Answer:
v = 2
Step-by-step explanation:
You can start by distributing -6:
7v - 20 = -6v + 6
To combine the like x terms, you can add 6v to both sides:
7v - 20 = -6v + 6
+6v +6v
13v - 20 = 6
Now add 20 to both sides to isolate the x term:
13v - 20 = 6
+20 +20
13v = 26
You can divide by 13 on both sides to find v,
13v = 26
÷13 ÷13
v = 2
Answer:
The domain is {3,6,−1,5,−4}
Step-by-step explanation:
1.
He fills 5/6 lb per bag.
If he fills up 6 bags, he will use 6 * 5/6 lb = 5 lb.
Since he gets peanuts in 2-lb bags, he'd use 2 1/2 2-lb bags.
If he fills double that amount, 10 5/6-lb bags, he will use 10 lb of peanuts which is exactly 5 2-lb bags.
Answer: He should buy 5 2-lb bags.
2.
Each board has length x.
He cuts 3/5 of the length.
Each leftover piece is 2/5 of the length, or 2/5 x.
When he puts together several of the leftover pieces, he has 4 times the length of the original board, or 4x.
4x/(2/5 x) = 4x * 5/2 x = 10x
He has cut 10 boards.
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
