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.
how can you solve ?
.
"2x" is equal to one number, to find "x", we will have to separate the "2" and the "x"
.

.
, to find "x", we will get rid of the "2" by dividing each side by "2"
.
= = , the "2" will cross out on the left side
.
= , you can check by replacing "x" with "5" in the equation
.
= = (True)
.

.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
A 45-foot rope is to be cut into three pieces. The second piece must be twice as long as the first piece and the third peice must be 9 feet longer than 3 times the length of the second piece. How long should each three peices be?
How do I write this problem algibraicly? How do I solve it? My Final is tomarrow please help.
-Andrew
.
So the total amount of rope is 45 ft, so, that means the length of all three rope lengths will equal 45
.
We have to name the lengths in terms of "x"
.
You can usually name one of the variables, in this case there are three, "x", it probably doesn't matter, but we will use the easiest way
.
We will name Length 1, "x"
.
The second piece must be twice as long as the first piece,
.
If the length 1 is "x", and length 2 has to be twice as long, length 2 = "2x"
.
We will work the third piece a little slower, because it is the hardest of the three
.
the third peice must be 9 feet longer than 3 times the length of the second piece,
.
the third peice must be 9 feet longer than 3 times the length of the second piece, which is "2x"
.
the third peice must be 9 feet longer than 3 times "2x"
.
the third peice must be 9 feet longer than 3(2x)
.
the third peice must be 9 feet longer than "6x",
.
You would now add "9" to "6x"
.
the third peice must be "6x + 9",
.
Length 3 = "6x + 9"
.
.
.
Length 1 =
.
Length 2 =
.
Length 3 =
.
All of these lengths will add up to 45, we can now have our equation
.

.
We can get rid of the parentheses
.

.
Now add like terms
.
=
.
We will move "9" to the right side
.
= = , to find "x" divide each side by "9"
.
= = , you can check your answer by replacing "x" with "4" in the equation
.
= = = = ( True )
.

.
Length 1 = =
.
Length 2 = = =
.
Length 3 = = = =
.
To show you that you can make "x" any of the lengths, I will briefly do "x" as the Length 2
.
Length 2 = , if length 2 is twice length 1, then length 1 =
, Length 3, is 9 more than three times the second's length, or
.
Length 1 =
.
Length 2 =
.
Length 3 =
.
You would then add these to equal 45 again
.
, you would solve to find "x" = 8, which was length 2
.

.
Length 1 = = =
.
Length 2 = =
.
Length 3 = = = =
.
If you even wanted to have Length 3 = "x" you could, but that would be the hardest and most difficult.
.
Length 1 =
.
Length 2 =
.
Length 3 =
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
First you would draw something sort of like this, you can make it more creative, and draw the actual pole
.

.
It will look like a right triangle.
.
We are trying to find "c", Since we know that it is a right triangle, we can use the Pythagorean Theorem, which will work only with right triangles
.
Pythagorean Theorem =
.
"a" and "b" refer to the legs of the triangle ( the horizontal and vertical lines ). I usually think of "a" as the vertical line, and "b" with the horizontal line, but it doesn't really matter.
.
All you do now is replace the variables with the numbers we know
.
= = = = , to find "c" we will take the square root of both sides
.
= = = or , a measurement cannot be negative so
.
If you wanted to be most accurate, you would simplify your answer
.
You can sometimes simplify radicals if you can find factors of the number that has a whole number as a square root, in this case we can take "16" out of "208"
.
= ()
.
= , this is the simplified form
.
If you rounded your answer, it would be 14.42 ft
.
You can round your answer, you need to if they asked you to, but to be the most accurate, you would say the guy wire is feet long, which would be your answer
.

.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
Graph the function y = |x+1|
.
Absolute value is how far the number is on the number line. Absolute value makes any number inside them positive.
.

.

.

.
Knowing this principle
.

.
We know that "y" will always be positive, since "y" equals an absolute value
.
All absolute value graphs look like a "V", the very point that the two lines meet will always be where "y" equals "0" ( since "0" is neither positive or negative, it doesn't have absolute value ), the "V" goes out from this point
.
Let us graph a few points
.

.
First we replace "x" with any number
.
We will replace "x" with (-1)
.
= = ,
.

.

.
Points are given as (x,y)
.
Our point is ( -1,0 )
.

.
We need to find at least two more points to make the graph, we need a point with "x" as a positive number, and one with "x" as a negative number
.
We will replace "x" with "5"
.
= =
.

.

.
Our point is (x,y), ( 5,6 )
.

.
We will now replace "x" with a negative number
.
We will replace "x" with
.
= =
.
( since absolute value makes all negatives positive )
.

.

.
Our point is (x,y) , ( -12,11 )
.

.
We could now draw the equation, by drawing a line from ( -1,0 ) to ( -12, 11 ) then keep drawing the line after ( -12 , 11 ), then we would draw a line from (-1,0) to (5,6) and beyond
.
We could find more points if we wanted to,
.
"x" as (-7), = =
.
( absolute value )
.

.
Our point is ( -7,6 )
.

.
"x" as "10", = =
.

.

.
Our point is (10,11)
.

.
Here is the graph
.

.
(for some reason graph doesn't make a complete "V" for some reason, don't worry )
.
Hope I helped, Levi

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Hi, Hope I can help
.

.
You are correct
.
If you subtract the same number log by the log, it is the same as one complete log as a fraction/division
.

.
This is where you got stuck, from here we can use a really easy method called "undo"
.

.
Since this equation has the same base/log (2) on both sides, we can just "undo" , get rid of, erase, cross out the logs
.
=
.
Now just solve for "x"
.
, we will multiply each side by (x+2) to get rid of the fraction
.
= = = = , we will use distribution on the right side
.
= = =
.
We will now move "x + 20" to the right side
.
= =
.
or , this is a quadratic equation, we can solve this equation by factoring
.

