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simplify the following radical expressions the square root of x times the square root of x
.
Here is the problem you are trying to solve
.

.
We first have to know what square roots are
.
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)
.
Examples: find , the answer would be , since you can multiply 5 twice ( or square "5" ) to get 25, , or
.
find , the answer would be , you can multiply "9" twice to get "81", you can also square "9" to get "81", , or
.
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.
.
Examples: = =
.
= = ( number in the sqrt sign )
.
= = (same number that is in square root sign)
.
(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")
.
Lets do the original question.
.
simplify the following radical expressions the square root of x times the square root of x
.
, 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 )
.
If the answer is the number( or letter) inside the square root sign
.
The answer would be , since it is inside the square root sign.
.
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"
.
The simplified number/variable/expression would be
.
Your answer is
.
Hope I helped,Levi

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14.) Solve each equation by using the quadratic formula

.
First we have to but the equation in the standard form
.
It is already in that form. (x is replaced with q)
.
,
.
A = (-8)
B = (-2)
C = 1
.
We have to know the quadratic equation, which is
.

.
We can replace A with (-8), B with (-2), C with "1"
.
= = = = =
.
There are two answers that "q" can equal ( + 6, - 6 )
.
= =
.
= =
.
q can be , and
.
You can check by replacing "q" with "", and "" in the original equation,
.
q = , = = = = = (True)
.
q = , = = = = = = (True)
.
q =
.
q =
.
Here is the graph of the equation
.

.
Where the curved line crosses the x axis, are the solutions to the equation
.
The curved line crosses where "q"(or "x") = , it also crosses the x axis where "q"(or "x") =
.
The two solutions are
.
q =
.
q =
.
Hope I helped, Levi

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an examination paper consists of 40 questions.
5 marks are given for each correct answer.
3 marks are deducted for each incorrect answer.
Kenny answered all 40 questions, getting x correct and y incorrect.
His total score for the examination was 56 marks.
(i)Write two equations to represent the above information.
(ii)Solve these equations to find out how many questions answered correctly
.
First we have to find the two equations.
.
First equation - Since there are 40 questions, both the wrong answered questions, as well as the right answered questions add up to 40 questions
.
If "x" is the number of correct answers, "y" is the number of wrong answers we can add these together and they will equal 40, our first equation is equal to
.
is our first equation
.
Second equation - 5 marks are given for each correct answer.
3 marks are deducted for each incorrect answer. His total score for the examination was 56 marks.
.
If he answered "x" number of problems right, he gets 5 marks for each problem that is right. To get the number of marks for right answers, you would multiply the number of marks for one right answer(5) by the number of right answers ("x"). So the number of marks for right answers would be or . If he answered "y" number of problems wrong, he gets 3 marks taken off for each wrong answer. To find the number of marks for wrong answers, you multiply the number of marks for one wrong answer (3) by the number of wrong answers ("y"). The number of marks for wrong answers would be or , these marks are taken away from the right answer marks (5x), if you take the marks away, his total marks would be 56, to find the equation, take the number of "wrong" marks ( 3y) from the "right" marks (5x) and that will equal 56, the equation would be
.
is the second equation, we found the two equations
.
Equation 1 =
.
Equation 2 =
.
To solve for "x" and "y", there are several methods you can use. We will use the easiest method for solving any system of equations.
.
First solve for a letter in both equations, doesn't matter which one, usually the easiest. We will solve for "x" in both equations
.
Equation 1, ,
.
To solve for "x" we will move "y" to the right side.
.
= = , rearranging
.
is our first answer
.
Second equation,
.
To start solving we will move (-3y) to the right side
.
= = , rearranging
.
To find "x" we will divide each side by "5"
.
= =
.
is our second answer, the two answers will equal each other, since both of them equal "x"
.
We can put them both in an equation, and then solve for "y"
.
= , now all you do is solve for "y".
.
We can cross multiply
.
= = = , If we rearrange the first part it becomes
.
We can use the distributive property to solve for "y" even more.
.
= = =
.
We will move (-5y) to the right side
.
= = , to solve it even more we will move the "56" to the left side
.
= = , rearranging we get
.
To solve for "y" we need to divide each side by "8"
.
= =
.
We found "y", , we can check by replacing "y" in the equation,
.
Replacing "y" with "18", = = = = (True)
.
To find "x" we will replace "y" with "18" in one of the original equations
.
Equation 1 =
.
Equation 2 = , we will use the first equation
.
Replacing "y" with "18", = =
.
To find "x" we will move "18" to the right side
.
= =
.
We found "x",
.
Our two answers are
.

.

