Answer:
(x + 2) (x + 3) = x² + 3x + 2x + 6 = 12 (multiply the binomials)
(x + 2) (x + 3) = x² + 5x + 6 = 12
(x + 2) (x + 3) = x² + 5x + 6-12 = 0 (add the like term and bring the positive 12 to the other side which makes it negative)
x² + 5x + 6 = 0
Using the snowflake method - (finding the factors of 6 that adds/subtracts to give you 5).
This method will give you the factors (x + 6)(x - 1)
ZERO PROPERTY RULE:
(x + 6) = 0
x = -6
(x - 1) = 0
x = 1
The two solutions to the equation are -6 and 1.
Well we know that the perimeters are equal so:
Psquare = Prectangle
we know perimeter for square is the 4 sides of same lengths added up or 4*s
the perimeter of a rectangle is the then4 sides with 2 being equal added up so 2*L + 2*W
we know that a square side equAls s and it says that s=8x. So:
Psqu = 4 * (8x) (substitute 8x for s)
we know that the rectangle L =10x + 8 and W =10. So
Prect = 2 *(10x + 8) + 2 * (10)
we know :
Prect = Psqu so:
4 * (8x) =2 *(10x + 8) + 2 * (10)
32x = 20x + 16 + 20
12x = 36
x = 3
So if x equals 3 we can sub x in for square perimeter
Psqu = 4 *(8 * 3)
P = 4 * 24
P = 96
we can check this with rectangle perimeter
P = 2 *(10 * 3 + 8) + 2 *10
P = 2 * 38 + 20
P = 96
Answer: 63 < N ≤ 66
Step-by-step explanation:
We have the set:
(66, 64, 65, 66]
First.
When we have an end with the signs "(" or ")" means that the element near the sign does not belong to the set, this would be an "open" end. Usually used for the symbols > and <
While the sign "[" or "]" (in some cases the symbols { and } are used instead)
means that the value next to it are included in the set. Usually used for the symbols ≤ and ≥.
Then in the set: (63, 64, 65, 66} the value 63 does not actually belong, and value 66 does belong.
Then this set is written as:
63 < N ≤ 66
Such that N is an integer number.