.
To find the factors, we have to have multiples of "-20", and the multiples have to add up to the middle term, or "1"
.
Factors of (-20)
.
(2,(-10)) No
.
(4,(-5)) No
.
(5,(-4)) Yes, (these factors add up to "1")
.
Since there was only , that means there are only "x's"
.
(x)(x), you would then put the factors inside
.
(x+5)(x-4) are the factors, you can check using the foil method, but I already checked
.
, now we can solve for "x", you can find "x" by putting each factor equal to zero
.
, now move "5" to the right side
.
=
.
, now move (-4) to the right side
.
=
.

.

.
These are your answers, but, you have to make sure and plug your answers into the original equation, and make sure that the numbers don't make a negative, because you can't take the log of a negative number
.
(-5), , we don't have to go any further, since we already found a negative, (-5) will not work
.
(4), = , there are no negatives, "4" will work
.
Here is the graph of the equation
.

.
Remember though that you cannot take the log of a negative, your only answer is
.

.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
It took Emily 25 min to ride her bike to the repair shop and 1h 15 min to walk back home. If she can ride her bike 8km/h faster than she can walk, how far is the repair shop from her house.
.
To find the answer we need to know a formula
.

.
We can also say , Emily went on her bike for a distance, and she went back to her home, the same distance
.
We don't know how fast it takes Emily to walk, so we will say she walks "x" km/h
.
She can ride her bike 8 km/h fast than she can walk, so she goes " x + 8 " km/h on her bike
.
It takes 25 minutes or hour ( it has to be the same measurement as the rate ) to ride her bike to the repair shop
.
It takes her 1hour 15 minutes, or 1 hour to walk back home
.
The rate of her on the bike multiplied by the time it takes on the bike will equal the rate of her walking multiplied by the time it takes her to walk
.
=
.
Now replace all the unknowns with what we know
.
rate on bike = (x + 8) km/hr
.
time on bike = hour
.
rate walking = x km/hr
.
time walking = 1 hours or hours
.
=
.
, now we will multiply the numbers out
.
= = , we will rearrange the left side
.
= =
.
, we will use the distribution method to multiply the left side out
.
= = = =
.
, to get rid of the fractions we will multiply each side by "12"
.
= =

.
Now we will use distribution
.
= = = = , now we will move "5x" to the right side
.
= = =
.
to find "x" we will divide each side by "10"
.
= = =
.
We found "x"
.
We can check by replacing "x" with "4" in our original equation
.
= =
.
The denominators cross out
.
= (True)
.
rate walking = x km/hr, we can replace "x" with "4"
.
rate walking = 4 km/hr
.
rate on bike = (x + 8) km/hr, replace "x" with "4"
.
rate on bike = (4 + 8) km/hr
.
rate on bike = 12 km/hr
.
+
+
+
.
rate on bike = 12 km/hr
.
time on bike = hour
.
rate walking = 4 km/hr
.
time walking = hours
.
We can now solve for our answer, since
.
=
.
The denominators cross out
.
=
.
This means that the distance is 5 km, (since that is the measurement)
.
Your answer is 5 km
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
Give an ordered pair (x,y)of numbers that satisfy the equation

.
This is a pretty easy problem
.
For this problem, you just pick a number for "x", "x" can be any number
.
We will use "1", now replace "x" with "1" in the equation
.
= = , now you just solve for "y"
.
We will move "4" to the right
.
= = , to get "y" to be positive, we will multiply each side by (-1)
.
= =
.

.

.
You can check by replacing the letters with numbers in the equation
.
= = = (True)
.

.

.
Ordered pairs are given as ( x,y ), our ordered pair ( or point ) is ( 1,0 )
.
This equation is a line, to find a line we need two points, we already have one point, let us find one more point
.

.
Name a number for "x", we will use (-1)
.
Replace the letter with the number, = =
.
Solve for "y", , we will move (-4) to the right side
.
= =
.
We will now multiply each side by (-1)
.
= =
.

.

.
Replace the letters with numbers in the original equation
.
= = = (True)
.

.

.
Ordered pairs are given as ( x,y ), our ordered pair, or point is (-1,-8)
.
To draw the equation on a graph, you draw a line through the two points (1,0) and (-1,-8)
.
Here is the graph
.

.
Two points that satisfy the equation are (1,0) and (-1,-8)
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help
.
Solve this system of equations
.

.
This system is a little easier than what we would have to do, but is the same concept
.
We need to solve for one letter in one of the equations, doesn't matter which one, or which equation, we will solve for "z" in the second equation, since it will be the easiest
.
, to solve "z", we will move "2y" to the right side
.
= = or
.

.
Now that we found "z", we can replace "z" with in the other two equations
.

.
replace "z" with
.
= , now just combine like terms
.
= = = , now we will move "3" to the right side
.
= =
.
is our first answer
.
Now lets replace "z" in the other equation
.
replace "z" with
.
= , once again just combine like terms, we will use the distributive property to solve even more
.
= = , remember the negative/positive signs
.
= =
.
now we will move "24" to the right side
.
= =
.
We will make everything positive by multiplying each side by (-1)
.
= , we will use the distribution method
.
= = , remember the signs
.
=
.
is our second answer
.
We will now put these two answers into a system
.

.
To make it easier, we will avoid fractions as much as possible
.
We will multiply the first equation by "5"
.
= = , using distribution
.
= = ,remember signs, =
.
is the new equation
.
Now we will multiply the second equation by "3"
.
= = , using distribution
.
= = , remembering signs, =
.
is the new equation
.
We will put the two new equations in the system
.

.
We will now use elimination to find "y", we will subtract the bottom equation from the top equation
.