.
We can check our answers by replacing "x" with "22", "y" with "18" in both of our original equations
.
Replacing "x" with "22", "y" with "18"
.
Equation 1 = = = (True)
.
Equation 2 = = = = (True)
.
, ( Since "x" was the number of problems he got right, he got 22 problems right )
.
, ( Since "y" was the number of problems he got wrong, he got 18 problems wrong )
.
He got 22 problems right
.
He got 18 problems wrong
.
Hope I helped, Levi

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First problem
.
1. A local coffee house donaated tweleve pounds of fresh roasted coffee. The students are running a fundraiser at school and decide to sell the coffee in bags. how many bags can be made if each bag contains 3/5 pounds? Explain how to get answer.
.
To find the answer, you would take the total number of pounds ( 12 ), and divide the total by how much is in a bag ( ) to get your answer
.
It is saying how many pounds are in 12 pounds. ( pounds is in one bag )
.
Lets do the math
.
= = = = = =
.
They can make bags. ( since there are twenty pounds in 12 pounds, one bag contains pounds )
.
First answer = bags
.
Second question
.
2.
The seats in a theater are divided into two sections. Section A has 15 rows Section B has 13 rows. There are 10 seats in aq row. How many seats are in the theater?
.
This is the way I solve this problem
.
Since each row contains 10 seats, multiply number of seats by number of rows in each section, and that will be how many seats in each Section
.
Section A has 15 rows, = seats
.
Section B has 13 rows, = seats
.
You add the two answers together to get the total number of seats in the theater
.
=
.
Your second answer is seats
.
Here is the way I would put the original equation
.
( Then you solve for "x" from there ), ( This is the same as the way Jamal solved the problem )
.
The other way ( Rosa's way ) is not wrong either
.

.
If we solved
.
= =
.
Lets compare the two ways of solving
.

.
We can use the distributive property to solve this problem as well
.
= = = (This is how Jamal solved)
.
If we multiply the numbers
.
= =
.
As you can see, you can solve this problem, and similar problems in different ways. You can solve math in several different ways sometimes, this is just one of many examples
.
First answer = bags
.
Second answer = seats
.
Hope I helped, Levi

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Solve each of the following problems by setting up and solving an algebraic equation. One of two supplementary angles is five times as large as the other. Find the measure of each angle.
.
Supplementary angles always add up to 180 degrees, so both angles will add up to 180
.
We need to find the two angles in variable form
.
One of two supplementary angles is five times as large as the other.
.
First angle =
.
Second angle = , we can name the " other angle", "x"
.
Other angle = , we can replace "other angle" with , in our two angles
.
First angle = =
.
Second angle =
.
Since these two angles add up to 180, we can put the angles into an equation, we will add the two angles together, and they equal 180
.
First angle =
.
Second angle =
.
, we can now solve for "x"
.
= = , to find "x" divide each side by "6"
.
= = = =
.
x = , we can check by replacing "x" with "30" in the original equation
.
= = = = ( True )
.
x = , we can replace "x" with "30" in our angle measurements
.
First angle = = =
.
Second angle = = =
.
is 5 times the second angle
.
First angle = degrees
.
Second angle = degrees
.
Hope I helped, Levi

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WHICH EQUATIONS OF LINES PASS THROUGH 0,6
Y=6X+5
Y=5X+6
Y=5X+3
Y=4X+6
.
Points are given as (x,y)
.
Point (0,6)(x,y), it means "x" = "0", "y" = "6"
.
To find if point (0,6) is a point on a line, all you do is replace "x" and "y" in the equations with the point, in this case (0,6)
.
Replace "x" with "0", and "y" with "6", in all of the equations
.
(0,6), = = = (False)
.
(0,6), = = = ( True) ( Point (0,6) is a point on the line )
.
(0,6), = = = ( False )
.
(0,6), = = = ( True ) ( Point (0,6) is a point on the line )
.
Here are the lines on a graph
.
Blue Line =
Redish Brown Line =
Green Line =
Purple Line =
.

.
The line equations, and , have (0,6) as a point
.
Hope I helped, Levi

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can somebody help me solve this problem. i need to find the equation of the line with these characteristics. I need to express my answer using either the general form or the slope-intercept form of the equation of the line.
x-intercept=2; containing the point (4,-5)
i forgot how to find the slope with only the, x-intercept = 2 given.
.
The slope intercept form of the equation is , where "m" is the slope, "b" is the y-intercept
.
The x-intercept is the point where the line crosses the "x" axis
.
x intercept is given as the point ( p, 0 ) where "p" is the "x intercept number", in our case, it would be ( 2,0 )
.
Now we have another point (2,0)
.
Now that we have two points we can find the slope of the line
.
The two points are (2,0) and (4, -5)
.
(2,0)(x1,y1) and (4, -5)(x2,y2)
.
The slope equation is , we can replace the variables with numbers
.
Our slope = = =
.
Our slope =
.
Our slope intercept form is , "m" is our slope, so we can replace "m" with
.
Our equation is now , to find "b", we will replace "x" and "y" with one of our two points ( doesn't matter which one ) ( we will use point (2,0), replace "x" with "2", "y" with "0")
.
(2,0)(x,y) , = = , we will move (-5) to the left side
.
= = = , we found "b", we can replace "b" with "5" in the original equation
.
= =
.
is the slope intercept form of the equation, for the general equation, we will multiply each side by "2"
.
= = = = , we will move (-5x) to the left side
.
= = , rearranging it becomes
.
=
.
is the general/standard form, we can check our equation by replacing "x" and "y" with both of our two points
.
The two points are (2,0) and (4, -5)
.
(2,0)(x,y) = = = = ( True )
.
(4, -5)(x,y) = = = = = ( True )
.
is the slope-intercept form of the equation
.
is the general/standard form of the equation
.
This is the line on a graph
.

