What is 3/8 + 1/8?? Please help its for a test
2 answers:
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The equation given is 
where a is some number.
We can solve for x by taking the square root of both sides.
Now let's think through what happens for various values of a.
TWO SOLUTIONS
If a is a positive number the above yields two solutions. Take for example:
There will be two solutions (one positive and one negative) as there are two numbers (here -7 and +7) that when multiplied by themselves give 49. That is,
and 
. The positive root is called the principal root and the negative root is called the secondary root. This will be the case anytime we take the root of a positive number.
ONE SOLUTION
If a = 0 there is only one solution. That is because
and 
. Zero is neither positive nor negative and it has only one root which is 0 itself. So in this case there is only one solution and it is 0.
NO (REAL) SOLUTIONS
If a is negative we would be taking the square root of a negative number. There is no (real) number that when multiplied by itself gives a negative number. Take for example
which gives us 
. The square root of -49 is not 7 because (7)(7)=49 which is positive. The square root of -49 is not -7 because (-7)(-7)=49 which is also positive. There is no real number that gives -49 when multiplied by itself. I say "real" numbers because there do exist imaginary/complex numbers but because of the way the questions was asked I imagine you may not know about these yet.
We can solve for x by taking the square root of both sides.
Now let's think through what happens for various values of a.
TWO SOLUTIONS
If a is a positive number the above yields two solutions. Take for example:
There will be two solutions (one positive and one negative) as there are two numbers (here -7 and +7) that when multiplied by themselves give 49. That is,
ONE SOLUTION
If a = 0 there is only one solution. That is because
NO (REAL) SOLUTIONS
If a is negative we would be taking the square root of a negative number. There is no (real) number that when multiplied by itself gives a negative number. Take for example
A Venn diagram is used to present the relationship between sets in a logical form
Please find attached the completed Venn diagrams for the questions with the contents outlined as follows;
1. The set of whole numbers 1 to 15 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
Set A = All even numbers in this set
Set A = {2, 4, 6, 8, 10, 12}
2. The set of whole numbers from 1 to 20
Set C = All even numbers = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
Set D = All multiples of 4 = {4, 8, 12, 16, 20}
3. The set of all whole numbers from 1 to 20
Set E = {2, 4, 6, 7, 9, 10}
Se F = {3, 4, 5, 9, 10, 13, 15, 16, 19,20}
Learn more about Venn diagrams here:
