For the third one, we can use synthetic division to find the remainder
We are testing if 1/2 is a root
1/2 [ 6 11 -3 ]
3 7
____________
6 14 4
The remainder is 4
2x^2 - 3x + 4
x + 2 [ 2x^3 + x^2 - 2x + 8 ]
2x^3 + 4x^2
___________________
-3x^2 - 2x
-3x^2 - 6x
4x + 8
______
x^2 - 2x + 4
x + 2 [ x^3 + 0x^2 + 0x - 4 ]
x^3 + 2x^2
_____________________
-2x^2 + 0x
-2x^2 - 4x
_______________
4x - 4
__________
- 12
x^2 - 2x + 4 - 12
_____
x + 2
5 [ 2 - 1 4 ]
10 45
2 9 49
Flip the coin 10 times...let any 8 outcomes be heads = C(10,8) = 45 sequences
Flip the coin 10 times, let any 9 outcomes be heads = C (10,9) = 10 sequences
Let all 10 outcomes be heads = 1 sequence
So.... 45 + 10 + 1 = 56 sequences
x = ounces of nuts
2x ounces of raisins
x + 2x = 24
3x = 24 divid both sides by 3
x = 8
2x = 2(8) = 16 ounces of raisins
Yep !!!!
We can arrange the Spiderman comics in 6! ways. the Archie comic books in 5! ways and the Garfield comic books in 4! ways
And we can arrange these groupings in 3! ways
So
( 6! * 5! * 4! ) * 3! = 12,441,600 different orders !!!
Here's the second one
A horizontal line has "0" rise and an infinite run
So the slope is
0 / run = 0
Thanks EP...another way
[ "Old" area ] x scale factor^2 =
20 x 20.5 ^2 =
8405 in^2