.
Hope I helped, Levi

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An ice cream truck stocks 5 gallons of peach ice cream each week. This is 17 gallons less than twice the amount of vanilla ice cream that the truck stocks each week. Find the number of gallons of vanilla ice cream stocked each week.
a. 9 gallons
b. 6 gallons
c. 16 gallons
d. 11 gallons
.
First we have to find the variable for number of gallons of vanilla ice cream. We can name the number "x". There is "x" number of gallons of vanilla ice cream stocked each week.
.
Now that we know how many gallons of vanilla ice cream ( "x" ), we can put it in a formula and solve for "x"
.
An ice cream truck stocks 5 gallons of peach ice cream each week. This is 17 gallons less than twice the amount of vanilla ice cream that the truck stocks each week.
.
It is saying that " 5 gallons of peach ice cream is 17 gallons less than twice the amount of vanilla ice cream that the truck stocks each week"
.
Let us change the word problem into a formula
.
" 5 gallons of peach ice cream is 17 gallons less than twice the amount of vanilla ice cream that the truck stocks each week"
.
" 5 gallons of peach ice cream = 17 gallons less than twice the amount of vanilla ice cream that the truck stocks each week"
.
" 5 gallons of peach ice cream = 2(amount of vanilla ice cream that the truck stocks each week) - 17 gallons "
.
the amount of vanilla ice cream is "x"
.
" 5 gallons of peach ice cream = 2(x) - 17 gallons "
.
we can get rid of the words, we only need numbers
.
, now we can solve for "x"
.
=
.
Move (-17) to the left side
.
= = , rearranging we get
.
=
.
We can now divide each side by "2" to get "x"
.
= =
.
, we can check by replacing "x" with "11" in the original equation
.
= = = ( True )
.
, since "x" was the number of gallons of vanilla ice cream stocked each week. The truck stocks 11 gallons of vanilla ice cream each week
.
11 gallons of vanilla ice cream is your answer, which is answer "d"
.
Hope I helped, Levi

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The sum of two numbers is 15. Three times one of the numbers is 11 less than 5 imes the other. The answer is 7 and 8. I just don't know how to set it up to solve.
.
We have to name the two numbers, we will name the first number "x", the second "y"
.
There are two equations
.
(1) The sum of two numbers is 15. Since we know the numbers ("x" and "y"), we can put the words as an equation
.
The sum of two numbers( "x" and "y") is 15. = = , this is the first equation
.
(2) Three times one of the numbers is 11 less than 5 times the other. We know the numbers ( "x" and "y" ), we can put the words as an equation
.
Three times one of the numbers("x") is 11 less than 5 times the other("y") = = , this is the second equation
.
Our two equations are
.
(1)
.
(2)
.
These are systems of equations, we can solve these problems several ways.
.
This is the way I usually solve these problems
.
First solve for a letter in both equations (doesn't matter which one, usually the easiest), we will solve for "x" in both equations
.
(1) , to solve "x" we will move "y" to the right side
.
= = , rearranging, =
.
, our first answer is
.
Lets solve "x" in our second equation
.
(2) , to solve "x" we will divide each side by "3"
.
= =
.
, our second answer is
.
Our two answers are
.

.

.
Since both our answers equal "x", the two answers equal each other
.
We can put them in an equation
.
, now we just solve for "y"
.
=
.
We will cross multiply
.
= = , rearranging
.
= , we will use distributive property
.
= = = (since it was a negative "11")
.
, we will move (-3y) to the right side
.
= = , we will now move (-11) to the left side
.
= , , divide each side by "8",
.
= = , rearranging,
.
, "y" = , we can find "x" by replacing "y" with "7" in one of our two equations
.
(1)
.
(2)
.
We will use the first equation (replace "y" with "7")
.
= = = =
.
, , you can check by replacing "x" with "8", "y" with "7", in both of our equations
.
(1) = = (True)
.
(2) = = = ( True )
.
,
.
Hope I helped, Levi

