All Answers 358506 Answers

2b-8=-1b+7

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OK....let's get the "b's" to the left and everything else to the right.

Add 1b to each side

3b - 8 = 7

Add 8 to each side

3b = 15

Divide by 3 on each side

b = 5

Don't forget to "check" your answer !!

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Here's a pretty simple way to do this. Let Tommy's cards =x. Then Pete's cards = 3x. And Andy's cards = 3x - 35.

So.....

[x] + [3x] + [3x - 35] = 259    simplify

7x - 35 = 259         add 35 to both sides

7x = 294       divide by 7 on both sides

x = 42

So Andy's cards = [3(42) - 35] = 91

$$\frac{x^{2/3}}{x^1}\\\\
=x^{2/3-1}\\\\
=x^{-1/3}\\\\
=\frac{1}{x^{1/3}}\\\\$$

This is 1/ (cuberoot of x)

P is the nmber Pete has etc   How many cards does Andy have?

P=3T

A=P-35  substitute in P=3T 

A=3T-35

P+A+T=259   substitute in P=3T

3T+A+T=259  ==>  4T+A=259 ==>   A=259-4T  

so

3T-35=259-4T

7T=224 WRONG 7T=294    edited from here

T=42

now A=259-4T 

A=259 - 4 x 42 = 259-168 = 91 

I think that is the answer but you should find Pete's number of cards and then check that the numbers work with the original words.  If it is wrong you can let me know.  If it is right then a thumbs up and a new post thankyou would be really nice. 

well say it had 5 pages,  1,2,3,4,5   You can see that the middle page is 3

Say it has got 6 pages   1,2,3,4,5,6    Then it has got 2 middle pages  3 ans 4

So the middle page will be the (total number of pages+1)/2

So you tell me Tangrachel what is the middle page/s?

Di you mean $$2x+\frac{1}{3}$$    

or do you mean   $$\frac{2x+1}{3}$$    ?   If this is what you mean then you need to use brackets.

sorry no fraction key

2 thirds would go in as 2÷3

5 and 3/4 take away 9 and 7/8

(5+3÷4)-(9+7÷8)=

I hope that helps. 

$$\left({\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{3}}}{{\mathtt{4}}}}\right){\mathtt{\,-\,}}\left({\mathtt{9}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{7}}}{{\mathtt{8}}}}\right) = -{\mathtt{4.125}}$$

Excellent answer anonymous!

Why don't you join up and then you could get proper credit! 

mean means average.

so add them up and divide by how many there are. 

This is your question

Sin ^2 63 + sin ^ 2 27/ cos ^17 + cos^ 73

This is what I think you actually meant

(Sin ^2 (63) + sin ^ 2 (27)/ (cos ^2 (17) + cos^2 (73))

You need to be more careful - anyway

$$sin\theta = cos(90-\theta)$$   and vise versa - you can see this if you draw a right angled triangle and take a look

therefore

sin63=cos27  and cos73=sin17    so the question becomes

$$\frac{cos^2 (27)+sin^2(27)}{cos^2(17)+sin^2(17)}\\
=\frac{1}{1}\\
=1$$

 Now please say thank you.  

1 16/16 = 1+1 = 2

But 1/4 of an inch is 4/16 of an inch and 13/16 is closer to 12/16 than it is to 16/16.

12/16 = 3/4

The answer is 1 3/4 inches  

Thanks for giving it a go anonymous!  We like everyone to join in.    

Good answer anonymous!

I just want to go over what you were saying.

Anything divided by itself is 1

so

 $${\frac{{\mathtt{7}}}{{\mathtt{7}}}} = {\mathtt{1}}$$

$$\frac{9^3}{9^3}=1$$

also

 $$\frac{5^7}{5^4}=5^7\div 5^4=5^{7-4}=5^3$$

so

$$\frac{9^3}{9^3}=9^{3-3}=9^0$$   BUT we know that    $$\frac{9^3}{9^3}=1$$

therefore

$$9^0=1$$      

Anything (except for 0) raised to the power of 0 is 1.     

$${{\mathtt{0}}}^{{\mathtt{0}}} = \underset{{\tiny{\text{Error: indeterminante}}}}{{{\mathtt{0}}}^{{\mathtt{0}}}}$$    Like it says 0⁰ is undefined    

Are you happy now bioschip? 

A really good answer Bioschip! 

Thanks Alan,

That is assuming you are talking about perpendicular height. 

$${\frac{{\mathtt{100\,000}}}{{\mathtt{1.072}}}} = {\mathtt{93\,283.582\: \!089\: \!552\: \!238\: \!806}}$$

Welcome to the forum garanceme.  I hope that you like it here.

It is great to see you answering a question.  (I gave you the thumbs up and the 3 point)

If you are answering a question like this you can just use the 'math(input=Result)' Button.

It is easier than reaching for a different calc and it displays the working.  

I think that is the same as

$$(2x+x\sqrt3)(2x+x\sqrt3-2x)^2(2x+x\sqrt3-2x\sqrt3)=144\sqrt3\\

Do you agree?\\

(2x+x\sqrt3)(x\sqrt3)^2(2x-x\sqrt3)=144\sqrt3\\


3x^2((2x)^2-(x\sqrt3)^2)=144\sqrt3\\

3x^2(4x^2-3x^2)=144\sqrt3\\\\

3x^2(x^2)=144\sqrt3\\\\

3x^4=144\sqrt3\\\\

x^4=\frac{144\sqrt3}{3}\\\\

x=\pm\left(\frac{144\sqrt3}{3}\right)^{(1/4)}\\\\$$

$${\left({\frac{{\mathtt{144}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}}{{\mathtt{3}}}}\right)}^{{\mathtt{0.25}}} = {\mathtt{3.019\: \!607\: \!296\: \!954\: \!21}}$$

I did this on the site calc

x ≈ ± 3.019607

That's assuming I didn't make any stupid mistakes.

