5 "Fun" math questions =)?

Question

NUMBER ONE 3/x + 2/x+4 = 8/x+1

NUMBER TWO 2x-5/x - 6/x+3 = 3/7

NUMBER THREE 12x^2 - 20x + 7 = 0

NUMBER FOUR 40x^2 + 8x - 32 = 0

NUMBER FIVE One pipe fills a pool in 4 hours. A second pipe used to drain the water from the pool can empty the pool in 8 hours. The owner of teh pool mistakenly opened both pipes. How long will it take to fill the pool if one pipe is filling and the other is emptying?


It would be nice if you showed your work =)

Thanks for all your help!

Answer 1

Not to be ... funny or anything, but... math is fun?

Sorry... got a kid with her Masters in Mathematics. She is proof that numerical dyslexia is not passed through the generations!

Good luck LOL

Answer 2

Hey, it's quite obvious that you have an assignment. But anyway, i'm a generous person and a Math freak too. So, i'll help you.

Number 5: This is a kind of work problem. If you have two pipes, one to empty and one to fill, the equation would be (1/x) - (1/y) = (1/z), where x is the time it takes to fill, y is the time to empty, and z is the total time to fill when the two pipes are open. So, (1/4) - (1/8) = (1/z). Then, (2/8) - (1/8) = (1/z). After which we get (1/8) = (1/z). So, z is equal to 8. Thus it takes 8 hours to fill the pool when the two pipes are open.

Number 4: 40x^2 + 8x - 32 = 0. First we factor out eight to get 8(5x^2 +x - 4). So you could cacel eight since zero divided by eight is 0. What's left is 5x^2 + x - 4 = 0. Then we factor it out to be (5x - 4)(x + 1) = 0. So x = -1 or x = 4/5.

Number 3: This one is simply factoring. 12x^2 - 20x + 7 = 0. When factored we get, (6x - 7)(2x - 1) = 0. So x = 7/6 or x = 1/2.

Number 2: (2x - 5)/x - 6/(x + 3) = 3/7. First we find the least common denominator which in this case is x(x + 3) or x^2 + 3x. So, [(2x - 5)(x + 3) - 6x]/(x^2 + 3x) = 3/7. Simplifying we get,
(2x^2 + x - 15 - 6x)/(x^2 + 3x) = 3/7. Simplifying further, we get (2x^2 - 5x - 15)/(x^2 + 3x) = 3/7 and 7(2x^2 - 5x -15) = 3(x^2 + 3x).
Then, 14x^2 - 35x - 105 = 3x^2 + 9x. After which, transfer all elements to one side. 11x^2 - 41x - 105. i'm kinda having a difficult time factoring sp just use the quadratic formula.

Number 1: We do the same steps in number 2. First get the least common denominator. Then simplify until your left with a fraction equal to 8/(x + 1). Then simplify.

I hope i helped you. Study well.

And lastly, you could send me your e-mail address (if you decide to choose me as best answerer) so that i could give you the answers. I'll solve it on paper, scan it and send it to you thru
e-mail. Btw, you could send me a message at . God bless always.

Answer 3

Okay, for #3
[20+- sqrt((-20)^2-4(12)7)]/ 2(12)
[20+- sqrt(400-366)]/24
[20+- sqrt(34)] /24

I hope that helped, the formula is

[-b +- sqrt(b^2-4ac)]/2a to solve the quadratic equation:
ax^2+bx+c=0

Answer 4

nice try....it could have been better if you'll say that its a hw.