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I am looking for someone to please show how the square root of (7.96) equals (2.82). I am a homeschooling mom and I have tried using the square root formula from our Pre-Algebra Textbook and still cannot find the answer to show as 2.82. Can someone please show us how to compute this so we may carry this into our lesson?
Thank you
.
is , I just used a calculator to find the square root, I don't know the formula, but you have the formula ( you could say , which would be the answer we got, you basically need to know your multiplication to find the square roots ) ( = , = ) ( you could use the calculator, or you would have to know that , and )
For the answer, they rounded it to the 100ths place, , since the answer is in the 100ths,
.
is
.
Now if it asked, find , the answer would have to be in the 100,000ths place, or (since the 7 rounds the "4" to "5")
.
It all depends on the number you are square rooting, ( If you are square rooting a number that only has a 10th place, your answer will be in the 10th place, if you are square rooting a number that has a 1,000,000th place, you round your answer to the 1,000,000th place)
.
They rounded it to the 100th place, most likely because the number they give you is in the 100ths ( to be totally accurate you wouldn't round, but you probably don't want to write all the 31+ numbers down for your answer, on a piece of paper, or computer )
.
, all they did was round to the 100ths place
.
Hope I helped, Levi

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CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM:
Solve the problem:
Janet drove 256 kilometers and the trip took 4 hours. How fast was Janet traveling?
.
This problem is pretty easy, we will use the distance formula ( D ( distance) = R (rate) * T ( time ) )
.
Janet drove 256 kilometers and the trip took 4 hours. How fast was Janet traveling?
.
Janet travels 256 kilometers, our "D", we are trying to find the "R" (rate), it takes Janet 4 hours, our "T" (Time)
.
In our equation,, , we are trying to find "R"
.
Since , lets replace the letters with the numbers we know
.
= , rearranging, =
.
= = , to find "R" we will divide each side by "4"
.
= =
.
Janet was traveling kilometers per hour ( since our "D" was given in kilometers, Our "T" was given in hours )
.
We can check by replacing "R" with "64" in our equation
.
= = (True)
.
Janet was traveling kilometers per hour, which is your answer
.
Hope I helped, Levi

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.
CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM:
Use the discriminant to determine the number of real solutions of the equation.

.
First we have to put the equation in stardard form ( in this case, we have "y" instead of "x" )
.
We need to move to the right side, we will subtract from each side
.
= =
.
If we rearrange, = , or
.
We will multiply each side by (-1), to make the variables positive
.
=
.
, we can divide each side by "2" to reduce the equation
.
= =
.
is the standard equation, , in our equation, a = 1, b = 3, c = 4
.
The quadratic equation is , the number in the radical , will determine if the equation has one, two, or no real solutions,
.
( is considered the discriminant )
.
If the number inside the radical is positive, the equation will have two real solutions, if the number inside the radical is 0, the equation will have one solution, if the number inside the radical is negative, there are no real solutions to the equation, since you can't take the square root of a negative number.
.
In our equation , a = 1, b = 3, c = 4
.
Lets replace the letters with our numbers in the quadratic equation
.
= = =
.
would be our answer, since the number inside the radical is negative () , this means the equation has no real solutions
.
Hope I helped, Levi

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.
The area of a rectangle is 30 cm^2. The perimeter is 26cm. What are the length and width of the rectangle.
this is what i have so far
a=lw so 30= lw
p=2L + 2W so 26= 2L+2W
I'm not sure if I am supposed to substitute the first equation into the second one or just try to isolate L and w.
.
You did everything right so far.
.
You have the two equations
.

.

.
(You can reduce the second equation by dividing each side by "2", = = = )
.
The two equations will =
.

.

.
We have two equations, or a system of equations
.
To find the "L" and "W", we will use the way I solve systems of equations, which is pretty easy
.

.

.
First solve for a letter ( doesn't matter which one, usually the easiest), we will solve for "W" in both equations
.
First equation
.
To get "W" by itself we will divide each side by "L"
.
= = , Our first answer =
.
Second equation
.
To get "W" by itself we will move "L" to the right side
.
= = or
.
Our second answer =
.
We can put our two answers in an equation, since both answers represent "W"(width), our two answers equal each other
.
=
.
We will use cross multiplication
.
= =
.
It becomes =
.
This is a quadratic equation, we will put it in standard form(move "30" to the left side)
.
= =
.
Standard form Since this is a quadratic equation, we can use quadratic formula( We can solve by factoring, or completing the square as well, but I believe the formula is easiest)
.
, , (a = (-1), b = 13, c = (-30)
quadratic formula = , replace the letters with numbers
.
= = = =
.
= =
.
= =
.
"L" can be either or
.
Just replace "L" in the second equation
.
= = , or
.
= =
.
Most likely and , it could be the other way around, you can check by replacing these answers in the first two original equations.
.
Hope I helped, Levi

