I started out trying to subtract a prime number from 85, and then
see whether I had a prime number remaining. I did this several
times, before I slapped myself upside the head.
-- 85 is an odd number.
-- To get an odd-number for a sum, you have to add one odd number
to one even number ... there's no other way.
-- So one of the prime numbers we're looking for must be
an even number.
-- The ONLY even number that's a prime number is ' 2 '.
So it must be one of them.
-- Subtract 2 from 85, and you have 83 left.
Is 83 a prime number ? Yes.
-- So the two numbers are 2 and 83.
If 83 were not a prime number, this wouldn't work, and I would have said
"There is no such pair of numbers.". That means it doesn't necessarily work
for every odd number.
Examples:
75 ===> 2 and 73 . \
55 ===> 2 and 53 . \
45 ===> 2 and 43 . \
Both primes. It works.
65 ===> 2 and 63 . 63 is not a prime. \
35 ===> 2 and 33 . 33 in not a prime. \
It doesn't work.
Answer:
See below in bold.
Step-by-step explanation:
If we draw a line from the point of intersection to the longest side of the rectangle it will meet it at the midpoint.
The same thing will happen when the line is draw to the shortest side.
So the point of intersection is 1/2 * 7 = 3.5 cm from the longest side and 15/2 = 7.5 cm from the shortest side.
No, they are not.
Have a good day!
Answer:x=3,-2
Step-by-step explanation:
x^2-x-6=0
x^2+2x-3x-6=0
x(x+2)-3(x+2)=0
(x+2)(x-3)=0
x=-2
x=3