- , the negative sign makes all the numbers negative
.
Now we need to add the equations
.

________________

.
= , to find "y" we will divide each side by "29"
.
= = =
.

.
Now replace "y" with "5" in one of the original 2 system equations
.

.
we will use the first equation
.
replace "y" with "5"
.
= =
.
Now we will move "10" to the rights side
.
= =
.
To find "x" we can divide each side by "3"
.
= = =
.

.

.
We can check our two answers by replacing "x" and "y" with the numbers in the other 2 system equation
.
= = = ( True )
.
Now all we need to do is find "z"
.
We need to use one of the three original equations
.

.
We will use the second equation
.

.

.
Replace the letters
.
= = , we will move "10" to the right side
.
= =
.

.
We can check our answers by replacing "x","y", and "z" in the other two equations
.

.

.

.

.
= = = (True)
.
= = = ( True )
.
These answers are given in the ordered pair ( x,y,z ), our ordered pair/answer is (-2 , 5 , -7 )
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
I need help!!
- A car travelled 470 km from Sudbury to Brandford in 5 hours. For part of the trip, the car travelled at 100 km/h. For the rest of the trip, it travelled at 90 km/h. How far did the car travel at each speed?
.
We will start fresh
.
First we need to know a formula
.
, or with abbreviations,
.
A car travelled 470 km from Sudbury to Brandford in 5 hours. For part of the trip, the car travelled at 100 km/h. For the rest of the trip, it travelled at 90 km/h. How far did the car travel at each speed?
.
This problem is a little tricky, since the car is going two speeds, instead of just one, we also have two different times.
.
This will mean we will have two unknowns, we can find the other unknowns with the information we have
.
A car travelled 470 km from Sudbury to Brandford in 5 hours. For part of the trip, the car travelled at 100 km/h. For the rest of the trip, it travelled at 90 km/h. How far did the car travel at each speed?
.
Remember that , we don't know the time or distance for either one of the speeds, but we know the total distance and total time
.
We can say that the time it took when the car went 90 km/h, the time it took would be
.
We can say that how long it took when the car went 100 km/h, the time it took would be , ( if you subtract the other time, from the total time, you will find the second unknown time )
.
It is the same concept with the distances
.
one distance would be
.
the second unknown distance would be
.
We can now find equations to this problem
.

.
Equation 1
.
if the car went 100 km/h ( rate )
.
if the car took hours ( time ), ( doesn't matter which time we could use "x" if we wanted, but we will use this one )
.
These two multiplied together will equal a distance , ( once again it doen't matter which distance, we could use "y" if we wanted )
.
Now we would put the words into a formula,
.
= , this is the first equation
.
Now we will use the other distance, time, and rate, to find the second equation
.
If the car went 90 km/h ( rate )
.
If the car took hours ( time )
.
If the car drove km ( distance )
.
Now replace "r", "t" and "d" with the other veriables
.
= , this is the second equation
.
Now we can put these two equations side by side
.

.
To make it easier, we will simplify the two equations
.
Equation 1, , we can use the distribution to simplify this equation
.
= =
(remember the signs
.
= , we don't have to move anything right now, so this is the simplified form
.
Equation 2, we will just multiply the "90" and "x"
.
= , this is simplified
.
Now we can start solving for the two unknowns
.

.
This is a system of equations, the easiest way to solve this system is by substitution
.
Since , we can just simply replace "y" in the first equation with "90x"
.
=
.
= , now we can just solve for "x", we will move (-100x) to the right side
.
= = , now we will move "470" to the left side
.
= = , to find "x" we will divide each side by "10"
.
= = = = ,
.
(remember "x" is the time in hours), we can replace "x" with "3" in the second equation, to find "y"
.
= = , , we can check our two answers by replacing "x" and "y" in the first equation
.
x = 3
.
y = 270
.
= = = (True)
.
Here are the simplified equations with the numbers
.

.

.
If we look at the formula,
.

.
This means that the car went 200 km at 100 km/h, and it went 100 km/h for 2 hours
.
The car went 270 km at 90 km/h, and it went 90 km/h for 3 hours
.
The distances add up to the total distance, as well as the time with the total time
.
The car went 200 km at 100 km/h
.
The car went 270 km at 90 km/h
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
how do i find the value of x in the equation ?
.
First of all, we have to get rid of the fractions
.
We have to find a common denominator with the fractions
.
The first fraction, , has "2" as its denominator
.
The second fraction, , has "3" as its denominator
.
To find the common denominator, we would just multiply the two denominators together ( since there is no lower denominator we could use )
.
=
.
"6" is the common denominator, now if we multiply the two sides of the equation, it will get rid of the fractions, since they both will cancel out
.
=
.
We can now use the distributive property,
.
= =
.
= , now we will simplify even further by dividing
.
= = = =
.
Now all we do is solve for "x", we will move "2x" to the left side
.
= = , now we will move "120" to the right side
.
= =
.

.
You can check by replacing "x" with (-30) in the very original equation
.
replace "x" with (-30), = = = = ( True )
.
You have to be careful with fraction equations, because the denominator of a fraction cannot equal 0, so if one of the answers make a denominator 0, then that answer cannot work
.
We don't have anything to worry about, since there are no "x"'s in the denominator
.

.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
If this is a Pythagorean Theorem, this is how you would find "x"
.
c=x+8
.
b=x
.
a=x+7
.
find x
.
Pythagorean Theorem is
.
Now replace the letters "a", "b", and "c" with what they equal in "x" terms
.
Replace "a" with (x+7)
.
Replace "b" with (x)
.
Replace "c" with (x+8)
.
= , now you would just solve for "x"
.
= , you would now use the FOIL meathod to multiply
.
= = = =
.
= = , Now we will combine like terms
.
= , we will now move everything on the right side to the left side
.
= = , now we have a quadratic equation
.
We will solve using the quadratic equation
.
Quadratic equation =
.
Quadratic equations are in the form
.
,
.
In our equation
.
a = 1
.
b = (-2)
.
c = (-15)
.
Now replace these letters with the numbers in the quadratic equation
.
= = = = =
.
= =
.
= =
.
You can check by replacing these numbers into the original quadratic equation
.
(5), = = = (True)
.
(-3), = = = ( True )
.
We could have used factoring to solve, but this only works sometimes
.

