Answer:
-factoring may not work; for instance, factoring will not find solutions that are not integers.
-very difficult to use on any quadratic that doesn't have extremely easy numbers. In most cases, factoring will only be simple if the answers are integers or commonly used fractions.
hope this helps :)
The positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170. This is obtained by taking the sum of first five numbers, squaring the sum and subtracting the sum of first five perfect squares.
The sum of first five positive integers = 1+2+3+4+5 = 15
Square of the sum of the first five positive integers = 15² = 225
The sum of the first five positive perfect squares =1²+2²+3²+4²+5²
=1+4+9+16+25
=55
The positive differenece = 225-55=170
Hence the positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170.
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Answer:
Step-by-step explanation:
The square of the sum of the first five positive integers:
(1 + 2 + 3 + 4 + 5)² = 15² = 225
The sum of the first positive perfect square:
1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55
225 - 55 = 200
The decimal number 0.45833333333 is equivalent to the fraction 11/27. We arrived at this answer by setting up an equation with the decimal as an unknown, then manipulating and solving the equation to find its equivalent fraction form.
The decimal number 0.45833333333 represents a recurring decimal where '58333' repeats itself infinitely. To convert recurring decimals into fractions, we can use a method involving algebra.
Let's represent 0.45833333333 as 'x'. We can express 'x' in the form of 0.45833... = x. Then, multiply both sides of the equation by 10 to the power of a number of repeating digits (which is 5 in this case): 10^5*x = 45833.33333...
Now, subtract the original equation from the one after multiplication, we get 99999x = 45833. Then, solve for 'x', x = 45833/99999. Simplifying this fraction gives us x = 11/27.
Therefore, 0.45833333333 as a fraction is 11/27.
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