K+2/3=-7
K+2=-7x3
K+2=-21
K=-19
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:
+5x-36
Step-by-step explanation:
To multiply binomials there are 2 ways. F.O.I.L., or the box method.
I will use the box method, and I hope it helps you!
After looking at the picture, this is not the answer quite yet.
Subtract 4x from 9x.
9x-4x=5x
So, the answer will be +5x-36
You want to divide 45 by 5.
45/5= 9
She used 9 yards of yarn for her knitting project.
I hope this helps!
~kaikers
Multiply the numerator and denominator by the same number.<span> Two fractions that are different but equivalent have, by definition, numerators and denominators that are multiples of each other. In other words, multiplying the numerator and denominator of a </span>fraction<span> by the same number will produce an equivalent fraction. Though the numbers in the new fraction will be different, the fractions will have the same value.</span><span>For instance, if we take the fraction 4/8 and multiply both the numerator and denominator by 2, we get (4×2)/(8×2) = 8/16. These two fractions are equivalent.(4×2)/(8×2) is essentially the same as 4/8 × 2/2 Remember that when multiplying two fractions, we multiply across, meaning numerator to numerator and denominator to denominator.Notice that 2/2 equals 1 when you carry out the division. Thus, it's easy to see why 4/8 and 8/16 are equivalent since multiplying 4/8 × (2/2) = 4/8 still. The same way it’s fair to say that 4/8 = 8/16.<span>Any given fraction has an infinite number of equivalent fractions. You can multiply the numerator and denominator by any whole number, no matter how large or small to obtain an equivalent fraction.</span></span>
