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Graph the line that has a slope of -3 and passes through the point P(0,3.

In order to see this maybe it would be easier if we understood what a slope is.
If we call the slope m
we can say that:
That is to say that the slope of a line is proportionate to:
how far a line rises or falls by (divided by) how far it goes left or right (on a graph)
So, if your slope is -3 we can say that it is or,
it falls (since its a negative number) -3 points at the same time that it moves to the right (because its a positive number) 1 point.
We could also say that for every point on the graph that the line moves to the right it falls 3 points.
To garaph this you can start by finding point (0,3) where x = 0 and y = 3.
Then, since your slope is equal to remember,
go 3 points down and 1 point to the right and make a second point.
Now draw a line between the two points you have made and that is your graph.
Just to see this principle, continue down from your second point that you made with the same pattern (3 down, 1 right) and you will see that the line you have drawn will always follow that pattern.
I hope this helps,
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SOLVE THE SYTEM BY ADDITION
-5X+2Y=10
X-3Y=11
First we can add these equations vertically.
-5X+2Y=10
....X-3Y=11
__________
-4X-1Y=21
Ok so far?
Now we can solve this result for one of the variables. Lets choose Y.
-4X-Y=21
We can add 4X to both sides to move it to the right.
-Y=21+4X
Then we can divide each side of the equation by -1 to make the Y positive.
Y=-21-4X
Now that we have the value for Y we can insert that value into one of our original equations.
X - 3(-21-4X) = 11
Ok?
Now we can solve for X.
first we can distribute the -3 with everything inside the parentesis.
X + 63 +12X = 11
Then we can subtract 63 from both sides.
X + 12X = -52
Then we combine like terms.
13X = -52
Then we can divide both sides by 13.
X = -4
Now that we know the value of X, we can substitute the -4 in the other original equation.
-5(-4)+2Y=10
Distribute.
20 + 2Y = 10
Subtract 20 from both sides.
2Y = -10
Divide by 2.
Y = -5
So X = -4 and Y = -5
To check this we can apply both results to one or both of the originals.
-5X+2Y=10
-5(-4)+2(-5)=10
20 -10 = 10 TRUE
X-3Y=11
(-4)-3(-5)=11
-4 + 15 = 11 TRUE
I hope this helps.
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This is an example where the Distributive property is needed.
In this case each number or variable within the (parenthesis)
must be multiplied by the number directly in front of the (parenthesis).
So:
the 4 must be multiplied by the (t) = 4t
and the 4 must also be multiplied by the (-5) = -20
or:
4(t-5)= 4t -20
I hope this helps
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The standard form of an equation is:
ax + by = c
So in the equation 5y=10x-25
ax = 10x, by = 5y and c = -25
So, in order to identify a, b and c, we need to first put it into standard form because when we do some of these numbers may change.
5y = 10x -25
First we can subtract the 10x from both sides of the equation.
-10x + 5y = -25
Now we have to distrubute the negative sign - in order to identify our true numbers...
10x -5y + 25
ax + by = c
so...
a = 10
b = -5
c = 25
I hope this helps.
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This is an absolute value equation so there will always be 2 solutions.
|3x+3|=7 and |3x+3|=-7
First:
|3x+3|=7
We can now remove the absolute value lines...
3x+3=7 and we can solve for x.
Subtract 3 from both sides...
3x = 4
Divide by 3...
x = 4/3
Second:
|3x+3|=-7
remove the absolute value lines...
3x+3=-7
Subtract 2 from both sides...
3x = -10
Divide by 3...
x = -10/3
So, our solution set is...
{-10/3, 4/3}
I hope this helps.
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This is an absolute value equation so there will always be 2 solutions.
|3x+2|=7 and |3x+2|=-7
First:
|3x+2|=7
We can now remove the absolute value lines...
3x+2=7 and we can solve for x.
Subtract 2 from both sides...
3x = 5
Divide by 3...
x = 5/3
Second:
|3x+2|=-7
remove the absolute value lines...
3x+2=-7
Subtract 2 from both sides...
3x = -9
Divide by 3...
x = -3
So, our solution set is...
{-3, 5/3}
I hope this helps.
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If the original temp was -15F and it increased by +18F...
We can show that as:
-15+18
or
18-15
which equals 3 degrees F.
Hope this helps.
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When solving equations remember order of operations:
PEMDAS (perenthesis, exponents, multiplication, division, addition, subtraction)in that order!
3x - 2(25 - 3x)= 40
First lets eliminate the parenthesis by distribution.
Multiply -2(25) and -2(-3x)
3x -50 + 6x = 40
now we can combine like terms.
9x -50 = 40
If we add 50 to both sides of the equation, we can isolate the 9x.
9x = 90
Now in order to solve for x we can divide both sides by 9.
x = 10
Thats it.
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Side a of a triangle is 4cm longer than side b. side c is twice as long as side b. What is the length of each side of the triangle if its perimeter is 28cm? p=a+b+c
First: What side do we know nothing about? side b.
So, we describe the other two sides in terms of b.
Side a of a triangle is 4cm longer than side b.
So, side a = b + 4
And we already said we know nothing about side b.
So, side b = b
Side c is twice as long as side b.
So, side c = 2b
Does this make sense so far?
Now lets combine these variables acording to the perimeter formula.
a + b + c = P
So...
b + 4 + b + 2b = 28
Now we can simplify and solve for b.
If we combine like terms we get...
4 + 4b = 28
Subtract 4 from each side to isolate the variable.
4b = 24
Now we can divide both sides by 4.
b = 6
Now that we know the value for b we can solve the word problem.
a = b + 4
a = 6 + 4
a = 10
And...
c = 2b
c = 2(6)
c = 12
so...
a = 10
b = 6
c = 12
We can check by addind these solutions together...
10 + 6 + 12 = 28
Correct!
I hope this helps.
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N-(-6)=4
If we go by the order of operations we need to simplify the parenthesis first.
Lets look at the problem like this...
N -1(-6)= 4
We know that a negative number multiplied by another negative number is positive, right?
so this means...
N + 6 = 4
now we simply isolate the variable N by subtracting the 6 from both sides of the equation.
N = -2
Thats it.
Good Luck

