Check the forward differences of the sequence.
If
, then let
be the sequence of first-order differences of
. That is, for n ≥ 1,

so that
.
Let
be the sequence of differences of
,

and we see that this is a constant sequence,
. In other words,
is an arithmetic sequence with common difference between terms of 2. That is,

and we can solve for
in terms of
:



and so on down to

We solve for
in the same way.

Then



and so on down to


Answer:

Step-by-step explanation:
In rectangle ABCD, AB = 6, BC = 8, and DE = DF.
ΔDEF is one-fourth the area of rectangle ABCD.
We want to determine the length of EF.
First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

The area of the triangle is 1/4 of this. Therefore:

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

Since DE = DF:

Thus:

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

Therefore:

Square:

Add:

And finally, we can take the square root of both sides:

Answer:
go to 100
56 is 56 percent of 100
28 is 56 percent of 50
Step-by-step explanation:
Answer:
x = 7 , y= - 6
Step-by-step explanation:
4x = -2 - 5y ___(1)
4x= 10 - 3y ___(2)
so, now by simultaneous equations,
10 - 3y = - 2 - 5y
2y = -12
y = -6
if y = -6
then, 4x= 10 -3(-6)
4x =28
x = 7
Answer:

Step-by-step explanation:
we know that
The perimeter of rectangle is equal to

In this problem we have


substitute in the formula and solve for L

simplify

