Math Homework help (NA)

TangoWhiskey

TangoWhiskey

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It's been a LONG time since advanced geometry, and I'm trying to help my daughter with some homework. I've done well up until this year, but this year is getting tougher. We're stuck on this problem, where we have to solve for 'x'. They've told her that two angles are equal.

angle a: 5x + 75 (five 'x' plus 75)
angle b: 24x² (I hope that superscript comes through, it's 24 'x' squared)

Will one of you "geniuses" help walk us through the solution? We've tried simplifying one side to '2 sqrt(6) x', etc., but can't seem to find a solution that gives us a real number.
 
Troy Whistman said:
We're stuck on this problem, where we have to solve for 'x'. They've told her that two angles are equal.

angle a: 5x + 75 (five 'x' plus 75)
angle b: 24x² (I hope that superscript comes through, it's 24 'x' squared)

Will one of you "geniuses" help walk us through the solution? We've tried simplifying one side to '2 sqrt(6) x', etc., but can't seem to find a solution that gives us a real number.
Click to expand...
Man, Steve, you are cruel, but I guess the price of avgas is going up :)

He's got you on the right track though, Troy. This is more of an algebra question really, since the angles are equal you can set the two formulas for them equal to each other, too:

24x^2 = 5x + 75

Rearrange the terms to put it in quadratic form:

24x^2 - 5x - 75 = 0

When you have "ax^2 + bx + c = 0", the solutions are:

x = (-b (+/-) sqrt(b^2 - 4ac))/(2a)


Can you read all that? One of your anwers will probably end up being negative, so throw that one out....

-Rich
 
Thanks, Steve and Rich. I was trying to solve it "algebraicly" like you, but didn't think to consider that I could move everything to one side = 0. Let me go over your answer with her and see what she says. Ain't this group GREAT!?
 
Troy Whistman said:
It's been a LONG time since advanced geometry, and I'm trying to help my daughter with some homework. I've done well up until this year, but this year is getting tougher. We're stuck on this problem, where we have to solve for 'x'. They've told her that two angles are equal.

angle a: 5x + 75 (five 'x' plus 75)
angle b: 24x² (I hope that superscript comes through, it's 24 'x' squared)

Will one of you "geniuses" help walk us through the solution? We've tried simplifying one side to '2 sqrt(6) x', etc., but can't seem to find a solution that gives us a real number.
Click to expand...

24x² = 5x + 75
24x² - 5x - 75 = 0

then the magic starts :

(8x - 15)(3x + 5) = 0

(8x - 15) = 0 or x = 15/8
and
(3x + 5) = 0 or x = -5/3

greg
 
Troy Whistman said:
It's been a LONG time since advanced geometry, and I'm trying to help my daughter with some homework. I've done well up until this year, but this year is getting tougher. We're stuck on this problem, where we have to solve for 'x'. They've told her that two angles are equal.

angle a: 5x + 75 (five 'x' plus 75)
angle b: 24x² (I hope that superscript comes through, it's 24 'x' squared)

Will one of you "geniuses" help walk us through the solution? We've tried simplifying one side to '2 sqrt(6) x', etc., but can't seem to find a solution that gives us a real number.
Click to expand...

It's been a LONG time but here goes.

5x + 75 = 24x²
24x² - 5x -75 = 0
(4x - 7.5) (6x + 10) = 0
4x - 7.5 = 0
4x = 7.5
x = 1.875

6x + 10 = 0
6x = -10
x = -1.6666...

x = 1.875, -1.666

using the factors
(8x - 15) (3x + 5) yields the same answer.

Am I even on the right page?
 
You guys are faster than I am.
 
Carol said:
It's been a LONG time but here goes.


using the factors
(8x - 15) (3x + 5) yields the same answer.

Am I even on the right page?
Click to expand...


You are on the same page with me, whether thats the right page is
questionable. :)


greg
 
My 17 year old son's solution to this problem:

"The real question is, will knowing the value of x make her any happier throughout her life? I mean, why are adults so caught up in the value of x anyway? I'd suggest she take a break and watch some MTV or something...." Then he put his headphones back on.

Picture me with a gun to my head.
 
Oh God Oh God Oh God.

I used to know this stuff cold.

It's Greek now.

Oy!
 
