Answer:
262 and 263 are consecutive natural numbers whose sum is 525.
Step-by-step explanation:
Natural number are a subset of real numbers consisting in positive integers (i.e. 1, 2, 3, 525) and two natural numbers are consecutive when distance between each other is equal to 1. (
,
) We can interpret the statement mathematically by means of the following expression:



Where
,
,
.
This system is reduced to a single equation and solved afterwards:




Now we evaluate
and
to obtain the natural numbers:


262 and 263 are consecutive natural numbers whose sum is 525.
Answer:
y=1/5x-31/5 (or y=0.2x-6.2 in decimals)
Step-by-step explanation:
x=5y-8 (original equation)
x+8=5y <u>(Addition Property of Equality)</u>
1/5x+8/5=y <u>(Division Property of Equality, </u><u>slope </u><u>of </u><u><em>original equation </em></u><u>is </u><u>1/5</u><u>)</u>
<u />
y-y1=m(x-x1) <u>(point-slope formula)</u>
y-(-5))=1/5(x-(6)) <u>(plug in the slope that was found earlier and the point given in the question)</u>
y+5=1/5(x-6)
y+5=1/5x-6/5 (Distributive Property of Multiplication) Note: 5 = 25/5
<u>y=1/5x-31/5</u> (Subtraction Property of Equality, and there's your answer)
<u>y=0.2x-6.2</u><em> </em>(This is the same answer, but written with decimals)
The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.
Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.
So, if we sum the first N odd numbers, we have

The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

The second sum is simply the sum of N ones:

So, the final result is

which ends the proof.
Answer:
120 pounds
Step-by-step explanation:
65% of y= 78 pounds
× y = 78 pounds
65y = 78 × 100=7800
y= 7800/65= 120 pounds
Answer
Find out the how many pounds of metal are in 1,950 lb of ore .
To proof
let us assume that the pounds of metal are in 1,950 lb of ore be x .
As given
In an ore, 9.8% of its total weight is metal.
ore weight = 1,950 lb
9.8% is written in the decimal form

= 0.098
Than the equation becomes
x = 0.098 × 1950
x = 191.1 pounds
Therefore the 191.1 pounds of metal are in 1,950 lb of ore .
Hence proved