Now you can either tell me I am wrong or you can say thank you!  

Yes - Good one David  

Hi Bioschip, DavidQD and anonymous,

I have seen commas used as decimal points (this is quite common - I think my students that used to do it were from African nations, maybe Sierra Leone? Not sure) but I have never seen periods (dots) used to separate place value!   

Which countries do that ?  Maybe DavidQD or our anonymous person could tell me?

Yes that's the question.

(((2x+x*sqrt(3))/2))(((2x+x*sqrt(3))/2-x)((2x+x*sqrt(3))/2-x))*((2x+x*sqrt(3))/2-x*sqrt(3)))=9*sqrt(3)

First I want to make sense of it!

Is this your question?

$$\left(\frac{(2x+x\sqrt3)}{2}\right)\left(\frac{(2x+x\sqrt3)}{2}-x\right)\left(\frac{(2x+x\sqrt3)}{2}-x\right)\left(\frac{(2x+x\sqrt3)}{2}-x\sqrt3\right)=9\sqrt3$$

It's too long - it won't display on one line!

yeah it is $100 000 000 000 but what is up with all the decimal points in Anonymous' anwer by bioschip

****

Some cultures interchange the use of commas (,) and decimals (.)

100.000.000.000 = 100,000,000,000

0,02580 = 0.02580

The calculator on this site uses either convention depending on context. Entering the above or similar formatted numbers will yield correct results.

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Note also, with the use of two specifically spaced commas the calculator will display results in scientific notation.

For example: enter 2^199 and the calculator will display 60 decimal digits; choose an arbitrary position to the right of the first digit and enter a comma, move three more to the right and enter another comma, then click the “=” (or press enter). The display will convert to (standard) scientific notation, with up to a 16-digit mantissa following the decimal point and its preceding value. (In this example, the value is 8.0346902212949514e59)

The same applies to extremely small values. For example (2^199 )^-1. In this case, choose an arbitrary place to the right of the first value after the decimal point, and place the second coma three values to the right. (In this example, the value is 1.245e-60).

The short version is: two comas, three values apart. The above also works with negative numbers.

This computer generated “calculator” is a brilliant peace of programming. At one time, this calculator would generate results with atomic accuracy at galactic distances (plus or minus the bugs and limitations of log and trig functions). Now, most functions (except for exponential) are rounded to 16 digits. This is more like galactic accuracy at atomic distances, but it keeps the FLOP load down when tens of thousands of users are seeking solutions.

Another feature of this calculator are “Easter eggs” hidden in the subs. Entering certain string combinations would generate German phrases. There were at least three, but none of them work anymore. The best were, “Speichern Sie diese Scheiße für die Vögel,” and “Führen Sie Sie gefickt bis, ja wissen.”

Here is a brilliant peace of programming and a great sense of humor.

~~D~~

Hi Bioschip,

I really like your logic there.  And of course you are correct.  6 IS ONE of the answers !   

When you have an equation like this with an x² term, there are usually 2 answers.

this is how it is done.   

$$x^2-2x-24=0$$ 

First I need to factorise this.  Factors are things that multiply to get the answers

I need 2 numbers that multiply to -24  (one will need to be neg and one pos)

they also need to add to -2   (How about -6 and 4, they work)

so the question becomes

$$(x-6)(x+4)=0$$      that is what Bertie got up to!

NOW, if two things multiply together to give 0 then one of them (or both of them) must equal 0.

so either $$x-6=0$$  or  $$x+4=0$$

so   $$x=6$$   OR    $$x=-4$$  

Maybe you would like to try this one   $$x^2+5x+4=0$$   ???

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NOW I want people to start learning to use LaTex which is how we display the maths stuff.

So here is a little lesson.

Press the LaTex button, type (x-6)(x+4)=0  then press ok.

See how it displays.  

If you want to know how to display anything else, please ask.  Remember, Members get priority answering.  

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Help you with what????

Thanks Mathwizard, it didn't occur to me that it was a minus sign, I just thought it was a dash!

$$\sqrt{-4\; }$$  has no solution in the real number system because nothing multiplied by itself equals a negative number.

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University people will tell you that  $$\sqrt{-1}= i$$  This is the base unit for all imaginary numbers.

so we could say that $$\sqrt{-4}=\sqrt{-1}\times\sqrt4 = i\times2=2i$$

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I think it would  be good if people started to learn LaTex.  That is what I used to write that maths stuff.

This is how to write sqrt of 4

click on the LaTex Formula button in the tool bar

enter \sqrt4  then press ok

It is that simple, if you want square root of 16 this is what you must enter

\sqrt{16}  then ok

If you didn't put the curly brackets then only the 1 would be under the sqare root sign.  

why don't you give it a go - if you would like to know how to write something else just ask.  

You ask one brother what the other brother will tell you is the correct way, then go the opposite way.

If you ask the truthful brother, he will respond with what the lying brother says, which would be the wrong way.

If you ask the lying brother he will lie about which path the truthful brother would say- so either way you go the opposite of what they say.