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No it is not correct.    

I think i did it the hard way,....

(x-1)(x-2)(x-3)=(6-1)(6-2)(6-3)   

So x=6 is one solution.  

It is a cubic so there is a total of 3 answers for x.   

The other 2 satisfy   x^2+k=0

Maybe there is a quicker way to do it but I expanded the left.

\((x-1)(x-2)(x-3) =5*4*3\\ x^3-6x^2+11x-6=60\\ x^3-6x^2+11x-66=0\\ \text{Then I divided the LHS by (x-6) and got}\\ (x-6)(x^2+11)=0\\ So \\ x=6,\;and\;\;x^2=-11\\ x^2=-11\\ x=\pm\sqrt{-11}\\ x=x=\pm\sqrt{11}\;i\\ \)

But you were not asked for all the x solutions you were asked for k and  k=11

Good answer BaldisBasics .... but you shoud also specify that x cannot equal 0 because you cannot divide by 0.   

Hint:

Expand     (a+b)^3     and see what you get.

Please no one answer over me.

Don't know... just thinking.  Lets say we start on the front.

4 minutes = 4 moves.

If the second last position (3rd) is front or back then it is impossible. So the 3rd position must be a side.

So the only posibilities that work are 

front side back side front       4*1*4*1 = 16ways

front side   side side front       4*2*2*1 = 16 ways

So there are 32 paths that end on the start face.

How many paths are there altogther?  Each side shares and edge with 4 other sides.

so that is 4*4*4*4 = 256

So I think the probability that the ant will finish on the face where it started is     32/256 = 1/8

The two triangles are similar.

Use the rules of similar figures to  work out the lengths.

Hint:

With similar figures 2 corresponding sides are in the same length ratio as any other 2 corresponding sides.

No one answer over me please.

There have been about a million of these questions lately.

Maybe you are all doing the same course.

(f-g)(x) means  f(x) - g(x)

You should be able to do the rest yourself.

Please no one answer over me.

I should not have to say this every time. 

If people give part answers it is because they are trying to teach, or force someone to learn.

If the person needs more help at least let them say so with an explanation of why.

This question talks about credit so it is an assessable task. So it should not be answered.

Certainly not in entirety anyway.

There is a post in the sticky topics about inserting pictures.  It is the second one.

Sticky topics are to the bottom right of your screen.

how did you post picture? cant figure it out and its not like the old tinypic

Thanks for your answer Max but .........you are talking to a little kid Max  and you have jumped steps  

(Sorry Nickolas, but on here you are a little kid. Enjoy the status while you can.)

\(7+(10-4)^2\div 4\times( \frac{1}{2})^2\\\)

Firstly Nickolas you need to learn the correct notation.

If you cannot write in Latex like I have then here are a couple of alternate correct methods.

7 + (10 − 4)to the power of 2      ÷     4 × (1/2)to the power of 2

or

7 + (10 − 4) ^ 2 ÷ 4 × (1/2) ^ 2

or

7+(10-4)^2 / 4*(1/2)^2

See how ^ means 'to the power of'.

and how divide and fractions are really the same thing.  Yea I know it is a bit confusing.

----------------------------------------------

Anyway, here is your answer.

As far as order of operation goes, it is

1) Inside brackets first.

2) powers  

3)  Multiplication and division, left to right

4) Addition and Subtraction, left to right.

------------------------------------------------

\(7+(10-4)^2\div 4\times( \frac{1}{2})^2\\ \text{get rid of brackets first}\\ =7+6^2\div 4\times \frac{1^2}{2^2}\\ \text{which means}\\ =7+6^2\div 4\times( \frac{1*1}{2*2})\\ \text{now do the powers}\\ =7+36\div 4\times \frac{1}{4}\\ \text{now multiply and division are equally important so you do them from left to right}\\ =7+9\times \frac{1}{4}\\ \text{mmm tricky, fraction multiplication.}\\ \text{9=9 divided by 1 = 9 over 1, I have to write it like that.}\\ =7+\frac{9}{1}\times \frac{1}{4}\\ =7+\frac{9\times 1}{1\times 4}\\ =7+\frac{9}{4}\\ \text{Note that }\frac{9}{4}\;\;\;\text{is the same as }\;\;9\div 4 \\ =7+2\frac{1}{4}\\ =9\frac{1}{4}\\\)

If you do not full understand some of these steps then you probably need to do a lot of work on basic fractions.

I/we can help if you want us too.  

Fractions are hard to understand. There are many concepts with them. And you will not be good at maths unless you master them very soon.

You need to master order of operation too. 

Thank you so much!

- x - = +

So, looking at the negatives (there are 5 on the left side), we get -10x = -5. Then, dividing by -10 results in x = -5/(-10) = 1/2.

thank you

Thanks, CPhill!!! 

You did not follow the rule of GEMDAS. Division comes before any Addition or Subtraction.

\(\frac{3}{4}+\frac{1}{3}/\frac{2}{12}-\frac{1}{2}\). Following GEMDAS, you would do \(\frac{1}{3}/\frac{2}{12}\) first. Since, when dividing fractions, you really multiply them by the recipricol, you would really do \(\frac{1*12}{3*2}=\frac{12}{6}=2\).

Following the communitive property of addition, you would then do \(\frac{3}{4}+2-\frac{1}{2}=2+\frac{3}{4}-\frac{1}{2}\), to subtract the fractions easier.

NOW is when you find the common denominator, which is 4. You then get \(2+\frac{3}{4}-\frac{2}{4}=2+\frac{1}{4}=2\frac{1}{4}\).

So, \(2\frac{1}{4}\) is your final answer!

According to GEMDAS, you do Division before Addition or Subtraction. I would split the problem into two seperate problems.

Since you start with division, start by doing \(\frac{1}{3}/\frac{2}{12}\). When dividing fractions, you take the dividend and multiply it by the reciprocal of the divisor, giving you \(\frac{1}{3}*\frac{12}{2}=\frac{12}{6}=2\).

So, now you have \(\frac{3}{4}+2-\frac{1}{2}=x\). Using the communitive property of addition, you can move the fractions closer together to make \(2+\frac{3}{4}-\frac{1}{2}=x\).

Now, you want a common denominator. The least common denominator is 4, so you can multiply \(\frac{1}{2}\) by 2 to get \(\frac{2}{4}\)

You should now have this: \(2+\frac{3}{4}-\frac{2}{4}\). Subtract the fractions first to get \(2+\frac{1}{4}\). Now, just add them together, to get \(2\frac{1}{4}\).

So, the final answer will be \(2\frac{1}{4}\), \(\frac{9}{4}\), or 2.25. Hope that this helped!

f(x)  = -sin(3x) - 1

We have the form   f(x)  =  Asin (Bx) + C

We are only concerned with  the "3"  = B

And

B  =  2pi  / period        ....so....

3 = 2pi / period            rearrange as

period  =   2pi / 3

freq  =  1 / period  =      1 / { 2pi/3)  =  3/(2pi)

Excellent, Jenny  !!!