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What is the equation of a line in standard form that passes through points
(6,2) which we will call (x1,y1) and
(9,10)which we will call (x2,y2).
First we need to find the slope of the line using the solpe formula:

So we plug in our points.

Then subtract

This is our slope.
Now we can use the point slope formula to get our equation.

Again lets plug in the variables.

Now we can simplify by multiplying the entire equation by 3 to eliminate the fraction.


Then we can distribute both sides.

Now we can combine like terms.
add 6 to both sides...

this is simplified as far as possible, now we just need to put it into standard form: ax + by = c
So we can subtract the 8x from both sides...

then we should distribute the - through the equation which means that we should change the signs of ALL the variables.

this is the final equation.
I hope this helps
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Graph the inequality

this reads that a number (x) is greater than or equal to -7
at the same time that it is less than 4.
This is how it would be plotted on a number line.

Where the RED dot marks the -7 you would insert a [ "left bracket" to indicate that x is greater than or equal to -7.
Where the GREEN dot marks the 4 you would insert a ) "right parenthesis" to indicate that x is less than 4.
your solution set would be...
[-7, 4)
I hope this helps.
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8u = 3u + 35
Lets solve for x.
First we combine like terms by subtracting 3u from both sides of the equation.
5u = 35
then, in order to isolate the variable, we can divide both sides by 5.
u = 7
this is your final answer.
I hope this helps.
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a man weighs 5\6 th his weight plus 30 pounds what is his weight? please help asap i need this tomorrow
If a man weighs 5/6 of his weight + 30lbs, then 30lbs represents 1/6 of his weight because 30lbs is all that remains.
So...
1/6x = 30
multiply by 6 to eliminate fraction...
6(1/6)x = 6(30)
perform operations...
1x = 180
simplify
x = 180 lbs.
Good Luck!
Alan