.
We could have listed all of the factors of (-15), the two factors would have to equal (-2)
.
We would start like this
.
( x )( x )
.
(1, -15) ( added = (-14))
.
( 5, -3) ( added = 2 )
.
( , ) ( added = (-2))
.
The factors would then be
.
( x + 3 )( x - 5) = 0
.
You would then set each factor equal to "0"
.
= = =
.
= = =
.
These are our two answers/solutions
.
You can check even further if we replaced "x" in our very original equation
.
(5), = = = = (True)
.
(-3), = =
= ( True )
.
Don't be fooled with your two answers, since this is a triangle, your answer cannot be negative ( you cannot have negative sides ), so (-3) is not an answer
.
The only answer that works is
.

.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
Find an equation of the line that is parallel to the line and that passes through the point (7,3)
.
We are trying to find a line parallel to this line
.

.
lines are given in the form , where "m" is the slope, and "b" is the y intercept
.
, this line has a slope of , and y intercept of "7"
.
We are trying to find a parallel line, so that means the line will have the same slope as the other, or
.
If we took the line form , we can start replacing the letters for our unknown line
.
We know that "m" is , since it is parallel to the given line
.
Our new formula is
.
( we replaced "m" with the known slope )
.
, we now have 3 variables, we will have to get rid of 2 of them
.
We are also given a point, (7,3)
.
Points are in the form of (x,y)
.
(7,3):(x,y)
.
x = 7
.
y = 3
.
, now replace the "x" and "y" with the numbers
.
= =
.
Now we just need to solve for "b"
.
, we will move the over to the left side
.
= = = = , or
.
You can check your answer by replacing "b" with in the equation
.
= = = (True)
.
Now just replace "b" in our original equation ( one where we had "x" and "y" )
.
=
.
is the line in point slope form, if you want it in standard form , here is how you would convert it
.
, you would first multiply each side by "3"
.
= , using distribution
.
= =
.
=
.
Now we need to move (-4x) to the left side
.
= =
.
Rearranging the left side
.
= , this is the standard form of the equation
.
If you want to see if a point is on a line you would replace "x" and "y" with the point (x,y)
.
Our point is (7,3)(x,y)
.
x = 7
.
y = 3
.
= = = (True)
.
The graph of this line is
.

.
It is parallel to the original line and has (7,3) as a point
.

.
Your line that you were looking for or your answer is
.
Standard form:
.
Point-Slope form:
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
Can you please help me find the solution for
your help is greatly appreciated.
.
I believe this is the equation,
.
For this equation, we can just factor this polynomial, and find the solutions
.
We can factor out an "x"
.
=
.
There are two solutions, so we have two equations, we have to let both of the factors equal "0", then solve for "x"
.
(x), , is our first answer
.
(x+20), = = , this is our second answer
.
and , are your two solutions
.
You can always use the quadratic equation
.
, you can also say
.
, quadratic equations are given in the form
.
Quadratic equation =
.
,
.
Our equation
.
a = 1
.
b = 20
.
c = 0
.
Now just replace the letters with the numbers
.
= = = =
.
= =
.
= =
.
and are your two solutions
.
Hope I helped, Levi

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.
solve for x

.
If you add to of the same logs together, that is the same thing as multiplying the terms together, with only one log, this is what I mean
.
=
.
The new log would be
.

.
From here we will change this logarthimic equation into an exponential equation
.
This is how you change a logarthmic equation ( logs are a power of a base )
.
=
.
For our equation
.
= =
.
Now we can move the "16" to the right and solve the quadratic equation
.
= = or
.
, we can factor this equation,
.
( x )(x ), first name all the factors of (-16)
.
One of these pairs will have to add up to (-6)
.
(, ) ( added will equal (-15) )
.
(, ) ( added will equal "15" )
.
(, ) ( added will equal "6")
.
(, ) ( added will equal (-6))
.
You put the highlighted factors into the parentheses with the "x"'s
.
, you can check by using the foil method, I checked and it is the same as
.
You can find "x" by placing both factors equal to "0"
.
= , move the (-8) over to the right side
.
= ,
.
or
.
= , move the "2" to the right side
.
= ,
.
and , the only thing left is to put these values into the original equation, logs can't be nagative, so we need to make sure that our answers don't create negative numbers
.
(x = 8), = = ( doesn't make negative, so "8" is a good answer
.
(x = (-2)), = = ( it creates a negative number, so (-2) is no good)
.
The only answer that works is ,
.
The graph of this equation is
.

.
Remember though that "x" can only equal "8", "x" can't be equal to (-2) since this answer made the logs negative
.

.
Hope I helped, Levi

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.
Please help me solve this equation:. The 5x+9 is in a square root.
.
Thank you
.
To get rid of the square root sign(radical sign), you square both sides
.
= , when you square a number in a square root, it will always be the number inside the sign
.
Ex. ( = = =
.
So, for our problem, the radical sign disappears if we square both sides
.
= , now we need to move "5x+9" to the left side
.
= = , this is a quadratic equation
.
Quadratic equations are in the form , We can solve this equation by using the quadratic equation
.
Quadratic equation =
.

.

