Answer:
The length and width are 11ft and 5ft respectively
Step-by-step explanation:
let the
length = L
Width = W
Area = LW = 55
The length is nine feet less than four times the width
L = 4W - 9
W (4W - 9) = 55
4W^2 - 9W -55 = 0
4W^2 - 20W + 11W - 55 = 0
4W(W - 5) + 11(W - 5) = 0
(W - 5)(4W + 11) = 0
W - 5 = 0 , 4W + 11=0
W = 5 or - 11/4
since the width cannot be negative, W = 5
LW = 55
L = 55/5
L = 11
The length and width are 11ft and 5ft respectively.
There are 64 people in the room.
Since the ratio for women increases 1 when 8 women enter the room, for every time there is 1 in the ratio there are 8 people. That means that originally you have to do 3x8 and 4x8. You get 24 and 32 which equals 56. Then when 8 more women enter the room, you get 64.
Answer:
![\[\sqrt{5}\]](https://tex.z-dn.net/?f=%5C%5B%5Csqrt%7B5%7D%5C%5D)
Step-by-step explanation:
The given vector is represented by (2,-1).
This can be represented in general form as (x,y) where x=2 and y=-1.
Magnitude of the vector represented as (x,y) is given by ![[\sqrt{x^{2}+y^{2}}\]](https://tex.z-dn.net/?f=%5B%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%7D%5C%5D)
Evaluating for the given values of x and y,
![\[\sqrt{2^{2}+(-1)^{2}}\]](https://tex.z-dn.net/?f=%5C%5B%5Csqrt%7B2%5E%7B2%7D%2B%28-1%29%5E%7B2%7D%7D%5C%5D)
![\[=\sqrt{4+1}\]](https://tex.z-dn.net/?f=%5C%5B%3D%5Csqrt%7B4%2B1%7D%5C%5D)
![\[=\sqrt{5}\]](https://tex.z-dn.net/?f=%5C%5B%3D%5Csqrt%7B5%7D%5C%5D)
Length of the vector is
60
D>0, there are 2 distinct real roots
Explanation:
3x2+6x−2=0
a=3,b=6,c=−2
The formula for discriminant is b2−4acSubstitute the given values.
b2−4ac
(6)2−4(3)(−2)
=60
therefore, D>0, there are 2 distinct real roots