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.
How do you factor completley:? Whats the answer?
.
We can find the first part of the number, by finding factors of "3" (1, and 3)
.
The first part of the answer is (3x )(x ), since all the numbers are positive we can put "+" in both of the factors
.
(3x )(x ) = (3x + )(x + )
.
Next, you need to find all factors of "10"
.
Factors of 10: (1,10) and (2,5):Factors in order ( 1,2,5,10 )
.
Next you have to multiply "3" and "1", by one of the two pairs of factors (10), the numbers we get will have to add up to "17"
.
Nope, we will switch the factors of "10"
.
Nope, we will use the other factors of "10"
.
Nope, we will switch the factors of "10"
.
True, we need to use the factors "5" and "2"
.
We have to put the "5" and "2" in the right place in the answer (Since we got the answer by , we will put the factors in opposite order that we did to find the addition answer)
.
(3x + )(x + ) = (3x + 2 )(x + 5 )
.
We can check our answers by multiplying the factors out, using the FOIL method
.
= = = = =
.
= = ( Our answer)
.
The two factors (Your answer) = and
.
The simplified equation =
.
Hope I helped, Levi

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.
Determine the value of "a" so that the line through (5,8) and (a,6) has a slope of
.
First we have to know what the slope is. The slope is how steep the line is. It is the slant of the line
.
These lines have negative slopes
.

.
As you can see, a slope that is negative means, the line (from left to right) is going down
.
Here are some lines with positive slopes
.

.
As you can see a slope that is positive, means the line(from left to right) is going up
.
Now that you know a little about slopes lets do the problem
.
Determine the value of "a" so that the line through (5,8) and (a,6) has a slope of
.
The slope is negative, so the line is going down(from left to right)
.
Here is one way to solve this kind of problem
.

.
If the point is (2,4) find a point (6,c) if the slope is
.
The slope is negative, so the line is going down.
.
The slope is , or
.
Since the slope is negative, ,
.
A slope of means you go down "7" and over to the right "4" times
.
If we do that, we will get our point
.

.
The point is (6,-3)
.
There is yet another way to solve this kind of problem
.
Determine the value of "a" so that the line through (5,8) and (a,6) has a slope of
.
We use the slope equation =
.
(ex. slope of (1,2)(x1,y1) and (2,4)(x2,y2), equation =
.
Replace the variables
.
= = , these two lines have slope of "2"
.
we can do the same for our problem
.
Determine the value of "a" so that the line through (5,8)(x1,y1) and (a,6)(x2,y2) has a slope of
.
Replace the variables in the equation = = = , we already know the slope, this equation we have =
.
Our equation = , now just solve for "a"
.

.
We will use cross multiplication
.
= = =
.
Using distribution
.
= = = ( since the "5" is negative, it will make a positive "15" since the "3" is negative too)
.
We will move "15" to the left side
.
= =
.
We will multiply each side by (-1)
.
= = = , divide each side by "3" to get our "a"
.
= =
.
We can check by replacing "a" with in our equation
.
= = = = = = (True)
.
a =
.
We found our point, if our point was (a,6), just replace "a" with , our point is (,6)
.
Here are the two points

.
Now draw a line through these points, this line has a slope of
.

.
The line equation = (slope -intercept form), or (standard form)
.
The point you were looking for is (,6)
.
Your answer is (,6)
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help
.
The length of a rectangular playing field is 5 meters less than twice its width. if 230 meters of fencing goes around the field, find the dimensions of the field.
.
First we have to find variables for length and width
.
The length of a rectangular playing field is 5 meters less than twice its width.
.
We can name the width "x"
.
The length of a rectangular playing field is 5 meters less than twice its width, if the width is "x", and the length is 5 meters less than twice the width, this is how you right the length, , width = "x" =
.
The length =
.
The width =
.
Since 230 meters of fencing goes around the field, we are trying to find the Perimeter of the field
.
The length =
.
The width =
.
The Perimeter of a Rectangle is =
.
They give us the Perimeter, 230 meters, so we can replace "Perimeter" with "230"
.
=
.
Since the width = , and the length = , we can replace "width" and "length" with our variables
.
= , now just solve for "x"
.
We will get rid of the parentheses, and use distribution
.
= = = (Since the "5" is negative the number will be negative)
.
Add like terms
.
= =
.
We will move (-10) to the right side
.
= = , To solve "x" we will divide each side by "6"
.
= = =
.
x = "40", we can check by replacing "x" with "40" in our equation
.
= = = = = ( True )
.
x = "40"
.
Our width and length in variable form were:(Just replace "x" with "40" in our equations)
.
The length = = = = 75
.
The width = = 40
.
Since the unit is the meter, our answers would be
.
The Length = 75 meters
.
The Width = 40 meters
.
Hope I helped, Levi

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Hi, Hope I can help,
.
Could you help with this problem? It is from a worksheet.
The excess of an angle over its supplement is 20 degrees. Find the angle.
I tried x/180-x = 20 It doesn' come out even.
.
Supplementary angles always add up to 180 degrees
.
first we have to find the variables of the angles
.
The excess of an angle over its supplement is 20 degrees (excess means exceeding, or more than)
.
One angles would be "x"
.
The other angle ( The excess of an angle over its supplement is 20 degrees) is "x+20" ( This angle is 20 degrees more than the first angle "x")
.
One angle = degrees
.
The second angle = degrees
.
Now just add the angles together (supplementary angles add up to 180 degrees
.
The equation would be , now just solve for "x"
.
= , add like terms
.
= =
.
Move "20" to the right side
.
= =
.
To solve for "x" we will divide each side by "2"
.
= =
.
x =
.
We can check by replacing "x" with "80" in our equation
.
= = = = (True)
.
x =
.
Our two angle measurements were: (Replace "x" with "80" )
.
One angle = degrees, degrees
.
The second angle = degrees, degrees, degrees
.
The two angles add up to 180 degrees, = (True)
.
The two angles are:
.
1. degrees
2. degrees, (the first angle's supplement)
.
Hope I helped, Levi

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Hi, Hope I can help
.
Solve the system by graphing.