I hate you guys (& gals) who can factor those things! Small numbers - sure. But 24 and 75? You just look at it and go "abracadabra" and write it out. :eek:
 
tparsons said:
I hate you guys (& gals) who can factor those things! Small numbers - sure. But 24 and 75? You just look at it and go "abracadabra" and write it out. :eek:
Click to expand...

Not exactly abracadabra but there are only so many factors for 24 and 75. Just monkeying around a couple of minutes finding two sets that yield a difference of 5 was not that tricky.

Trying to remember how to start to solve the problem was the tricky part. Like Spike, I used to know this stuff down cold. It was Steve's hint that made the rest easy.

Here's one I was amazed to learn that quite a few local high school students had a problem with:

You paid the check for dinner at a restaurant. The final amount of your tab was $143.75 which included the 15% tip for your server. How much was the bill for your food and drinks?
 
Steve said:
Since the angles are equal, the two expressions are equal. Subtracting one from the other will give you what?

For a small fee I will provide the answer and the steps taken to arrive at that answer.

:)
Click to expand...

It's lovely quadratics! I haven't had to know quadratics in years, sad. Man this work stuff is boring.

Cheers,

-Andrew
computer science nerd who spends most of his time writing legalese and building financial models
 
river_rat said:
24x² = 5x + 75
24x² - 5x - 75 = 0

then the magic starts :

(8x - 15)(3x + 5) = 0

(8x - 15) = 0 or x = 15/8
and
(3x + 5) = 0 or x = -5/3
Click to expand...


Oy, I need to go review Quadratic Equations... been too long since I last did them (which goes to prove the point of "when will I use this again??").

In both Greg's answer and Carol's, I can't figure out how the 5x in the equation disappeared... how did you get rid of it??

Oh, and one more question (which I will go research after I post this): what does "quadratic" mean, anyway? I see "quad", I think "4", yet quadratic equations deal with 3 variables, a, b, c.
 
Carol said:
You paid the check for dinner at a restaurant. The final amount of your tab was $143.75 which included the 15% tip for your server. How much was the bill for your food and drinks?
Click to expand...

What percentage of sales tax was added to the check? :rofl:

Jeannie
 
Troy Whistman said:
Oy, I need to go review Quadratic Equations... been too long since I last did them (which goes to prove the point of "when will I use this again??").

In both Greg's answer and Carol's, I can't figure out how the 5x in the equation disappeared... how did you get rid of it??

Oh, and one more question (which I will go research after I post this): what does "quadratic" mean, anyway? I see "quad", I think "4", yet quadratic equations deal with 3 variables, a, b, c.
Click to expand...


Factor the equation: 24x² - 5x -75 = 0 into
(4x - 7.5) (6x + 10) = 0

4x · 6x = 24x²
4x · 10 = 40x
6x · 7.5 = -45x
7.5 · 10 = 75

If x = 1.875 then (4x -7.5) = 0
If x = -1.666 then (6x + 10) = 0
 
Last edited:
Maverick said:
What percentage of sales tax was added to the check? :rofl:

Jeannie
Click to expand...

Smart a** :)

You don't calculate the tip using the total including the sales tax? Could be a significant amount in some places like New York City. Wow.
 
Carol said:
Smart a** :)

You don't calculate the tip using the total including the sales tax? Could be a significant amount in some places like New York City. Wow.
Click to expand...

Since the question was "how much was the bill for your food and drinks", not "how much was the bill for your food and drinks, including tax", I think she was thinking correctly--the question can't be answered without knowing the unknown--the tax rate.

I don't think (correct me if I'm wrong!) that she was trying to shortchange the waitress by deducting the tax amount. :)
 
Troy Whistman said:
Since the question was "how much was the bill for your food and drinks", not "how much was the bill for your food and drinks, including tax", I think she was thinking correctly--the question can't be answered without knowing the unknown--the tax rate.

I don't think (correct me if I'm wrong!) that she was trying to shortchange the waitress by deducting the tax amount. :)
Click to expand...

I knew that :) Jeannie is cool.

I should have worded the question so that it was clearer.
 
SCCutler said:
Oh God Oh God Oh God.

I used to know this stuff cold.

It's Greek now.

Oy!
Click to expand...

It was greek back then, too. Phi, chi, epsilon... :D
 
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