.
For our equation
.
a = 4
.
b = (-5)
.
c = (-9)
.
Now replace the letters with these numbers in the equation
.
= = = = =
.
= =
.
= =
.
and , we can check by replacing "x" with these two numbers in the original quadratic equation
.
, = = = = = = = (True)
.
, = = = = = (True)
.
Since this was not our very first original equation, we have to make sure that the number inside the radical, is not negative, and make sure that the statement is correct
.
, = = = = = (True)
.
, = = = = (False), is not an answer
.

.
The line only crosses at one point on the x axis, at point (,0)
.
is your answer
.
Hope I helped, Levi

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.
Does the square root of 0 equal undefined, no solution, or 0
.
Here are some more examples
.
or (-5) ( , or , , or )
.
or (-3) ( , or , , or )
.
The square root of a number is multiplied by itself to get the number inside the square root
.
So for , what number multiplied by itself will equal "0"?
.
The answer is "+0" or "-0", or just "0"
.
( , or )
.
It is not undefined, because it does exist, and no solution is the same as undefined
.
So your answer is
.
Hope I helped, Levi

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.
Solve by substitution or elimination method:
.
3x - 2y = 8
-12x + 8y = 32
.
Solve by substitution or elimination method:
.
7x - 5y = 14
-4x + y = 27
.
Solve by substitution or elimination method:
.
-4x + 3y = 5
12x - 9y = -15
.
First we will solve the first system with substitution
.
3x - 2y = 8
-12x + 8y = 32
.
First we need to solve for a variable in one of the two equations, doesn't matter which letter, or equation, we will solve for "y" in the first equation
.
, we will move (-2y) to the right side
.
= = , now we need to move "8" to the left side
.
= = , to find "y" we need to divide each side by "2"
.
= =
.
, since "y" is equal to , we can replace "y" in the other equation with , then just solve for "x"
.
= , now just solve for "x"
.
= = , now we will use the distribution method
.
=
.
Remember the + and - signs, , adding the "x"'s
.
= = ( False )
.
This means ( when the x's or y's cancel out, and there is a false statement) that there are no solutions, these lines are parallel, there is no intersection, and therefore no solutions
.
Here is the graph of this system
.

.
Now we will solve the second system, by elimination
.
7x - 5y = 14
-4x + y = 27
.
Elimination is when you add the two equations together, and it gets rid of a variable, first we need to make sure the x's or y's in each equation are the same, or the negative of the other
.
We can eliminate any variable ( either x or y )
.
We will get rid of the y's
.
We need to either get both y's to "5y" or "-5y" or we need to get them to "y" or "-y", we will change the second equation to "5y"
.
, to get "y" to change to "5y" we need to multiply each side by (5)
.
= =
.
We will need to use the distribution method
.
= =
.
Remember the signs, , this is our new equation
.
Now we will bring the firt equation to our second new equation
.

.

.
We will now add the equations
.

.

.
=
.
= =
.
=
.
It will become = , to find "x" we need to divide each side by
.
= = = , we can now replace "x" with , in one of the two original equations
.
7x - 5y = 14
-4x + y = 27
.
We will use the second equation
.
= = =
.
Now we need to move to the right side ( we will convert "27" into "13ths"
.
= = = =
.
, we can check our answers by replacing "x" and "y" in both original equations
.

.

.
First equation, = = = = = = ( True )
.
Second equation, = = = = = , ( True )
.

.

.
Solution sets are in the form (x,y), our solution set is ( , )
.
The graph of the system is
.

.
The intersection is your answer
.
Now we can do the last system
.
-4x + 3y = 5
12x - 9y = -15
.
We will use the elimination method of solving this problem
.
Remember elimination is where you get rid of a variable
.
We will multiply the first equation by "3" to get rid of the "y"
.
= = we will use distribution
.
= =
.
Remember signs, , now we can add the new first equation to the second equation
.

.

.
= =
.
= = =
.
= =
.
It will become = (True)
.
This means ( when both x and y cancel out, and there is a true statement) that this is the same line, both equation will be one line, there is an infinite number of solutions ( since the equations are equal to one line )( or the second line is put on the first line )
.
Here is the graph of this system
.

.
Your answers are
.
First system of equations = " no solutions " ( since they are parallel lines )
.
Second system of equations = ( , ) ( the lines intersect at point ( , )
.
Third system of equations = " infinite solutions " ( since the two equations are the same line )
.
Hope I helped, Levi

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Which of the following is an ordered pair solution of y=-1/2x+1/4?
A. (2,-1/2)
B. (1,1/4)
C. (-2,5/4)
D. (-1, -5/4)
.
Ordered pairs are given as (x,y), so all you do is (for "A", replace "x" with "2", and "y" with )
.
The correct ordered pair will be a true statement
.
A. (x,y)(2,), = = = (False)
.
B. (x,y)(1,), = = = (False)
.
C. (x,y)(-2,), = = = (True)
.
D. (x,y)(-1, ), = = = ( False )
.
The ordered pair is "C" ( -2, )
.
( -2, ) is the ordered pair solution
.
Hope I helped, Levi

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.
If one side of a right triangle is 12 and its hypotenuse is 13, what is the length of the other side?
.
The formula to find the Hypotenuse or sides is , where "a" and "b" are the sides, and "c" is the hypotenuse
.
We can replace "c" with the length of the hypotenuse (13), and we can replace "a" or "b" with "12" ( we will replace "a" )
.
a = 12
.
b = unknown
.
c = 13
.
= =
.
We will now move "144" to the right side
.
= = , now we just take the square root of both sides
.
= = or
.
Since lengths cannot be nagative, the length of the other side is "5"
.
You can check by replacing "b" with "5" in the equation
.
= = = , (True)
.
The length of the other side is "5"
.
is your answer
.
Hope I helped, Levi

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.
can somebody help me solve this equation:
.
first we must take the log of both sides, log is the inverse function of an exponent, it is also the power of a base function
.
The two sides will have a base of "10"
.

