Melody

Is it just the x that is under the square root?

(x-5√x +1)(x-4) =6(√x -1)^2

log2(1/16) = -4

It is a bit complex for a 12 year old.  :)    But a log is a power, 

\(If\;\;log_2\frac{1}{16}= -4\;\;\;then\\ 2^{-4} \;\;must \;\;equal\;\; \frac{1}{16}\\~\\ \frac{2^{-4}}{1}=\frac{1}{2^{+4}}\qquad \mbox{because that is how negative indices work}\\ \frac{1}{2^4}=\frac{1}{2*2*2*2}=\frac{1}{16}\\ so\\log_2\frac{1}{16}= -4 \)

Thanks for the points Gibsonj338  I appreciate that

BUT

Do you understand my answer?  Do you hav any questions ?

**     Also can the answer -2 < x < 1 be explained?

ok you must understand this before you can possible understand the other bit.

This means that x has to be between -2 and +1

If you graphed it it would look like this

This might help too

Clancy is right, most calcs do have such a button but the web2.0 calc does not. :(

say you have 4.678 hours this is what I would do.

4 hours

0.478*60 = 28.68        28 minutes

0.68*60 = 40.8  seconds

4.678 hours = 4 hours, 28 minutes and 40.8 seconds

Is this what you mean?

\(M=kL^3\\ \mbox{Now look at what happens to the right hand side if L is doubled}\\ k(2L)^3=8kL^3\\\)

So when k is doubled, L becomes 8 times greater.       (That is 2^3 greater)

Oh, you should have written  L3 as L^3   :)

If I understood the question, I might be able to answer it ://

7. Chairs in a hall are arranged in 35 rows of 18

35*18 = 630  chairs altogether

(a) How many rows would there be with 21 chairs to a row?

630/21 = 30    There would be 30 rows

(b) How many chairs would there be in each row if there were 15 rows?

630/15 = 42  chairs in each row   :)

2.Given that 5cm on a map represents 4km on the ground;

(a) Calculate the distance in km, between 2 villages which r represented on the map by points 7.5cm apart

If you are going to do these as fraction equations, you need to learn to use the units properly.

See how I have done it with the km on the top of each fraction and the cm on the bottom.

When I solved the equation the equation the cm literally cancelled out!  (There was one on the top of the fraction and one on the bottome of the fraction.)

\(\frac{d }{7.5cm}=\frac{4km}{5cm}\\ d=\frac{4km}{5cm}\times \frac{7.5cm}{1}\\ d=\frac{4*7.5km}{5}\\ d=6km\)

(b) Express the scale of the map in the form 1:n

(idk what it means by that, so i didn't answer that 1)

5cm represents 4km

You have to make the units the same so

5cm represents 4000m

5cm represents 400000cm

So the ratio is

5 : 400000

Divide both by 5

1 : 80000

Sorry, I didn't see part b

1. A map is drawn to a scale of 1:50000. The distance between 2 places, A n B is 5cm on the map.

(b) 2 towns r 24km apart. Calculate in centimetres, their distance apart on the map.

24*10000

= 240000cm

(idk if its correct)

2 towns are 24km apart

1 cm to 50000 cm   becomes

1cm  to  500 metres  which is

2cm   to  1 km

2*24cm  to  1*24km

48cm represents 24km

Lets see if I can do this with algebraic fractions

I'd start with changeing 50000cm to km

50000 divided by 100 divided by 1000 = 0.5

so 1 cm represents 0.5km

\(\frac{1cm}{0.5km}=\frac{d\;cm}{24km}\\ \frac{1cm\times 24km}{0.5km}=\frac{d\;cm}{1}\\ \mbox{The km cancel out and you get}\\ \frac{24cm}{0.5}=d\\ d=48cm \)

So 24 km is represented by 48cm

Teachers teach these problems quite differently from one another and that tends to make it harder.   ://

Have a look at the next one again yourself ://  Then I will check it.

 I have not looked at it at all yet . :(