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
Answer: x = 15
Step-by-step explanation:
8x - 23 is half of 10x + 44
2 (8x - 23) = 10x + 44
16x - 46 = 10x + 44
Subtract 10x from both sides
6x - 46 = 44
Add 46 to both sides
6x = 90
Divide both sides by 6
x = 15
Answer:
8,999,999
Step-by-step explanation:
The sum of 3 consecutive integers will be 3 times the middle one. So, the cube will have factors of 3 and 100,000. The cube must have additional factors of 3² and 10, so will be 90×3×100,000 = 27,000,000.
Since the middle number is 9,000,000, the smallest number is 1 less:
8,999,999
- Find the product of (3a⁴ + 4)²
Use binomial theorem to expand .
To raise a power to another power, multiply the exponents. Multiply 4 by 2 to get 8.