.
, if there is an exponent in a log such as (x+2), and (x-2), you take the exponents and multiply them by (
.
), in this case , and
.
,
.
We can rearrange the two sides
.
=
.
we can use the distribution to multiply the numbers out
.
= =
.
Remember the signs
.
,
.
now we need to get all the "x"s on one side, we will move , to the left side
.
=
.
=
.

.
Now we will move to the right side
.
=
.
=
.

.
We can take out the "x"s on the left side ( since they both have it in common
.
=
.
To find "x" you would divide both sides by
.
= =
.
=
.
= (rounded)(you have to solve using a calculator)
.
You usually check by replacing "x" with the answer, but in this case, it would be hard since the answer never stops ( I checked it, and it is right )
.
Hope I helped, Levi

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.
factor -9b+63
.
First we need to find what is in common in both terms ( -9b and "63")
.
They both have a (-9) in common, now divide both terms by (-9)
.
=
.
=
.
Now we can combine the two answers, which equals , this makes up the second factor, first is (-9)
.
The factored form =
.
You would get the original polynomial if you used the distribution method
.
= = , remember the signs
.
, our original polynomial, they most likely want you to have "b" positive, so is your answer
.
Here is another way of factoring
.
They both have a "9" in common, now divide both terms by "9"
.
= =
.
=
.
Now we can combine the two answers, which equals , this makes up the second factor, first is "9"
.
The factored form = , we can check by distribution
.
= = (Remember signs)
.
, our original polynomial
.
They most likely want your "b" to be positive, so your factored answer is
.

.
Hope I helped, Levi

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.
parallel, perpendicular or neither:


.
These equations are in the form of , where "m" is the slope, "b" is the y intercept
.
The slope of the first line is "1"
The slope of the second line is (-1)
.
If lines are parallel, their slopes would be the same, these lines are not parallel
.
If lines are perpendicular, their slopes will be the negative reciprocal of each other
.
Reciprocal of the first slope would be , if you put a negative on it, it would be , which is equal to the second slope
.
Reciprocal of the second slope would be , if you put a negative on it, it would be , which is the first slope
.
These lines are perpendicular ( the numbers after the slopes don't matter, in finding if lines are parallel, perpendicular, or neither ) ( the numbers after the slopes are where the lines cross the y axis )
.
Here is the graph of the two lines
.

.
Hope I helped, Levi

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.
The length of the shadow of a flagpole was found to be 72 feet. The shadow of a 3 foot picket in line with the flagpole was 4 feet. what is the length of the flagpole
.
This is fairly easy, to solve this we use a proportion
.
The ratio( or fraction) of the length of the flagpole to its shadow is equal to the ratio ( or fraction ) of the length of the picket to its shadow
.
The equation would be
.
length of shadow of flagpole is 72 feet
.
length of flagpole is unknown( so we will call it "x" feet)
.
length of picket shadow is 4 feet
.
length of picket is 3 feet
.
Let us put the numbers in place of the words in the equation
.
=
.
We can get rid of the "feet" in the equation
.
, now we can solve for "x", we will use cross multiplication
.
= =
.
, now let us multiply both sides
.
, to find "x" we will divide each side by "4"
.
= = , you can check by replacing "x" with "54" in the equation
.
= , you can go further by using cross multiplication
.
=
.
=, multiplying both side, = ( True )
.
"x" was the length of the flagpole, since "x" = 54, the flagpole is equal to 54 feet, don't forget to put the right unit, in this case it is feet
.
Flagpole = 54 feet
.
Hope I helped, Levi

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.
3x+y=5
-2x+3y=4
.
There are several ways to solving these systems of equations, I will show you an overall easy way of doing it
.
First, solve for a letter, usually the easiest one, we will solve for "y" in both equations
.
First equation, , we need to move "3x" to the right side
.
= = or , if we rearrange it.
.
Our first answer is
.
Let us solve for "y" in the second equation,
.
, first we need to move (-2x) to the right side
.
= = or , rearranging it
.
, now we need to divide each side by "3" to get "y"
.
= =
.
is our second answer
.
Since "y" equals one number both of our answers will equal each other
.
First answer =
.
Second answer =
.
These two answers will equal each other
.
= , we will use cross- multiplication
.
=
.
, rearranging the left side
.
, now we can use the distribution method
.
=
.
Remember the negative and positive signs
.

.
Now we can solve for "x", let us move (-9x) to the right side
.
= = , now we need to move "4" to the left side
.
= = , now we can divide each side to find "x"
.
= = , , you can check by replacing "x" with "1" in the equation
.
= = = = ( True )
.
, to find "y", replace "x" with "1" in one of the two original equations
.
3x+y=5
-2x+3y=4
.
We will use the first equation
.
= = , now we will move "3" to the right side
.
=
.

.

.
We can check our answers by replacing both "x" and "y" in the two original equations. ( x = 1 ) ( y = 2 )
.
= = = ( True )
.
= = = ( True )
.

.

.
A solution set is in the form (x,y), our solution set is ( 1, 2 )
.
Hope I helped, Levi

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.
Solve
.
Absolute value will always make the numbers inside positive, absolute value is the distance away from "0" on the number line
.
|5| = 5, it is 5 units away from zero
.
|-5| = 5, it is also 5 units away from zero
.
, to get rid of the absolute value signs, we can say the left side equals 10, as well as (-10), since the absolute will make it positive, so we really have two equations
.
, and , now let us solve for "x"
.
First equation,
.
We need to move (-4) to the right side
.
= = , to find "x" we need to divide each side by "7"
.
= = , we can check by replacing "x" with "2" in the equation
.
= = = (True)
.
Now let us solve the second equation,
.
We need to move (-4) to the right side
.
= = , to find "x" we will divide each side by "7"
.
= = , we can check by replacing "x" with ()
.
= = = (True)
.
Your two answers are ( ), and ( )
.
If we replaced these two numbers into the original equation, they should work
.
replace with "2", = = = = ( absolute value means that it is "10" units from "0" )
.
replace with ( ), = = = = ( True ) ( Remember, the absolute signs will make any number positive, absolute value is just how far the number is from "0", (-10) is 10 units from "0"
.
Your two answers are
.

