Solution :
We have to prove that 
(De-Morgan's law)
Let 
then 
and 
and so 
and 
.
Thus, 
and so 
Hence, 
.........(1)
Now we will show that 
Let ⇒
Thus x is present neither in the set A nor in the set B, so by definition of the union of the sets, by definition of the complement.
and 
Therefore, 
and we have .............(2)
From (1) and (2),
Hence proved.
1. second option
2. first option
Answer:
- x = 4
- length = 19 ft
- width = 11 ft
Step-by-step explanation:
The area is given by the product of length and width.
A = LW
209 = (4x +3)(4x -5)
209 = 16x^2 -8x -15
224 = 16x^2 -8x
You could rearrange and use the quadratic formula at this point, but we elect to "complete the square".
14 = x^2 -(1/2)x
14 +1/16 = x^2 -1/2x +(1/4)^2 . . . . . add the square of half the x-coefficient
(x -0.25)^2 = 14.0625
x = 0.25 ± 3.75 . . . . . . take the square root; add 0.25
Only positive values of x are useful here, so we have
x = 4
Then the dimensions are ...
length = 4x +3 = 4(4) +3 = 19 . . . feet
width = 4x -5 = 16 -5 = 11 . . . feet
Answer:
$270
Step-by-step explanation:
Multiply 1000 by .03 or 3%. Then mulrioly that number by 9 because it is that amoint of interest for nine months.
