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:
Step-by-step explanation:
a). Trapezoid ABCD has one acute angle, one obtuse angle and two right angles.
Since, angle B is an acute angle, mark the vertex A' having acute angle.
Similarly, Obtuse angle A' for A and other vertices.
b). Rigid transformation doesn't change the size and shape of the image.
Therefore, all angles and measure of sides of ABCD will remain unchanged.
Measure of angle A' = 130°, m∠B' = 50°
m(A'D') = m(AD) = 6 units
m(C'D') = m(CD) = 4 units
<span>44 > 7+s+26
</span><span>44 > s + 33
11 > s
or
s < 11</span>
(8/4) = (10/x)
8x = 4 x 10
8x= 40
x = 40/8
x=5
It will take 5 hours.