.

.
Hope I helped, Levi

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.
If you are wanting us to solve this quadratic equation, here is how you do it.
.

.
The easiest way you can solve this is by factoring, in this case we can
.
First we need to write the "y"'s in parentheses
.
It is only "y" squared so there will be two "y"'s
.
( y )(y )
.
Next, we need to find the rest of the factors of this quadratic
.
If the factors of the third term, in this case "9", add up to the middle term( in this case (-6)), it can be factored
.
factors of "9" added together
.
(9) + (1) = 10
.
(-9) + (-1) = (-10)
.
(3) + (3) = 6
.
(-3) + (-3) = (-6)
.
The last pair of factors add up to the middle term
.
Now we will put the factors in the parentheses with the "y"'s
.
( y )(y ) = (y - 3 )(y - 3 )
.
This is the factored quadratic
.
( y - 3 )(y - 3 ) = 0, you can check by using the FOIL method ( First, Inner, Outer, Last )
.
= (F) = (O) = (I) = (L) , Remember the negative signs on the "3's"
.
, combine the like terms, (forget about the multiplication sign, it is just being weird) = ( True )
.
now we take each of the factors and have them equal "0", then solve for "y"
.
First factor = ( y - 3 )
.
, removing the parentheses
.
, moving (-3) to the right side
.
=
.
, the other factor is the same, so we would get the same answer.
.
your answer is , you can check by replacing "y" with "3" in the original equation
.
= = = = ( True )
.
You can also use the quadratic formula, for every quadratic equation, make sure your equation is in the form ( in this case "y" ) it is
.

.
a = 1
.
b = -6
.
c = 9
.
= = = = = =
.
Your answer is
.
Hope I helped, Levi

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.
An improper fraction is where the numerator( or top number ) is larger than the denominator ( or bottom number ), an improper faction can be changed to a mixed number ( a whole number, and a fraction )
.
A proper fraction is where the numerator is smaller than the denominator
.
would be proper, since the numerator is smaller
.
Here are some more examples of proper fractions
.
, ,
.
Here are some examples of improper fractions
.
, ,
.
You can write these numbers as mixed numbers
.
You just say how many times can the bottom number ( denominator go into the top number ( numerator ),( or just divide the numbers ), and whatever the remainder is the fraction
.
, 2 goes into 3 one time, so we would put a 1, there is a remainder of one so we would have a fraction of , so the mixed number would be
.
1
.
, 5 goes into 10 two times so we put a 2, there is no remainder, so our fraction would be , our mixed number ( in this case a whole number) would be
.
2 , or just "2"
.
, 99 goes into 700 seven times, so the number would be 7, there is a remainder of "7" so the fraction would be , the mixed number would be
.
7
.
This is how you change a mixed number to an improper fraction
.
Let us change some mixed numbers to improper fractions
.
Change 4 to an improper fraction, to do this, you take the whole number ( 4 ), and multiply by the denominator/ bottom number of the fraction ( 5 ), once you multiply, you add the top number or numerator ( 3 ) to your product, then you put your answer over your denominator you started with to get your improper fraction
.
Here is how you do it
.
4 , Multiply the whole number by the denominator of the fraction
.
= , then you add the numerator of the fraction
.
= , then you put your answer over the original denominor
.
, this is the improper fraction
.
Hope I helped, Levi

