x^3-10x^2=27x-18=0 has no solutions
x^3-10x^2-27x-18=0 has 3 solutions
x^3-10x^2-27x-18=0 also has three solutions
3/1 is the answer follow the line
Answer: 9 years
Step-by-step explanation:
Let the present age of Ashley be x.
Then the present age of Alfonso =x+8
Five years ago,
Ashley's age = x-5
Alfonso's age = x+8-5 = x+3
According to the question,
Hence, the present age of Ashley =9 years
answer:
B. 2:6 is equal to 1:3
2 and 6 are both even so you can split both of them in half and you would get 1 and 3
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.
