Since line c and d are parallel, line a can act as a transversal. Thus, x=124 degrees because of the alternate exterior angle relationship that can be seen.
Do you know answer or not please give me answer
divide total bags by number of hours
30 bags / 3 hors = 10 bags per hour
he racked 10 bags per hour
Multiply the equation 2x+7y=-1 by -2
add to othe equaiton
4x-3y=-19
<u>-4x-14y=2 +</u>
0x-17y=-17
-17y=-17
divide both sides by -17
y=1
sub back
2x+7y=-1
2x+7(1)=-1
2x+7=-1
minus 7 from both sides
2x=-8
divide both sides by 2
x=-4
x=-4
y=1
(x,y) is normal form
(-4,1) is answer
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.