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5(X+3)+X=4(X+6)-3
This isnt so bad, it just looks like alot so why dont we just work on one section at a time. lets start with the left side of the equation.
5(x+3)+x
if we follow the order of operations we can use the distributive property with the 5(x+3)+x. this means 5 times x and 5 times 3 + x. Multiply first!
so we get...
5x + 15 + x
does this make sense so far?
now we can add the "like terms" (the x's) together.
5x + x = 6x
so now we have re-written the left side of the equation as...
6x + 15
OK?
Now we put that aside and look at the right side of the original equation.
4(x+6)-3
if we follow the order of operations we can use the distributive property with the 4(x+6)-3. this means 4 times x and 4 times 6 - 3. Multiply first!
so we get...
4x + 24 -3
ok?
now we can combine like terms (the 24 -3).
4x + 21
Good!
now that we have simplified this equation we can put it back together.
6x + 15 = 4x + 21
Does this look a little easier to deal with?
Now we can combine like terms across the equals sign.
We need to isolate the x variables on one side of the equation in order to solve for x. If we subtract the 15 from both sides and we subtract the 4x from both sides we have...
6x - 4x + 15 - 15 = 4x - 4x + 21 - 15
then we can simplify, the 15's cancel on the left and the 4x's cancel on the right...
6x - 4x = 21 - 15
then we combine the terms.
2x = 6
now we can completely isolate the x by dividing both sides by 2...

the 2's cancel out...

or
x = 3
this is our final answer.
I really hope this helps you out.
Please let me know if you have any questions.
Good Luck!
Alan

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OK, no problem...
Lets just take these one step at a time.
-2-4(2y-1)=(6-2y)3
What if we just work on one side of the equation at a time, that might help.
So all we have is the left side:
-2-4(2y-1)
If we follow the order of operations we know that we should work with the parenthesis first using the distributive property, forget about the -2 for now.
So we have...
-4 X 2y and -4 X -1
this becomes -8y and -4 or -8y -4
ok so far?
now if we bring back the -2 we have...
-2 -8y -4
Does this make sense?
Then we can combine like terms (the -2 and the -4)
-8y -6
Ok?
Now we put that aside and work on the right side of the equation...
(6-2y)3 or we could look at this like 3(6-2y)
So now we have...
3 X 6 and 3 X -2y
this becomes 18 and -6y or 18 - 6y
ok so far?
now that we have re-written the equation lets bring it back together...
-8y -6 = 18 - 6y
does this make sense?
now we need to solve for y...
we can combine like terms again accross the equals sign.
In order to do that we can add 6 to both sides and we add 6y from both sides to make it look like this...
-8y - 6 + 6 + 6y = 18 + 6 - 6y + 6y
the 6's will cancel on the left side and the 6y's will cancel on the right.
-8y + 6y = 18 + 6
now we can combine the terms...
-2y = 24
ok so far?
now to completely isolate the y variable we can divide both sides by -2...

the -2's cancel on the left side

and we can reduce the right fraction to
-12
so our final answer is...
y = -12
I hope this helps.
Please let me know if you have any more questions!
Good Luck.
Alan

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-8(2y-4)=9(4-2y)
This isnt so bad if we just remember the order of operations.
First let's use the distributive property on both sides of the equation...
Lets start with the left side:
-8(2y-4)
this means...
-8(2y)and -8(-4)= -16y + 32
then the right side:
9(4-2y)
this means
9(4) and 9(-2y)= 36 - 18y
so now our equation looks like...
-16y + 32 = 36 - 18y
now we need to arrange this equation so that the y variables are on the same side of the equation...
so if we add 18 y to both sides...
-16y + 18y + 32 = 36 - 18y + 18 y
which becomes...
2y + 32 = 36
now we can subtract 32 from both sides to isolate the y variable...
2y + 32 - 32 = 36 - 32
this becomes
2y = 4
Now in order to completely isolate the y variable we can divide both sides by 2

This becomes...
y = 2
this is the answer.
I hope this helps.
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2L + 2W = P Sovle for L
First let's isolate the 2L by subtracting 2W from both sides of the equation...
2L = P - 2W
Now, in order to solve for L we can simply divide both sides of the equation by 2.

the 2's cancel on the left side of the equation, but they cannot cancel on the right because of the subtraction.

So this is as far as we can go, it cannot be simplified any further.
I hope this helps.
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Evalute: if a = 6 and c = 8?
If we plug in the indicated variables, we have...

if we follow the order of operations, we have...

and...

if we divide 240 by 4...
the answer is 60.
i hope this helps.
good luck!

