All Answers 358149 Answers

Hit the "2nd" button...you should see the "atan" button on the second "page"

I used to use that second form of factoring, too, Rom. It drove my teachers crazy!! I asked them why a radical wasn't just as valid as an integer in a factored expression since they were both "real" numbers......They use to say, "Because you can't do that." I told them, "But, I just did!!"

I believe "Anonymous" made a slight mistake, here.

The +8x in the answer should be -8x

Very interesting what Melody said......there is a book by Petr Beckmann entitled "A History of Pi". I don't know if it is still in print, or not, but it is quite fascinating. However, the last half of the book requires some fair knowledge of upper maths!!

One funny note....Many years ago, The State Legislature of Indiana in the US once tried to "legislate" the value of pi!!! Go figure....

Just divide the numerator by the denominator....that will give you your decimal equivalent.

You divide 100 by the denominator (bottom #) and multiply that answer by the numerator (top #).

Example: 2/5 in decimals is 100 divided by 5 = 20 and then 20 times 2 = 40. Since decimals are out of 100 your answer wound be 2/5 = 0.4

Using the arcsin function, we have

arcsin(3/7.6)  ≈ 23.25°

Realize that this angle might also lie in the 2nd quadrant, as well.

There, the angle would be ≈ 156.75°

Okay,

So what Alan has demonstrated is that there is no specific answer because many different quadrilaterals can have these side lengths.

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Hi Alan,

I am impressed with your use of GeoGebra.   I have not found it very intuitive and have not progressed passed the real basics.

I believe you can also convert your diagram to Latex code and implant it that way!

I want an easy way to make and use a number line.  I did it last time with GeoGebra just by cutting out the y axis but it wasn't as good as I would have liked.  Do you know if this sort of thing can be done properly with GeoGebra?

Maybe Heureka knows if you do not ?

Let's see if we can solve this......

In the second equation, we can add y to both sides and subtract 2 from both sides.

So we have

y = x^2 - 2     and

y = -3x + 2     So setting the "y's" equal, we have

x^2 - 2 = -3x + 2     Subtracting everything on the right on both sides, we have

x^2 + 3x - 4 = 0       And factoring, we have

(x + 4) (x - 1) = 0     And setting both factors to 0, we have

x = -4 and x = 1        And using y = -3x + 2 and substituting both values of x

We find that y = 14 when x = -4 and y =  -1 when x = 1

So our solutions are  (-4, 14)  and ( 1, -1)

Please note:

I have put the address for this thread in the sticky note labeled

"Information pages worth keeping or developing"

pi is an irrational number and cannot be expressed as a fraction or as a decimal.  When expressed as  a decimal the digits keep going for ever without any pattern.  Hence whenever it is expressed as a fraction or a decimal it is always an approximation.

This may be of interest to some people it is from Wikipedia.

Pi can be calculated in ta number of ways.  Here are a couple.

Yeah, Alan....I realized that I could have "manipulated" the Geogebra generated object to produce any number of quads with these sides....this one just had a right angle which was fairly easy to deal with.

....But, at the moment.....I'm still looking for a missing zero along with my pal Sisyphus.....no more time for this "four-sided" silliness!!

Hi Heureka,

You have an excellent argument.

BUT

what if you start with   $$x=\dfrac{40}{(\frac{-1}{10})}\\\\$$    and then continue with a similar argument to yours.

I think that you end up with $$\frac{40}{0}=\:-\infty$$  

It can't equal   $$-\infty \quad and \quad +\infty$$   at the same time therefore it is undefined.

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I really need to learn to write limits using Latex! 

also

\frac{40}{(1/10)}

$$\frac{40}{(1/10)}$$

How did you get it to write the fraction upright on the bottom more neatly than mine?

I had to go into display mode else it was too squashy.

Thank you.

find all the common factors and bring them to the front of the expression.

In this case 10y is a common factor.

$$30y^3-50y=10y\left(3y^2-5\right)$$

it should be fine to stop there, but if you want to go nuts you can do this.

$$30y^3-50y=30y\left(y^2-\frac 5 3\right)=30y\left(y-\sqrt{\frac 5 3}\right)\left(y+\sqrt{\frac 5 3}\right)$$

Let the amount Ethan has saved be x.

175 = 25 + 3x

150 = 3x

50 = x

Ethan has saved $50.

$${\frac{{\mathtt{122}}}{{\mathtt{0.2}}}} = {\mathtt{610}}$$

$${\mathtt{108}}{\mathtt{\,\times\,}}{\mathtt{108}} = {\mathtt{11\,664}}$$

(1,-1) and (-4, 14)

di you know how to use systems (of equations)

yes.

by using pythag. thrm. and basic trig u can find the angle measures.

use pythg. thrm. to find missing side

tan^-1(base/missing side)= bottem angel

good luck 

steps 

1 distribute negitive 

5x^2-11x-9   -2x^2+3x-5

you can do this cause everything is just + and -

2 combind like terms

5x^2-2x^2 +3x-11x  -9-5

3x^2 +8x -14

Thats the most symplified it gets

Rom and CPhill:

Yes, evidently quite a workout! Thank you both for taking the time to do it and explain it so methodically. I feel like my comprehension of the answers you gave to this particular problem has increased my confidence in converting word problems to workable algebra formulas more than perhaps any other word problem I've recently encountered. Much appreciated!

Melody:

Thanks for the tip; done, and will be sure to do in the future. And its great to see you too! Haha, nice glasses, yes. How's the weather in Sydney this time of year? 

Impressive calculations, but the quadrilateral isn't unique - see illustration below (drawn to scale in Geogebra). Compare the blue and red quadrilaterals, both on the same black baseline.

2991

$${\mathtt{2\,991}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1\,992}} = {\mathtt{4\,983}}$$

Start by letting the number be 1000a+100b+10c+d so its reverse is 1000d+100c+10b+a.

Adding these together we get 1001(a+d)+110(b+c).  This must equal 4983.

I'll leave you to take the reasoning further!