Melody

Let x be the total number of guppies

5/16 of x go in the first tank

8/16 of x go in the second tank

so 3/16 of x go in the third tank

the difference between tank 2 and 3 is   (5/16)x

\(\frac{5}{16}*x=100\)

You can finish it.

A fraction line is really just a divide by sign  

example

\(1)\quad \frac{5}{6}=5\div 6\\ 2) \quad 5\frac{3}{4}=5+3\div4\)

Now just put it in any calc and you will get the decimal equivalent.

Some calculators, like this Web2.0 calc   will do this for you automatically.

2x(x - 10) = -50 + 2x

\(2x(x - 10) = -50 + 2x\\ 2x^2-20x-2x+50=0\\ 2x^2-22x+50=0\\ 1x^2-11x+25=0\\ x=\frac{11\pm\sqrt{121-100}}{2}\\ \text{sum of the roots =}11\)

Answered on the 10th  by apsi...

And we are still waiting for you to respond.

Your answer is correct too  

also it is probably obvious but I accidentally replaced h with f  (I didn't use it anyway)

Hi Blank, 

Here is the pic.  (maybe next time you could display some of your own working for us)

Note that a=a'    and   k_1=k   (because it is an isosceles triangle)

I added g, it is g that you need to find in terms of the original letters.

Width of alley= k+g

\(cos75= \frac{g}{a}\\ g=a*cos75\)

So width of alley = k + a*cos75

At this point I have answered the question but it is not very difficult to go further.

Using pythagoras a=sqrt(2k^2)

And cos75 can be estimated on the calculator (which is sensible since it is a real life situation)

But the exact value of cos 75 can also be found using the expansion of cos(45+30)

Yes that is right :)

How many are there altogether?

Which ones are prime?

Which ones are even?

Answer those and get back to me.

What have you done already, by yourself?:

hint:

pythagoras's theorum

then

similar triangles

I have responded.