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In a problem such as this we can figure it out much like we would figure out a student's average grade for a series of tests. We add all the scores together and divide by the number of scores. Only, in this case there is one unknown in that series of tests, lets call that x.
82 + 64 + 98 + x
These are the four scores that we have, correct?
Now we simply add these together and divide by the number of scores, 4.
And we want that result to be greater than or equal to the minimum grade she must get in order to recieve credit, 70.

now, to make it easier to work with, we can multiply the entire equation by 4 to cancel out the denominator, remember to multiply both sides of the equation...

the 4's cancel and we can multiply the 70 by 4...

then we perform the indicated operations.

subtract 244 from both sides...

So 36 is the minimum grade the student can get on the test to average a 70.
I hope this helps.
good luck!

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10x+2y=7
y=-5x+3
We can solve this system of equations using the elimination method.
But first we need to put each equation in standard form so that they look the same. You have...
10x + 2y = 7
y = -5x + 3
The top equation is already in standard form so we just need to get the -5x in the bottom equation on the left side by adding it from both sides.
10x + 2y = 7
5x + y = 3
Now we are ready to begin eliminating variables.
First we need to decide which coefficiant to work with in order to cancel out or "eliminate" the other.
For instance, we have 10x and 5x.
What do we need to do to the 5x in order to cancel out the 10x?
What if we multiply the second (bottom) equation by -2?
10x + 2y = 7
-2(5x + y = 3)
When we distribute, we get...
10x + 2y = 7
-10x - 2y = -6
Now we can add our system to solve the equation. Like so...
10x + 2y = 7
-10x - 2y = -6
_______________
0 = 1
Is this statement true 0 = 1?
NO!
So the solution is inconsistent.
We can write the answer as...
zero, 0 or empty set, { }.
I hope this helps.
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Solve the system by substitution.
4x -12y = 5
-x + 3y = -1
First we need to figure our which equation we want to use as the substitution and solve for one of the variables.
-x + 3y = -1 seems like the best choice since the x variable has the coefficieant of 1. So lets solve for x in order to isolate the variable.
-x + 3y = -1
lets subtract 3y from both sides to isolate the x.
so...
-x = -3y - 1
now we can distribute out the - sign to make it easier.
x = 3y +1
now we simply substitute our new equation for the variable x in the secound equation 4x - 12y = 5
4(3y +1) -12y = 5
Now we can just solve.
4(3y +1) -12y = 5
12y +4 -12y = 5
4 = 5
is this possible?
No.
so our solution 0 or empty set { }.
I hope this helps.
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The trick to solving this type of word problem is to pick out what we know about each of the variables.
Lets go peice by peice.
The sum of two numbers is 90.
So since we know nothing about either number, lets just call them x and y.
easy enough...
x + y = 90
OK so far?
Now lets look at the next statement to try to find some clues.
The second is 10 more than 4 times the first.
So the second number y is 10 more than 4 times the first x.
So we dont know anything about the first number, but know an awful lot about the second in relation to the first.
lets see...
So, couldn't we say that
the first number x + 4 times the first number x + 10 = 90.
or... x = x and y = 4x + 10.
So...
x + 4x +10 = 90
Now we can just solve for x.
x + 4x +10 = 90
first we can subtract 10 from both sides of the equation.
x + 4x = 80
then we can add the variables
5x = 80
now we simply divide both sides by 5
x = 16.
now in order to find the value of y we just plug in the value for x
If y = 4x + 10 and x = 16 then...
y = 4(16) +10
y = 64 + 10
y = 74
so, x + y = 90
or 16 + 74 = 90
true!
I hope this helps.
Good luck!



What are the two numbers?

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This isn't too bad.
We can solve this system of equations using the elimination method.
But first we need to put each equation in standard form so that they look the same. You have...
8x - 4y = 16
y = 2x - 4
The top equation is already in standard form so we just need to get the 2x on the left side of the equation by subtracting it from both sides.
8x - 4y = 16
-2x + y = -4
Now we are ready to begin eliminating variables.
First we need to decide which coefficiant to work with in order to cancel out or "eliminate" the other.
For instance, we have 8x and -2x.
What do we need to do to the -2x in order to cancel out the 8x?
What if we multiply the second (bottom) equation by 4?
8x - 4y = 16
4(-2x + y = -4)
When we distribute, we get...
8x - 4y = 16
-8x + 4y = -16
Now we can add our system and eliminate the x (for now) and solve the equation for y. Like so...
8x - 4y = 16
-8x + 4y = -16
_______________
0 = 0
This is as far as you can go.
Since the outcome is 0 = 0, we can write the answer as...
{(x,y)\ y = 2x - 4}
This can be read as:
The variables x and y such that y = 2x -4.
I hope this helps.
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Yes.
Every RATIONAL number (1, 4.5, 10 1/2, -27, 75/5, 0) is a REAL number.
However, not every REAL number , is a RATIONAL number.
Although some numbers that appear to be irrational are actually rational because they can be reduced i.e.
I hope this helps.
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Simplify.

