Gauss' method for addition relies on the fact that you can 'pair' certain numbers together. Look at the example:
1+2+3+4+5+6+7+8+9+10
We could manually add all these together from left to right but a clever way to think about this is if we add together the ends of the sum (10+1) we get 11. If we then move one in from the ends and add these (2+9) we also get 11. This means that 1+2+...+9+10 is the same as 11+11+...+11+11.
Because each 2 numbers adds to 11 we know the total number of 11's we have to add together is the length of the sum divided by 2. In our case 5 (10 ÷ 2). We need to add 5 lots of 11 to get our answer. This is the same as 11 × 5 which is easily seen to be 55.
(If you add the 10 numbers together on a calculator you'll see 1+2+3+4+5+6+7+8+9+10 = 55) so this method really makes it a lot quicker.
Looking at your sequence, if we pair the ends together we get 401 (400+1) and we multiply this by the length of the sequence divided by 2. In your case, 200 (400 ÷ 2).
So the sum of all the numbers from 1 to 400 must be 401 × 200 = 80,200.
Remember the steps:
1. Pair the ends together and add them
2. Times this number by the length of the sequence halved
Hope this helps.
Answer:
Step-by-step explanation:
Givens
- The top soil weighs 40 pounds per bag.
- The mulch weighs 20 pounds per bag.
- The cart can only carry up to 480 pounds.
Notice that the restriction is a maximum of 480 pounds, that means the inequality must include the sign 
.
Now, let's call 
the top soil and 
the mulch, the inequality that represents this problem, would be
It’s True.. you take the “extreme” variable from each proportion and cross multiply them before setting them equal to the product of the two “means” (which are just the other 2 numbers in the proportions).
Answer:
5
Step-by-step explanation:
Just grap any two consecutive terms in the sequence. lets say -55 and -50
-50-(-55) = 5
you can check this by picking two other terms
Answer:
If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
Step-by-step explanation:
