9x^2 - 42x + 49 is a perfect square trinomial. It factors to (3x - 7)^2
If the area is 64m^2 set this equal to the factors and solve.
(3x - 7)^2 = 64
Take the square root of both sides.
3x - 7 = + - 8
3x - 7 = 8 3x - 7 = - 8
Add 7 to both sides.
3x = 15 3x = - 1
Divide both sides by 3.
x = 5 x = -1/3
x cannot be -1/3 because it would make the length negative.
The answer is x= 5
I don't know any <em><u>slick</u></em> way to do this. I would just list the prime numbers
between 40 and 50 and test them one at a time.
The prime numbers between 40 and 50 are: 41, 43, 47
<u>Test 41:</u>
-- add 1 . . . 42
-- prime factors of 42 . . . 2, 3, 7
-- sum of the factors . . . 12
<u>Test 43:</u>
-- add 1 . . . 44
-- prime factors of 44 . . . 2, 11
-- sum of the factors . . . 13
<u>Test 47:</u>
-- add 1 . . . 48
-- prime factors of 48 . . . 2, 3,
-- sum of the factors . . . 5
Maybe I'm not understanding how to list prime factors, but so far,
I haven't found any number that answers the question.
Maybe if I write the prime factorization of 44 like this:
44 = 2 * 2 * 11
Now the items in the prime factorization do add up to 15.
So the answer would seem to be <em>43.</em>
==================================
<em />
<em>"Associate with people who are likely to improve you."</em>
I would say the parakeets make up 14% of the shelter.
This is not factorable. It can be easily tested using the radicand expression of the quadratic equation. (Perfect square= Factorable, No Perfect= Not Factorable.)
