∠1 and ∠2 are RIGHT ANGLES, VERTICAL ANGLES, and SUPPLEMENTARY ANGLES.
Hope this helps!
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:
23.1m
Step-by-step explanation:
we define x to be the actual distance, y to be the distance on map (y=15.4cm)
if the map scale is 3:750, then by definition of scaling, x and y must satisfy:
we isolate x:
Answer:
<h2>A = 57</h2>
Step-by-step explanation:
Use the Pick's theorem
Let P be a polygon in the plane whose vertices have integer coordinates. Then the area of P can be determined just by counting the lattice points on the interior and boundary of the polygon!
In fact, the area is given by
where <em>i</em> is the number interior lattice points, and<em> b</em> is the number of boundary lattice points.
Look at the picture.
Substitute:
48(miles/hour)*(1 mi/5280 ft)(1 hour/60 min)
-----
= (48*1*1)/(1*5280*60)(ft/min)
