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I'll second what Melody said....nice graphic, too!!!........"points" from me......Welcome aboard!!!

Well it all started.... when you were born...........

If 5(x) - 17 = -(x) + 7, then x is equal to 4.

To find the variable "x", we need to isolate the variable on one side of the equation so that the answer can be displayed on the other side. To do this, we need to cancel out (or turn into 0) either "5(x)" or "-(x)" by adding a certain amount to both sides of the equation to make one 0. Let's try "-(x)" because it's closer to 0 than "5(x)" is. To cancel it out, we can add "x" to both sides like so:

5(x) + x - 17 = -(x) + x + 7

If we add "5(x)" and "x" we will obtain "6(x)", and if we add "-(x)" and "(x)" we will have 0:

6(x) - 17 = 0 + 7

We also know that any number added to 0 will give that number, so we can simplify "0 + 7" like so:

6(x) - 17 = 7

However, "x" is not the only value on its side of the equation, so next we can try to cancel the "- 17" by adding, not subtracting 17 to each side of the equation. If we were to subtract 17 from negative 17, we would end up with negative 34, not 0. We can manage this like so:

6(x) - 17 + 17 = 7 + 17

Now we can simplify "- 17 + 17" to obtain 0:

6(x) - 0 = 7 + 17

Next we can simplify "6(x) - 0" to get "6(x)" and "7+17" to get 24:

6(x) = 24

Finally, we must make "6(x)" into "x" by dividing each side by 6. This will eliminate that pesky "6" before the "x" so that we can see the answer:

6(x) / 6 = 24 / 6

Dividing "6(x) / 6" will give us "x" and dividing 24 by 6 will give us 4, so:

x = 4

I hope this helped.

-pokemonfan58

Your question does not make sense.  Perhaps you should check it.

What an excellent answer Pokemonfan58!   I'd thumbs up you twice if i could.  But I can't. 

Oh. Dont forget that it is area so it is 43units²

I see that you are new.

Welcome to Web2.0calc forum.   We hope that you learn lots and have a great time here!

With answers like that, you are going to be invaluable to this forum. 

works fine for me too.  

$$\begin{array}{rll}
210&=&5*42\\
210&=&5*7*6\\
210&=&5*7*2*3\\
\end{array}$$

So the prime factors are 2,3,5and 7

I'm afraid I don't know exactly what you mean, but I assume you mean a shape that overlaps another shape like so:

To find the combined area of a shape and another shape that is overlapping it, you must ensure that you can find the area of both the two shapes and the the area that the two shapes overlap. In the case in the picture, we can find the area of the red and blue rectangles, along with the purple area in between them.

The formula for finding the area of a rectangle is "a = l * w" where "a" is the area, "l" is the length, and "w" is the width. Using this, we can the find the area of the red rectangle by plugging in 7 for length and 3 for width:

a = 7 * 3

or...

a = 21

Using the very same method, we can find the area of the blue rectangle using 6 as length and 4 as width:

a = 6 * 4

or...

a = 24

Finally, we can find the area of the purple rectangle (the area overlapped by the two rectangles) using 2 as length and 1 as width:

a = 2 * 1 

or...

a = 2

Now that we know this, we can add the area of the two rectangles to get:

24 + 21 = 45

However, since the shapes overlap, we need to subtract the overlapping area to get:

45 - 2 = 43

Thus, the combined area of these two rectangles is 43. I hope I helped.

-pokemonfan58

This is what I think

1)   10!/(2!3!5!)

$${\frac{{\mathtt{10}}{!}}{\left({\mathtt{2}}{!}{\mathtt{\,\times\,}}{\mathtt{3}}{!}{\mathtt{\,\times\,}}{\mathtt{5}}{!}\right)}} = {\mathtt{2\,520}}$$

2)   I'm going to work out how many ways they are together

Just think of the 2 pin b***s as just 1 ball (they are glued together) but then multiply by 2 because they can be glued in 2 different ways

9!(3!5!)=  (This has been edited after Alan's comments)

$${\frac{{\mathtt{9}}{!}}{\left({\mathtt{3}}{!}{\mathtt{\,\times\,}}{\mathtt{5}}{!}\right)}} = {\mathtt{504}}$$

so the number of ways that they are not together is

$${\mathtt{2\,520}}{\mathtt{\,-\,}}{\mathtt{504}} = {\mathtt{2\,016}}$$

This is what I think but it may not be correct.

You do realise though that you are a medievil Doctor of Medicine.  Not a Dr of Mathematics. ?!?!

I think that thee has made an error Dr Tud,

The effective annual interest rate be of no consequence. 

For one the 4 monthly effective rate is important and for the other the 3 yearly effective interest rate is important.

It is common for the starting point to be the effective yearly rate and work the other 2 out from there but really this only increases the complexity of the question and it is of no importance.

For now at least I am sticking by my answer!  I have checked my logic and it appears to be correct.

In conclusion, I thank thee for your presentation but I think that thou hath erred.

Lady Guinevere.

hi Jasmoye,

welcome to web2.0calc forum  

What is it that you want to do?

To solve non-linear simultaneous equations, you must find the point at which they overlap. This can be done by finding the "x" and "y" values that apply to both equations.

Let's assume we have the following two simulatenous equations:

y = 3x

y = x + 12

We know that in each of these equations both "3x" (the same as 3 multiplied by x) and "x + 12" are equal to the variable of "y". Since the two equations are simultaneous, or occuring on the same graph, 3x and x + 12 must be equal. Thus, we can safely infer that:

3x = x + 12

Now we can simplify this equation using algebra. We can start by subtracting x from both sides to cancel out the "x" on the right side:

3x - x = x - x + 12

We can see that on the right side of the equation, "x - x" can be simplified to equal 0, so we can cancel that out to get:

3x - x = 0 + 12

or...