.
Points are given as (x,y), to find points on both of these lines, you just replace "x" with any number and solve for "y"
.
Lets find some points on the first line
.
, (we can use any number for "x", then we solve for "y"
.
Lets replace "x" with "2", = =
.
We will move (-2y) over to the right side
.
= = , we will move "4" to the left side
.
= = =
.
To get "y", we will divide each side by "2"
.
= = ,
.
"x" = 2
"y" = 1
.
Since points are given as (x,y), this point would be (2,1)
.
(2,1) is a point of the line(We can check by replacing "x" with "2", "y" with "1", = = = (True)
.

.
Lets find another point,
.
Lets replace "x" with "0"
.
= = =
.
We can multiply each side by (-1) to get (-2y) positive
.
= = , to find "y" we will divide each side by "2"
.
= =
.
"x" = 0
"y" = (-2)
.
Another point on the line is (0,-2)(x,y)(we can check by replacing "x" with "0", "y" with (-2), = = = (True)
.

.
Another point on the line is (-4,-8), We can check by replacing "x" with (-4), "y" with (-8), = = = (True)
.

.
Lets draw a line through the points,
.

.
Now lets find some points for the second equation,
.
Lets replace "x" with , = =
.
"4y" has to equal "4", so , divide each side by "4", = =
.
x =
y = 1
.
One point on the line is (,1 )(We can check by replacing "x" with ,"y" with "1", = = = (True)
.

.
Replace "x" with "4", = =
.
"4y" will have to equal "31", , dividing each side by "4" will get "y"
.
= =
.
x = 4
y = , or 7
.
The point is (4,), (we can check by replacing "x" with "4", "y" with , = = = (True)
.

.
Another point on the line is ( 0, ), ( we can check by replacing "x" with "0", "y" with "", = = = (True)
.

.
Lets draw a line through the points
.

.
These lines are parallel, they don't have any points that intersect each other, there is no solution to the system of equations
.
Hope I helped, Levi

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.
Five more than of a number is of that number. Find the number
.
We are trying to find a number, since we need to find one number, we have 1 variable
.
We will name the variable/number "x"
.
Five more than of a number is of that number. Find the number(replace "a number", and "that number" with "x")
.
Five more than of "x" is of "x". Find the number
.
This is how you would write the equation
.

.
We will multiply it out
.
= =
.
We will need to get rid of the fraction by multiplying each side by "12"
.
= = =
.
= = =
.
We will need to move "3x" to the right side
.
= = = =
.
To find "x"(our number) we will divide each side by "5"
.
= = =
.
"12" is our number, we can check by replacing "x" with "12" in our equation
.
= = = = (True)
.
Your answer is
.
Hope I helped, Levi

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Hi, Hope I can help,
.
Find The slope and y-intercept of the graph of the equation
.
This is the slope intercept form, the general form = ( where "m" is the slope, "b" is the y intercept)
.
y intercept = (0,y), where the line intercepts the y axis("x" = 0, "y" = any number(depends where the line crosses the y axis))
.
In our equation ( )
.
Slope = "7"
.
Y intercept = "3", the point = (0,3)
.
Hope I helped, Levi

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.
I have no idea how to set up this problem! Once the equation is set up i know how to solve it. Do you have any suggestions concerning word problems?
.
HERE'S THE EQUATION...
A coin purse contains an equal number of nickels, dimes and quarters. The total amount of money in the purse is 680 cents. How many nickels are in the coin purse?
.
This is how you set it up, since there are an equal number of each coin, we really only have one variable "x"(number of each coin
.
It tells us the value in the purse, we have to know the value of each coin(25 cents = quarter, 10 cents = dime, 5 cents = nickels)
.
To find the value of each coin that is in the purse, we multiply the value of the coin, by the number of coins(examples: five quarters will have a value of = = cents, seven nickels will have a value of = = cents)
.
In our case, the values of each coin are
.
Quarters = = =
.
Dimes = = =
.
Nickels = = =
.
If we add all of our values(25x,10x,5x) together, it will come up with a total value of 680 cents
.
Our equation = , now we can solve for "x"
.
= , to get "x" we will divide each side by "40"
.
= =
.
There are 17, of each coin,
.
you can check by replacing "x" with "17" in our equation
.
= = = ( True )
.
your answer is
.
Hope I helped,Levi

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Hi, Hope I can help
.
what is the answer for
.
You have to get "x" by itself, to get rid of the fraction and solve for "x" you would just multiply each side by "5"
.
= = = = =
.
x = , we can check our answer by replacing "x" with in our equation
.
= = = = = = = = (True)
.
x =
.
You can also solve the answer this way,
.
Since these are equal fractions, we can use cross multiplication
.
= = =
.
To find "x" divide each side by "13"
.
= = = =
.
You can also check by using cross multiplication(replace "x" with )
.
= = = = = (True)
.
x =
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
Can someone help me with this one.
Determine whether the graphs of the equations are parallel lines, perpendicular lines or niether.


