So even postive integers are by defention in form 2k where k is a natural number so
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=

so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct
Answer:
He needs to sell 100 souvenirs
Step-by-step explanation:
We want to know the number of souveniers John has to sell
Let the number of souveniers he sold at the game be s
At a rate of $0.25 per souvenier, the amount earned on souveniers for s souveniers will be:

Now, if we added this to the amount he earns per game, we will have the total $35 earned for working at one game.
Thus, mathematically:

Answer:
36.1 meters
Step-by-step explanation:
Since this is a rectangle, the parallel sides are equal to each other, meaning we technically already know all the side lengths.
I'll choose to look at the bottom triangle in this case
30 is already there, and the other leg should be 20. Knowing this, we can plug these into the pythagorean theorem.
20 is A, 30 is B, and the missing side is C

C, the missing side to the nearest tenth is 36.1 meters
The answer is true, the inverse of f(x) IS a function !