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...add to both sides


........add to both sides


....both sides multiply bu


...or...

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let integers be and
given:
the difference of two integers is
.....1
one integer is one-third of the other integer,
....2
solve this system:
.....1
....2
__________________
.....1..plug in from 2
....solve for







now find
....2

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if the measure of angle is equal to the measure of angle , then we have
...we can solve this for





....plug it in measure of angle C:




measure of angle C:
now we have: , then
the measure of angle

the measure of angle =====

the measure of angle
now in all measure of angles we have only one unknown variable, and we also know that
...plug in , and
...solve for






now find the measure of each angle:













check:

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you have the quadratic in the form
set it equal to zero and solve for
...use quadratic formula
...note that , and





solutions:


..........first is at point (,)
or


..............second is at point (,)

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If there were eggs when put into groups of there have been a of eggs.

We need to find where




where , , , and are the number of when the eggs are put into groups of , , , and .
there is when the eggs are put into groups of there will automatically be when they are put into groups of or groups of . So we can forget groups of and .
The number which is by and is , but isn't divisible by , so the smallest number which will divide by , , and is .
So we need

but also

The easiest way to solve this is to try values ,, ,, ,... for to get values of , , , , ... for , and to pick the first of these which divides by . This is .
So the number of eggs is .
Adding to a valid solution will also give a valid solution.
So the next solution is .
All the solutions are , , , , , ... (i.e. add each time)

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...move to the left and to the right side of equal sign (recall that sign changes in this case)




we can check result by plugging in
...recall:when multiplying two negative numbers, the product will be positive number

...true; so, is a solution for

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calculations that are measured in square units (you using it in case you measure area):
Answer
The amount of carpet needed to cover a floor-relates to area
The amount of sod needed to cover a dirt yard-relates to area
The amount of paint needed to cover a wall -relates to area
-------------------------
these are not answer because:
The amount of water needed to fill a bucket relates to volume.
The amount of fencing needed to surround a garden relates to perimeter.

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if segment bisects segment , but segment does bisect , then segment and segment have only one point in common and it id end point of segment (either point r or point s lies is midpoint of segment )
so, it is possible...

draw a line segment perpendicular at a point or on a line segment

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...here you have a linear function; so, the graph will be a line
to graph a line you need two points to plot on the Cartesian coordinate system
easiest way to find these points is to set and find which will be , and to set and find which will be
...if , will be:


so, is at (,)

...if , will be:



so, is at (,)
now you are ready to plot these points on the Cartesian coordinate system and draw a line through

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4,10,1,7,1,8,1,5,2
The mean represents the average or the sum of the data divided by the number of pieces of data :

The median is the value in the middle of a set of ranked data:
1,1,1,2,4,5,7,8,10

The mode is the piece of date that occurs most frequently.


The midrange is the value half way between the lowest and highest
values in a set of data. It is found by adding the loweast and highest values and dividing the sum by .

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answer is: Rectangle with vertices at (-1, -7), (-1, -6), (5, -6) , (5, -7)
here are the lengths of its sides:
(-1, -7), (-1, -6),

Solved by pluggable solver: Distance Formula to determine length on coordinate plane

The distance (d) between two points is given by the following formula: Thus in our case, the required distance is For more on this concept, refer to Distance formula.

(5, -6) , (5, -7)

Solved by pluggable solver: Distance Formula to determine length on coordinate plane

The distance (d) between two points is given by the following formula: Thus in our case, the required distance is For more on this concept, refer to Distance formula.

(-1, -6), (5, -6)

Solved by pluggable solver: Distance Formula to determine length on coordinate plane

The distance (d) between two points is given by the following formula: Thus in our case, the required distance is For more on this concept, refer to Distance formula.

(-1, -7), (5, -7)

Solved by pluggable solver: Distance Formula to determine length on coordinate plane

The distance (d) between two points is given by the following formula: Thus in our case, the required distance is For more on this concept, refer to Distance formula.

here are the lengths of sides of rectangle ABCD on a coordinate grid are A(2, 6), B(2, 7), C(8, 7) and D(8, 6):

A(2, 6), B(2, 7), :

Solved by pluggable solver: Distance Formula to determine length on coordinate plane

The distance (d) between two points is given by the following formula: Thus in our case, the required distance is For more on this concept, refer to Distance formula.

C(8, 7) and D(8, 6)

Solved by pluggable solver: Distance Formula to determine length on coordinate plane

The distance (d) between two points is given by the following formula: Thus in our case, the required distance is For more on this concept, refer to Distance formula.

A(2, 6),C(8, 7)

Solved by pluggable solver: Distance Formula to determine length on coordinate plane

The distance (d) between two points is given by the following formula: Thus in our case, the required distance is For more on this concept, refer to Distance formula.

B(2, 7),D(8, 6)

Solved by pluggable solver: Distance Formula to determine length on coordinate plane

The distance (d) between two points is given by the following formula: Thus in our case, the required distance is For more on this concept, refer to Distance formula.

you can prove this way that all other rectangles are not congruent to ABCD

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Identity Properties
The additive identity is :

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Solved by pluggable solver: Plot a number on a number line

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....1
....2
__________________
you can solve this system by addition; add 1 and 2
....1
+
....2
_____________________





now find
....1

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in the form
...common denominator for and




or

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the reciprocal of is
if will be:
....both sides multiply by to get a rid of denominator

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For each question, if you have to answer all of them, you can either answer it true or false; so for questions , the number of ways is

But, if you have an option to either answer it true, answer false, or leave it blank, this is ways for each of questions, so the total number of ways is .