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.
Solve each system of equations:
x+2y=12
3y-4z=25
x+6y+z=20
.
There is no fast way to solving these problems, but I will show you, what I believe is the easiest way, how to solve these problems
.
First we have to solve for a variable, we will need to solve for "y" in each equation, since they all have a variable "y" ( It usually doesn't matter, but in this case it does.
.
First equation, x+2y=12. (solve for "y")
.
, We can solve for "y", first we will move the "x" to the right side
.
= = , we can rearrange the right side
.
= , to solve for "y" we will divide each side by "2"
.
= =
.
is our first answer
.
Second equation solve for "y", 3y-4z=25
.
, we need to move (-4z) to the right side
.
= = , we can rearrange the right side
.
= , to solve for "y" we will need to divide each side by "3"
.
= =
.
is your second answer
.
Now let us solve the last equation for "y", x+6y+z=20
.
, first we will move the "z" to the right side
.
= = , now let's move the "x" to the right side
.
= , , let us rearrange the right side
.
= , to solve for "y", we will divide both sides by "6"
.
= =
.
is our third answer
.
Now let us put all of our answers side by side
.
First,
.
Second,
.
Third,
.
Since all three answers are equal to "y" all of them are equal to each other, first we have to have both "x" and "z" in all equations
.
First, , this has no "z's" so this equation would be
.
Second, , this has no "x's" so this equation would be
.
Third, , this already has both "x" and "z"
.
Here are the new equations
.
First,
.
Second,
.
Third,
.
All of them equal each other, first we will let the first two equations equal each other
.
, we will use cross multiplication
.
= =
.
, we will rearrange the left side
.
= , now we can use the distribution method to solve even more,
.
= = =
.
Don't forget to use the positive, and negative signs
.
, we will move the (-3x) and "0z" to the right side
.
= = , now we will move the "50" to the left side
.
= = , rearranging we get
.
=
.
is our first answer
.
Now we can use the last two equations ( we can use the middle equation twice
.
Second,
.
Third,
.
, we can use cross multiplication
.
= =
.
, rearranging the left side
.
= , we will use the distrubution method,
.
= =
.
Remember the signs, , we will move "-3x" to the left side
.
= = , we will now move "-3z to the left side
.
= = , we will lastly move "150" to the right side
.
= =
.
is the second answer, once again let us put our two answers side by side
.
First,
.
Second, , we can reduce this equation by dividing each side by "3", = = =
.
Our new equations are
.
First,
.
Second,
.
Now we need to solve for a variable again, doesn't matter which one, we will solve for "x"
.
First, , we need to move "8z" to the right side,
.
= =
.
Rearranging the right side, = , we can solve for "x" by dividing each side by "3"
.
= =
.
is our first answer
.
We can now solve for "x" in the second equation,
.
, we will move "9z" to the right side
.
= = , rearranging the right side, =
.
is our second answer, let us put our two answers together
.
First,
.
Second,
.
Since our two answers equal "x" they will equal each other
.
= , using cross-multiplication
.
=
.
, rearranging the left side
.
= , using distribution
.
=
.
Remember the signs, , we will now solve for "z", we will move (-27z) to the left side
.
= = , now we will move (-14) to the right side
.
= = , to solve "z" we will divide each side by "19"
.
= = , to check our answer we will replace "z" with (-4) in our equation
.
= = = = (True)
.
Now that we know that , we can replace it in one of the equations with two variables
.
First,
.
Second,
.
We will use the second equation, replace "z" with (-4)
.
= = = , lets move (-36) to the right side
.
= =
.
Let's check our answer by replacing "x" with "6", and "z" with (-4) in the equation,
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= = = = (True)
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"x" = "6"
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"z" = (-4),
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Now we can find "y" by replacing "x" and "y" in one of the three original equations
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x+2y=12
3y-4z=25
x+6y+z=20
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We will need to use the third equation, replace "x" with "6", "z" with (-4)
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= = = = , we will move "2" to the right side
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= = , to find "y", divide each side by "6"
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= = , we can check by replacing "x" with "6", "y" with "3", "z" with (-4) in the equation
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= = = = ( True )
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x = 6
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y = 3
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z = (-4)
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We can check by replacing the other two original equations
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= = = (True)
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= = = (True)
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x = 6
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y = 3
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z = (-4)
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ordered pairs are given as (x,y,z), our ordered pair = ( 6,3,-4)
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Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
Not sure if this is the right section but will someone please help.
Find the LCM of and
Thanks
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First, we can see if the two "numbers" can be factored
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To find factors of something, you have to put the "m's" in paretheses ( since " = ,
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For , (m )(m ) , next we have to find all factors of (-5), and the factors have to add up to (-4), the middle term
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Factors of (-5), (-5) and (1), (-1) and (5), now add each pair of factors
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,
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The first pair of factors add up to (-4), our middle term
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We can put (-5) and (1) in our paretheses
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(m )(m ) = (m - 5)(m + 1), if we used the FOIL method we would come up with our original equation
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(m - 5)(m + 1) = = = =
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(Remember the negative and positive signs, = (Our answers are true)
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The factors for our first "number" = (m - 5)(m + 1)
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Now we will find the factors of the second equation,
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First, we put the "m's" in parentheses, (m )(m )
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Remember, the factors of "7" add up to the middle term "8"
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Factors of "7", (-7) and (-1), (1) and (7)
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Adding them we get,
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The second factors work. We can put the factors in the parentheses
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(m + 1)(m + 7), If we used the FOIL method,
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(m + 1)(m + 7) = = = =
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Remember signs, = ( our factors our true )
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Our factors for our second "number" = (m + 1)(m + 7)
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We can now put the factored equations side by side
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Equation (1), (m - 5)(m + 1)
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Equation (2), (m + 1)(m + 7)
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To find the LCM, we count all the DIFFERENT factors
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All factors put together = (m - 5)(m + 1)(m + 1)(m + 7),
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There are three different factors, (m - 5)(m + 1)(m + 7), ( both numbers have (m + 1) in common, so we only count that factor once )
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The LCM would then be , if we expanded it,
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The LCM =
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Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help
.
I need help with this problem.
It is Solve for C: S= C + RC
Thank you for your help.
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To solve for "C" we have to isolate, or get "C" by itself
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We will rearrange,
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=
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We can factor the "C" out of the right side
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=
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Now that we have only one "C" we can get "C" by itself
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We will divide everything by (R+1)
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= = = = ,
.

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Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
simplify the following radical expressions the square root of x times the square root of x
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Here is the problem you are trying to solve
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We first have to know what square roots are
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To find the square root of something, we are trying to find a number you can square (multiply twice) to get the number, , you are trying to find "x", this case it would be , ( or , if you are using negative square roots)
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Examples: find , the answer would be , since you can multiply 5 twice ( or square "5" ) to get 25, , or
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find , the answer would be , you can multiply "9" twice to get "81", you can also square "9" to get "81", , or
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If you multiply a square root of a number by itself( or square it), it will always equal the number in the square root sign.
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Examples: = =
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= = ( number in the sqrt sign )
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= = (same number that is in square root sign)
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(We don't know the exact square root, but from the examples, we know the answer would be , because )( The answer is the number inside the square root sign, or "33")
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Lets do the original question.
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simplify the following radical expressions the square root of x times the square root of x
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, this is the same as all the examples, except that it is a letter.( It doesn't change the way we solve this problem though )
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If the answer is the number( or letter) inside the square root sign
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The answer would be , since it is inside the square root sign.
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To find the square root of a number, you would need to find a number multiplied by itself, or squared to get that number (or letter). So since we found the square root of "x" ( ), and we are multiplying by the same number, we are saying , which would be equal to "x"
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The simplified number/variable/expression would be
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Your answer is
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Hope I helped,Levi