3x - x = 12

Also, we can simplify "3x - x" to give an  answer of "2x":

2x = 12

To simplify what we have now, we can divide each side by 2:

2x / 2 = 12 / 2

We can see that "2x / 2" is equal to "x" and that "12 / 2" is equal to 6, so we have a final answer of:

x = 6

Now that we know "x", all we have to do is find "y". This is really easy: we can just plug it into one of our first equations: "y = 3x" or "y = x+12". We'll do "y = 3x" for the sake of simplicity:

y = 3(6)

We can simplify "3(6)" by multiplying 3 and 6 to obtain an answer of 18, giving us our answer for "y":

y = 18

Points on a graph are shown as (x,y), so through using algebraic methods, we were able to find that the two equations intersect at the point (6,18).

What if we dont want to enjoy our week melody....I mean you cant tell people what to do! I dont care if you are queen guinevere!

1 gravity because no matter how weak the gravity is eventually you will go down ....Only thing that dosent equal down is zero gravity

works wonders for me. prehaps its your internet/web browser? 

The present value of a perpetuity-immediate (not perpetuity due) be C/i

The present value of a perpetuity-immediate of 10 is 10/i where i be the interest of land's userers. This be the interest for 1 annum, not 3. For 3, the effective  interest  be (i+1)^3 – 1.

Here the value of v is set to the inverse of

$$\ ( i+1): v=\frac{1}{(i+1)}.$$

The units of the Kingdom be Euros and marked as thus: €

$$v^{3}.\frac{10}{(i+1)^3-1}=32 \ Be\ the\ present\ value\ of\ the\ first\ perpetuity$$

$$\ Multiply \ by \ (i+1)^3 \ yieldeth \rightarrow \\
\hspace{150pt} \ 10v^3.(i+1)^3 = 32(i+1)^6 -32(i+1)^3$$

$$\\ In\ that\ v^3*\ (i+1)^3\ = \ 1; \rightarrow 10=32(i+1)^6-32(i+1)^3 \\
\ and \ becometh\ \rightarrow \ 0=32(i+1)^6-32(i+1)^3-10$$

With the magick of the quadratic there be a number that cometh forth. Aye! Two numbers, one be less than nothing. Sir CPhill was hither sent on a quest for nothing, and he findeth nothing, too, or not. This be less than nothing; I shall leave it for the gods, and taketh the weightier part.

$$\ (i+1)^3 = 32 \pm\frac {\sqrt{2304}}{64}=1.25$$

$$\ (i+1)^3=1.25 \
\\ and\ the\ user's\ rate\ be\
\\\sqrt[3]{1.25}-1= 0.0772 \ per\ \ annum\
\\ And\ for\ four\ moons\ be\ \sqrt[3]{1.0772} -1
\\The\ present\ value\ of\ the\ perpetuity-immediate \ be
\\\frac{1}{\sqrt[3]{1.0772} -1} \ =\ 39.84.\ In\ the\ units\ that\ be\ reinout-g's\ Euro$$

                                                                                                                    €

Presented to and for her Royal Highness

by sevice of

Morgan Tud M^-1

2x-6=1.2-x

2x+x-6=1.2

3x-6=1.2

3x=1.2+6

3x=7.2

3\7.2

X=2.4

Well..bertie, as you can tell, probability isn't my strong suit.....I am happy when my answer actually agrees with anyone's .....but, when I actually agree with myself, it's truly odd !!!    LOL!!!

We need a permutation for this one.

(5 P 2) = 20

If we had just wanted to count all the possible sets that could be formed by choosing 2 people from any 5, the answer would have been 10. But, the permutation considers order within sets.

Thus, the set {person 1 , person 2} is considered a different set from {person 2 , person 1}.

It's where e^(3x) = 70

Take the natural log of both sides

 Ln e^(3x) =  Ln 70     And by  a property of logs, the left side just becomes 3x...so we have..

3x = Ln 70                  Divide both sides by 3

x =  Ln70 / 3    ≈ 1.416

Let's take it term by term

4x* 2x^2  =  4*2*x*x^2  =  8x^3

4x *(-7x) =  4*(-7)*x*x = -28x^2

4x*3 = 4*3*x = 12x

Put it all together...

8x^3 - 28X^2 + 12x

And that's it ... !!!

natasza...I've made a change to one of these answers ....No. 5....I saw what it wanted....I realized that my answer to the y° part was incorrect and I also saw that it wanted an answer  for "x°"...look at it again!!

IMHO = In My Humble Opinion

NO!!...I'm not blaming you.....it's just hard to determine some of the labellings...not your fault !!!

What Does "IMHO" Mean? :)

Sorry, I did Not Create The Problems. And I Apologize for any Trouble it Caused?

Thank You for All the Answers and Thorough Explanation! :)

Nice one Phill -re the 39 runners, two different methods, identical results, can't be bad !

Let's find "theta" in the first triangle....we know an opposite side and an adjacent side.....the thing that relates these is the tangent...so we have

tan(Θ) = 2/3    .... now......we need to take the inverse tangent to find this angle....so we have...

tan^-1(2/3) = about 33.7 degrees

So...in the second triangle, we have

tan(33.7) = 5/x     or, rearranging slightly...   x = 5/ tan(33.7)  = about 7.497 or just 7.5

And there you go......