Thank you!
.
First we have to get the two lines in the slope intercept form, ("m" is the slope, "b" = y intercept)
.
First equation
.

.
We will move (-8y) to the right side
.
= =
.
We will move (-18) to the left side
.
= =
.
= , To get it in slope intercept form, we have to divide each side by "8"
.
= =
.
= =
.
is the slope intercept equation of , we can check our answer by replacing "x" and "y" with any point on the line, in both of the different forms of equation
.
We will use the points (-6,0)(x,y) and ( 2, 3)(x,y)( replace "x" with (-6), replace "y" with "0" for our first check, replace "x" with "2", replace "y" with "3" in our second check
.
(-6,0), = = = (True)
.
(-6,0), = = = = (True)
.
Lets check with a different point
.
(2,3) , = = = (True)
.
(2,3) , = = = = = (True)
.
is our first answer
.
Second equation (We are changing equation into slope intercept form )
.

.
We need to move "32x" to the right side
.
= =
.
= , To get the equation in slope intercept form, we will divide each side by "12"
.
= = =
.
=
.
The slope intercept form of the equation is
.
Lets check using two points again, Lets use (0, ) and (, 0)(We will do the first point first)
.
(0, ), = = = (True)
.
(0, ), = = = (True)
.
Second check(second point)
.
(, 0) , = = = (True)
.
(, 0), = = = = (True)
.
is our second answer.
.
Our two equations in slope intercept form are
.

.

.
The slope of the first line is , the slope of the second line is
.
If two lines are parallel, their slopes would be the same(our lines are not parallel)
.
If two lines are perpendicular, their slopes are the negative reciprocal of each other
.
(examples of negative reciprocals: and , and , and , to find the negative reciprocal of a number, switch the denominator and numerator with each other and add a negative sign)
.
Our two lines are perpendicular, is the negative reciprocal of ( the numbers to the right of the "x" , Our "b's" don't have to be the same)
.
Here are the two lines in a graph( lines are in slope-intercept form)
.
= green line
.
= red line
.

.
As you can see the lines are perpendicular
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
I would mean alot to me if someone could help me out on this problem
I did find a smiliar question to mine, but could really understand how i would get the answer.
Consider the points P(10,2),Q(1,11), and R(-8,2) on a coordinate plane. Where must the point S be located so that the quadrilateral PQRS is a square?
i found the slope of PQ i got -1
I found the slope of QR i got 1
then what do we do after gettting the slope
please help
.
First we need to plot the three points on a graph
.
Here are the 3 points
.
(P)(10,2) = red
(Q)(1,11) = green
(R)(-8,2) = blue
.

.
We will need to find two equations,
.
1.equation of the line from the unknown point(x,y) to (-8,2)
2.equation of the line from the unknown point(x,y) to (10,2)
.
The line from the unknown point (x,y) to (-8,2) is parallel to the line from (10,2) to (1,11)(Line PQ)(redish brown line)(line has slope of (-1))
.
Since we are trying to find the equation of the line (contains unknown point(x,y) and (-8,2)), the line we are trying to find is parallel to the line with the slope of (-1), since parallel lines have the same slope, we know our unknown line has the slope of (-1), we can replace "m" with (-1) in our slope intercept equation, , where "m" is the slope, "b" is the y intercept
.
= = , since we have a point on the line (-8,2), we can replace "x" and "y" with (-8,2)(x,y)
.
= =
.
To solve for "b" we will move "8" to the left side
.
= = = =
.
"b" = (-6), we can replace "b" with (-6) in our equation
.
= =
.
We can check by replacing "x" and "y" with (-8,2)(x,y)
.
(-8,2) = = = (True)
.
One of our two equation we have to solve is (Line RS),
.

.
we will now solve for the second unknown line equation
.
2. equation of the line that contains the unknown point(x,y) and (10,2)
.
This line is parallel to the line that contains (-8,2) and (1,11)(Line QR)(green line)(line that has slope of (1)).
.
The line that contains the unknown point and (10,2) is parallel to the line , (They both have the same slope)
.
The line that contains the unknown point and (10,2) has a slope of "1", lets replace "m" with "1" in our slope intercept equation
.
= =
.
Since the line contains (10,2) we can replace "x" and "y" with (10,2)(x,y)
.
= = , we will move "10" to the left side to solve "b"
.
= = = = , we can replace "b" with (-8) in our equation
.
= , We can check by replacing "x" and "y" with (10,2)
.
(10,2), = = = (True)
.
(Line QS) is our second equation we had to solve
.

