If N is a positive integer, it must be either even or odd.
If N is odd, then N-1 will be even.
If N is even, then N-1 will be odd.
Either way, when you multiply n and n-1, one of those expressions is going to be an even number, and any number multiplied by an even number is an even number.
Hope this helps! :)
Answer:
3x(x - 4)(x + 2)
Step-by-step explanation:
Given
3x³ - 6x² - 24x ← factor out common factor of 3x from each term
= 3x(x² - 2x - 8) ← factor the quadratic
Consider the factors of the constant term (- 8) which sum to give the coefficient of the x- term.
The factors are - 4 and + 2, since
- 4 × 2 = - 8 and - 4 + 2 = - 2, thus
x² - 2x - 8 = (x - 4)(x + 2) and
3x³ - 6x² - 24x = 3x(x - 4)(x + 2)
Octogon
sides=4
draw lines from the outside angles to the center so they form 8 equal triangle sections
find the area of each triangle and multiply by 8
area of triangle=1/2 base times height
base=4
the height is the distance from the center of one side of the octogon, to the center=5
so area=4 times 1/2 times 5=4 times 5=10
8 triangles so 8 times 10=80
the answer is 80cm^2
the diagram included below shows area for a pentagon
The first thing to do is find the slope of the given line m = (y2-y1)/(x2-x1). We need to find the slope because it is required to find the slope of the perpendicular line.
m = (-7-5)/(5+11) = -12/16 = -3/4
Now we find the midpoint of the line, this is where the perpendicular bisector be. Using the Midpoint equation
M=((x1+x2)/2,(y1+y2)/2)
M=((-11+5)/2, (5-7)/2)
M=(-6/2, -2/2)
M=(-3,-1)
Now that we have the slope and midpoint we can find the perpendicular bisector. A line is perpendicular to another if, when you multiply their slopes together they equal -1. To do this we simply invert the numerator and denominator of our current slope and flip the sign from negative to positive.
So, -3/4 becomes positive 4/3 for our new line. So for our perpendicular line we now know two things, the slope and a point on it (the bisector point). To find the equation of the line we need to plug the known point and slope into the equation y = mx + b and solve for b.
-1 = 4/3(-3) + b
-1 = -4 + b
b = -1 + 4
b = 3
Now we can build our equation for our perpendicular line
y = 4/3x + 3
Answer: C
Step-by-step explanation: Because that table is showing (x - y)