First we need to simplify by factoring in order to cancel these expressions.
The numerator in the fraction on the right is the difference of two squares.

We can factor this as (a+b)(a-b)because if we FOIL these out we get
In the denominator of the same fraction we can factor out a -1 in order to make the expression read (y-z) which is NOT the same as (z-y).
So now we have...

Now we can cancel out all of our like terms.
(y-z) in the numerator of the first expression can cancel with (y-z) in the denominator of the second expression.

(a+b)in the denominator of the first expression can cancel with (a+b) in the numerator of the second expression.
Which becomes...

Or...
-(a-b)
or...
(-a+b)
or...
(b-a)
This is in its simplist form.
I hope I explained this thoroughly enough for you.
Good Luck!

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Intersections and Unions.
First we must understand that a union includes ALL the terms expressed by each variable.
An Intersection includes only those terms that are contained in both variables.
So...
If p={-3,-2,0,1,5}
T={0,1,6,9}
and S={-3,1,6}
find T U S
We need to find the Union of T = {0,1,6,9} and S = {-3,1,6}
So if we follow our rules for Unions we must include ALL the terms expressed by each variable.
So...
T U S = {-3,0,1,6,9}
NOTE: We only have to list each number once.
If this problem asked for the Intersection of T & S we would have...
T & S = {1,6} because these are the only terms that are included in both variables.
I hope this helps.
Good Luck!

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The lenght of a recetangular playing field if 5 ft less than twice its width.If the perimeter of the playing field is 230 feet, find the lenght and width of the field.
First lets set this problem up as an equation acording to what we already know.
Since we know nothing about the width, lets call that x.
If the length is 5 ft less than twice the width, then The length can be represented as...
2x - 5
The formula for perimeter is 2w + 2l so...
2x + 2(2x - 5) = 230
Now we solve for x...
2x + 4x -10 = 230
6x -10 = 230
Now we can add 10 to both sides of the equation...
6x = 240
Divide by 6...
x = 40
So, the width is 40ft.
To find the length...
2(40)-5 = 75
So, the length is 75ft.
Now we can check our answers to the original equation.
2(40) + 2(75) = 230
80 + 150 = 230
TRUE.
I hope this helps
Good Luck!

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You didnt specify, but I imagine you would like to simplify this expression.

Lets start with the -243.
We can think of this as
We know that the cubed root of -27 is -3.
So we can take out the -3 and leave the 9 under the radical
Next we look at the .
We know that the cubed root of is x, so that can come out as well.

Finally we lookat the .
We can think of this as
From this we know that the can come out 3 times as with 1 remaining under the radical.

This is the most this expression can be simplified
I hope this helps.
Good Luck!

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Simplify and write with positive exponents only

First we can simplify the numerator and the denominator by using the rules for multiplying exponents.

Then we can add the exponents in the numerator...

Then we perform the indicated operation...

The final result is 1
I hope this helps
Good Luck!

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Find the slope of the line through the pair of points.
(-9, -6) and (-9, -8)
When finding the slope of a line (m) passing through 2 points (-9, -6) and (-9, -8) we can use the slope formula.

Lets use point (-9,-6) as (x1,y1) and point(-9,-8) as (x2,y2).

This means...

Then perform the indicated operations...

Which is undefined.
The slope formula gives us a fraction that tells us the value of the slope m.

The rise tells us how a line moves verticaly on a graph, and the run tells us how a line moves horizontaly on the same graph.
So if the rise is -2 and the run is 0 then we know that the line does not move horizontaly, or it is a vertical line.
So the slope is undefined.
I hope this helps.
Good Luck!