Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.
Answer:
80,00
Step-by-step explanation:
According to my research, the formula for the Area of a rectangle is the following,

Where
- A is the Area
- L is the length
- W is the width
Since the building wall is acting as one side length of the rectangle. We are left with 1 length and 2 width sides. To maximize the Area of the parking lot we will need to equally divide the 800 ft of fencing between the <u>Length and Width.</u>
800 / 2 = 400ft
So We have 400 ft for the length and 400 ft for the width. Since the width has 2 sides we need to divide 60 by 2.
400/2 = 200 ft
Now we can calculate the maximum Area using the values above.


So the Maximum area we are able to create with 800 ft of fencing is 80,00
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Read more on Brainly.com - brainly.com/question/12953427#readmore
It is three hundred fifty-six thousandths.
The amount to be paid after 3 years is $23,329.97.
<h3>What is Compound Interest?</h3>
In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest.
Given:
P= 20,000
r= 5.2%
t= 3 years
r = R/100
r = 5.2/100
r = 0.052 rate per year,
Now, solve for A
A = P
A = 20,000.00
A = 20,000.00
A = $23,329.97
Learn more about Compound interest here:
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Answer:

Step-by-step explanation:
Rewrite the given polynomial in the form ax² + bx + c:

To find the zeros, set the function to zero and solve for x using the quadratic formula.

<u>Quadratic formula</u>:

Therefore,
Substituting the values into the quadratic formula:






The sum of the roots of a polynomial is -b/a:

The sum of the found roots is:

Hence proving the sum of the roots is -b/a
The product of the roots of a polynomial is: c/a

The product of the found roots is:

Hence proving the product of the roots is c/a
Therefore, the relationship between the roots and the coefficients is verified.