Melody

That is much better. And no the answer is not 6.

\(x(3x-4) \le \frac{(6x^2-3x+5)}{10}\\ 10x(3x-4) \le 6x^2-3x+5\\ \)

Now you have to expand the left-hand side

then

take all the terms to the left side so that it is   <=0

then

Factorise the left side.

Now if you let the left side equal y

then y must be less than or equal to 0

The left side, when you put it equal to y, will actually be a concave up parabola.

Find the roots of the parabola.

Any integers between the roots will be solutions to this problem.   :)

Give it a go 

Present it properly, by editing it, and I will think about helping you.  But you need to be quick, 

Just work on the LHS it is actually not particularly difficult.

you will need to know the expansion for \(tan(2\theta)\) and from that   \(tan(4\theta) \)

The rest will just fall out.  Give it a go. :)

I am not so sure that period and midline are terms that can be used for this.

As for reflection.... reflection across what line?

Here is the graph

The least common multiple will be 3*3*5*x

The highest common factor is  some factor of 45

so

\(\frac{3*3*5* \boxed{x} }{\text{some factor of 45}}=\frac{33}{1}\\ \frac{3*3*5*\boxed{11}}{\boxed{3*5}}=\frac{3*11}{1}\)

So the least common multiple is 3*3*5*11

The highest common factor is  3*5

so they are both multiples of 15 and ours must be a multiple of 11 as well ... 3*5*11=165

So I think the two numbers are  45 and 165

Thanks Heureka and Tiggsy.

Now I have some homework   

That is a good observation guest.    

Let CD be x units in length and let the height be h

so what is BC?

what is DE?

You need to find    AreaACD = xh/2

Set up formulas for the two areas that you know.

Solve them simultaneously to find the value of xh 

Note: you probably can solve for x and h independently but it is easier to find the value of xh

I'd be interested to see the solution for this one too.   

You should do this with a Venn diagram.

Two overlapping circles inside a rectangle

There are 2 with no siblings that leaves 28 with a brother or a sister or both.

Let x be the number with both.

22 have a brother so  22-x have a brother but no sister.

25 have a sister so 25-x have a sister but no brother

so we have    22-x  +  x  +  25-x = 28

Solve that, find x

Draw the vent diagram properly.

Find the desired probability.