wombat

\(C=\sqrt{{A}^{2}-{B}^{2}}\)

where we know that; \(C=8\) and; \(A=17\)

just put those numbers in for now;

\(8=\sqrt{{17}^{2}-{B}^{2}}\)

we need \({A}^{2}\)--\({B}^{2}\)to equal \({8}^{2}\) therefore;

\({17}^{2}-{B}^{2}=64\)

Minus 64 from both sides;

\({17}^{2}-{B}^{2}-64=0\)

Then add \({B}^{2}\) to both sides;

\({17}^{2}-64={B}^{2}\)

\({17}^{2}-64\) is equal to \(225\)

therefore \({B}^{2}=225\)

and \(B=15\)

\(23=u/2 -14\)

We start by adding 14 to both sides;

\(37=u/2\)

Now we times both sides by 2

\(74=u\)

ta dah! - u=74

population density is usually put in units of pop/km^2;

so if 40 of your km^2 have 320 deer in them;

\(\frac{320}{40} = 8\)deer/km^2

could be a different question if it asked for the density in pop/miles^2

{nl} \({x}^{2}-30x+225\) right?

your square, by defenition, has equal length sides;

area = the length of one side squared

perimiter = the length of one side times 4

therefore the conversion from area to perimiter is;

     square root and times by 4

try quadratic factorising;

first we need some information;

     - the signs are negative and positive and therefore both signs must be negative in the brackets

     - \(\sqrt{225}=15\)

     - the question has given you the area in a 'quadraticy' way - it is likley therefore that factorising it will work

then do it!

\((x-15)(x-15)\)

as;

\(side length\times sidelength = (x-15)(x-15)\)

we can conclude that the length of one side is \(x-15\).

Next we need to find the perimiter - which is the sidelength times 4

\((x-15)\times4\)

\(4x - 60\) = perimiter

hope this helps

firstly you need to know the equation for the circumference of a circle;

\(pi\times d\)  or  \(pi\times 2r\)

in this example we know that;

\(pi\times2r = 14pi\)

divide both sides by \(pi\);

\(2r = \frac{14pi}{pi}\)

simplify;

\(r = 7\)

and there you go - the radius is 7cm

The general rule in simplifying is to try make everything as 'nice' as possible;

     - fractions are not 'nice'

     - divisible multiples are not 'nice'

     - decimals are not 'nice'

     - brackets are not 'nice'

     - having unknowns on different sides is not 'nice'

     - powers (negative and positive) are not 'nice' - unless they lead to decimals

if you have any of these you need to try and get rid of them

You need to have a few basic skills in order to simplify things;

    - being able to work signs (negatives and positives)

    - being able to expand brackets

    - adding, multiplying and dividing fractions

    - multiplying, dividing, rooting and putting to a power the whole equation

simplifying is often the first step in any longer question - it really helps if you nail this

many of the steps involved involve doing the same thing to both sides of an equation

on to some easier examples;

 
\(x + 12 - 4 = 3x + 2\)

firstly - you swap the unknowns (x values) to one side - in this case we moved the x values to the right by;  \(- x\) from both sides

\(12 - 4 = 3x - x + 2\)

secondly you need to get the non x values on the oppsite side - so we \(- 1\) from both sides;

\(12 - 4 - 2 = 3x - x\)

now you need to collect the like terms - notice that up until this point we have done very little maths, only swapping and changing parts of our equation

so; \(12 - 4 - 2 = 6\)

and; \(3x - x = 2x\)

so we end up with our new equation;

\(6 = 2x\)

as we know - divisible multiples are not 'nice' - and as both 6 and 2 are multiples of 2 we can divide the whole equation by 2;

\(3 = x\)

and there you go - simplifying

I know this is pretty simple and i havent even covered multiple unknowns, brackets, fractions, powers, surds and logarithms and indeed many other things i either cannot remember right now or i can't even do.

I hope this awnsers your question about swapping parts of an equation from one side to another

not a huge amount of info :P

If you are asking what that symbol means, it simply refers to a line starting at A and ending at B

take a look at this image;

http://www.math4ged.com/wp-content/uploads/2011/07/ged-math-triangle-properties-21.png

In this you will see the verticies (corners) marked as letters A,B and C

in this case - your notation refers to the line starting at A and ending at B - which is 10ft

--->

AB  -  line from A to B

  /\

ABC -  angle at B

hope this helps

Not from australia no - its just the name i have always used online

i won't pretend to be amazing at maths - but ill give it a stab

a guest no longer sir!

expand;

2.5 - 3.5x = 8 - 4x - 6

take x to one side;

2.5 - 8 + 6 = 3.5x - 4x

collect;

0.5 = -0.5x

times 2;

1 = -1x

x = -1

ta dah!