Let 3<em>n</em> + 1 denote the "number" in question. The claim is that
(3<em>n</em> + 1)² = 3<em>m</em> + 1
for some integer <em>m</em>.
Now,
(3<em>n</em> + 1)² = (3<em>n</em>)² + 2 (3<em>n</em>) + 1²
… = 9<em>n</em>² + 6<em>n</em> + 1
… = 3<em>n</em> (3<em>n</em> + 2) + 1
… = 3<em>m</em> + 1
where we take <em>m</em> = <em>n</em> (3<em>n</em> + 2).
1) The given equation is 3x-3y=15
To solve for y we subtract 3x both sides:
3x-3x-3y=-3x+15
-3y=-3x+15
With y term -3 is multiplied .We perform the opposite operation both sides that is divide by -3 both sides we have:
y=x-5
Option A :y=x-5 is the right answer.
2) |2x-1|=3
We can remove the absolute sign by forming equations taking both the positive and negative signs:
2x-1=3 or 2x-1=-3
Solving the two equations for x:
2x=3+1 or 2x=-3+1
2x=4 ,x=2. 2x=-2 , x=-1 .
Option a)x=2 or x=-1 is the right answer.
3) 2< 3x-1 ≤ 5
Adding 1 to all the sides we have:
3<3x≤ 6
Dividing by 3 :
1<x≤ 2.
There are five hundred and one more pennies than nickels
Answer:
B
Step-by-step explanation:
B
Answer:
11
Step-by-step explanation:
5 1/2 x 2= 11
