k better.
Plug this k value into the function
f(x) = 2x^6 + 3x^5 - 1
f(-1) = 2(-1)^2 + 3(-1)^5 - 1
f(-1) = 2(1) + 3(-1) - 1
f(-1) = 2 - 3 - 1
f(-1) = -1 - 1
f(-1) =-2
The remainder is -2
We can confirm this through synthetic division or polynomial long division.
There are several approaches.
(5/3)x^2 - 5 = 0 has the coefficients a=5/3, b=0 and c = -5.
Thus, the quadratic formula would be appropriate here:
-0 plus or minus sqrt(0^2 - 4(5/3)(-5) )
x = -------------------------------------------------------
2(5/3)
plus or minus sqrt(100/3)
= ------------------------------------
10/3
3 10
= ------* ----------- = sqrt(3) (answer)
10 sqrt(3)
