Let one number be x.
Let the other number be y.
x + y = 49
x - y = 7
Subtracting both equations,
2y = 49 - 7 = 42
--- y = 21
--- x = 21 + 7 = 28
Hence the two numbers are 21 and 28.
Answer:
The first option is correct, 12/30 and 25/30
Step-by-step explanation:
To get common denominators, you need to find the GFC (greatest common factor) of 5 and 6, which is 30. Then you would need to make the fractions equal the same as the original fractions, by multiplying.
2/5 = ?/30 <- you can see that 30 is 6 times more than 5. so this means you multiply 2 by 6 to get 12. 12/30
5/6 = ?/30 <- you can see that 30 is 5 times more than 6. so this means you multiply 5 by 5 to get 25. 25/30
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.
6 7/10 maybe i dont know...................