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the answer to £ at a percent (which is equal to ) interest rate per year for years will be:
£
so, adding interest you have to pay for years, you will have to pay £

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let be democrats and republicans
In the 107th Congress, the US House of Representatives had a total of democrats and republicans; so, we have
....1
There were more republicans than democrats; so, we have
.........2
now, we are going to solve this system:
....1
.........2
______________________

....1...solve for
...plug it in 2
.........2.solve for




now find

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(,)

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1)
=
=
=


2)
=
=
=
=


3)










3)






4) ...in case you have this




but, ...in case you have this

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.....1
....2
____________________________

.....1...solve for
....1a...plug it in 2
__________________
....2
...solve for





now find
.....1

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A parabola is of the general form , and you have that.
If is the parabola (looks like a smiley face), if is the parabola (looks like a sad face).
It is to note that for your question, you have the opposite , instead of , you goes up.
In case of will be on , and when this occurs, a positive value means it will go to the , so it will look like a letter .

first, you can do is to find the vertex using
...this is value...plug it in and find value




so, the vertex is at the point (,)

In this example you can factor to find the , the possible values for in our general form, when .
So,

........substitute with
...group
...factor out from first group and from second group
...set

if ..->...
if ..->...

So the parabola passes through the on the graph at and . As parabola are symmetrical, the of is halfway between these, ie .
So sub this value into the original equation to find the lowest point of the parabola.
...now set and solve for to find

...so, there is at the point (,)
you can also take few other positive and negative values for , calculate and plot that points too, and you are ready to draw a graph

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You can use
three of curly brackets, put formula or equation in, and close using three of curly brackets again
symbol for multiplication is *, for division is /,
if you have a fraction, put it in parentheses ()
You can also use HTML.
here is some information you need to see:
http://www.algebra.com/services/rendering/

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to simplify , all you can do here is just to write it as a product
same for

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there is no possibility to chat, but you can post your questions here and they will be answered...:-)

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there are 4 possibilities:
+ +
Nothing new here, just add as usual.
+ -
You are going to the right and then to the left, so they are fighting with each other, and you don't get very far. Ignore the signs and subtract the bigger one minus the smaller one. The bigger one wins out as far as which direction you are going, so it determines the sign of your answer.
- +
You are going to the left and then to the right, so again they are fighting, so just like in the last case, you ignore the signs and subtract the bigger one minus the smaller one and the bigger one wins and determines the sign of your answer.
- -
Now you are going to the left and then going to the left again, so to determine how far you are going you ignore the signs and add, and since you will end up to the left of , the sign of your answer will be negative.
or, simple:

Like Signs - Add and the sign is the common sign.
Different Signs - Subtract and use the sign of the bigger one.

Our original subtraction of positive numbers like 7-5 can be take care of by adding a negative, since 7+-5 give the same answer as 7-5, so we can generalize this to a definition for subtracting any two signed numbers. So to subtract two signed numbers you change it into an addition problem by changing the second number to its opposite.
To subtract, change the sign of the second number and add. And that's really all there is to it. You just have to remember to do it, and that takes practice.

combinations of plus and minus for multiplication of signed numbers:
+ +
No negative numbers here, so nothing new.
+ -
Multiplying by positive numbers means repeated addition, so the same thing should be true when you multiply it by a negative number. The repeated addition of a negative number gives a negative number and the absolute value, that is the size without the minus sign, is simply the product of the two absolute values. This means when you multiply a positive number times a negative number, you multiply the two numbers ignoring the signs, and the sign of the answer is negative.
- +
We want multiplication to be commutative, so this should be done the same way as +-.
- -
This one is slightly trickier to understand, and I've never seen a convincing physical interpretation of it. Mainly you have to accept this on the basis that it is the only mathematically consistent way to define it given the other definitions. There are a number of ways to think about it. If -+ is - then -- somehow has to be something different, so it must be +. Or you can think of it as, since -+ is - then multiplying by a minus must change the sign, so in a minus times a minus the first minus must change the sign of the second one to plus. An interesting more formal way of seeing it is to use the distributive property. Take an example with numbers to make it friendlier.
,
but also by the distributive property

So whatever is, when you add it to you have to get , and the only thing you can add to and get is . Anyway, however you see it, it seems that the only possible thing for the product of two negatives to be is a positive.
Again just like with addition we can make this easier to remember by collapsing it down to just two cases, and here it is really much simpler that with addition, because with multiplication you always multiply, so all you have to worry about is what the sign of the answer will be.
Always multiply
Like signs, sign is +
Different signs, sign is

The same rules about signs hold for division as for multiplication. Also if you have a problem that is all multiplication and division, you can just ignore the signs and then figure out what the sign of the answer is by counting up the minuses and if it is even the answer is plus and if it is odd the answer is minus. But be careful, you can only do this if the problem is all multiplication and division.

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