Let n = 0, 1, 2, 3, 4, 5, 6, 7....
When n = 0 then 0^2 + 0 = 0. n = 1 we have 1^2 + 1 = 2. And when n = 2 we have 2^2 + 2 = 6. When n= 3 we have 3^2 + 3 = 12. When n = 4 we have 4^2 + 4 = 20. When n = 5 we have 5^2 + 5 = 30. When n = 6 = 6^2 + 6 = 42. And finally when n = 7 we have 7^2 + 7 = 56. So at n = 1, 2, ...7, ... Our values are = 2, 6, 12, 20, 30, 42, and 56. It is obvious that n is always an even number. Hence n^2 + n is always an even integer for all positive integers.
When n = -1 we have (-1)^2 - 1 = 0 when n = -2 we have (-2)^2 -2 = 2. When n = -3 we have (-3)^2 - 3 = 6. When n = -4 we have (-4)^2 - 4 = 16 - 4 =12. When n =-5 we have (-5)^2 -5 = 20. When n = -6 we have (-6)^2 - 6 = 30. When n = (-7)^2 - 7 = 42. Hence n^2 + n is always even for all integers
Hi there!
The answer is : 0.15p = p - 150
Here's why :
First store :
15% of p is the same thing as saying 15% times p and 15% is equal to 0.15, which explains the 0.15p
Second store:
p is reduced by 150, which explains the p - 150
Since the price of the both stores are equal, it explains why 0.15p is equal to p - 150
There you go! I really hope this helped, if there's anything just let me know! :)
Answer:
Add 8 to the y value of point p, (4, -2 +8)So the location of the second light is on point (4,6)
Answer:
x1 = -1, x2 = 2, x3 = -4, x4 = 0
If it wants everything in terms of what x4 equals then the system is inconsistent since x4=0
Step-by-step explanation:
Once you have it in that reduced row echelon form it's super easy.
The first column is x1, second is x2 and so on.
The first row says x1 + 0x2 + 0x3 + 0x4 = -1, or in other words x1 = -1. You can do this for all the rows.
this does mean that x4 = 0, so if the instructions are saying it wants everything n terms of x4, you can't do that so it is inconsistent.
Answer:
Step-by-step explanation:
The shaded area is the difference of areas of the rectangle and the square.
<u>Rectangle:</u>
- A₁ = (x + 10)(2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50
<u>Square:</u>
- A₂ = (x + 1)² = x² + 2x + 1
<u>Shaded region:</u>
- A₁ - A₂ =
- 2x² + 25x + 50 - (x² + 2x + 1) =
- 2x² + 25x + 50 - x² - 2x - 1 =
- x² + 23x + 49