.
We found our two unknown equations(our two unknown line equations)
.
(Line QS)
.
(Line RS)
.
We can now solve for both "x" and "y" to get our unknown point, this is the way I solve systems of equations
.
First solve for a letter(doesn't matter which one)(since we don't have to do anything to solve for "y"(it is solved already for us), we will put the two answers that "y" is together into an equation(since "y" is one number, both of the answers equal each other)
.
Here are our two answers
.

.

.
Lets put them together
.
= , we will move (-x) to the left side
.
= = , We will move (-8) to the right side to solve "x" even more
.
= =
.
We will divide each side by "2" to get "x"
.
= =
.
"x" = 1, we can replace "x" with "1" in one of the two equations to get "y"
.

.

.
We will use the first equation
.
= = =
.
"y" = (-7), we can check our answers by replacing "x" and "y" in our two equations
.
"x" = "1"
"y" = (-7)
.
= = = (True)
.
= = = ( True)
.
"x" = "1"
"y" = (-7)
.
Since points are given as (x,y), our unknown point(Point "S") is (1,-7)
.

.
You can find this answer by a shortcut
.
Since this is a square, the diagonals are the same, you could measure the distance between (-8,2) and (10,2)(18 squares), you would just go from (1,11) and move down 18 squares, and you would find the other point
.
Unknown point( Point "S") = (1,-7)
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi hope I can help,
.
Here is the graph of
.

.
This graph holds points with (x,-3), Meaning "x" can be any number, as long as "y" is (-3)
.
Hope I helped,Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
Write an equation of the line that is parallel to and passes through point (0,-3).
PLEASE HELP- Thanks!
.
You are trying to find a parallel line to , which means the line has the same slope
.
the slope intercept form of a line = , ( "m" = slope )("b" = y intercept)
.
Since we know the slope of both lines ( slope = 3)(parallel lines have same slope), We can replace "m" with "3" in our equation
.
= =
.
Since the line includes the point (0,-3), points are given as (x,y), we can replace "x" and "y" with the numbers( replace "x" with "0", "y" with (-3) )
.
= = =
=
.
We can replace "b" with (-3) in our equation
.
= =
.
You can check our equation by replacing "x" and "y" again, with (0,-3)(x,y) in our equation
.
= = = (True)
.
is your answer,
.
Here are the graphs of the two lines
.
green line =
red/brown line =
.

.
As you can see, line is parallel to
.
is your answer
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help
.

.
We are trying to solve for "p", first we will use the distribution method to get rid of the parentheses
.
= = = (remember to also put the right signs( ) (we had all positive numbers)
.
Now we will rearrange the numbers
.
= , now we will add like terms
.
=, (12p)(-10+40)=18, =
.
We will move "30" to the right side
.
= =
.
To find "p" we will divide each side by "12"
.
= =
.

.
"p" = (-1)
.
We can check by replacing "x" with (-1) in our equation
.
= = = = = (True)
.
"p" = (-1),
.
Hope I helped,Levi

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Hi, Hope I can help
.
the problem is how many 's are in 1. I don't know how to work this out. thanks
.
This is pretty easy, all you do is divide from
.
Here is the solution
.
= = =
.
There are 's in 1
.
is your answer
.
Lets do some other problems
.
How many 4's are in 8, = , there are two 4's in 8
.
How many 9's are in 63, = , there are seven 9's in 63
.
How many 10's are in 5, = , there is of 10 in 5
.
How many 12's are in (-2), = , there is of 12 in (-2)
.
How many 7's are in , = = , there is of 7 in
.
In our problem
.
How many 's are in 1, = =
.
Our answer = or ,(that's how many 's there are in 1)
.
Hope I helped, Levi

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Hi,Hope I can help
.
Find four consecutive integers such that twice the first subtracted from the sum of the other three integers is sixteen.
.
consecutive means " in order"(examples: 45,46,47,48 . Sunday, Monday, Tuesday)
.
To find the 4 consecutive numbers, we have to find the variables for all four numbers
.
Since consecutive means " in order "(we are trying to find 4 numbers that come right after the other(example of consecutive numbers: 22,23,24,25,26)
.
We can always name the first number of any "consecutive numbers" - "x"
.
"x" is our first number, to find the other numbers, we will add "1" each time(we are trying to find numbers that come right after the other)
.
2nd number = (add "1" to our first number "x") = "x+1"
3rd number = (add "1" to the second number "x + 1", ("x + 1 + 1")) = "x+2"
4th number = (add "1" to the third number "x+2",("x+2+1")) = "x+3"
.
(If there was a fifth number you would add "1" to the fourth number "x+3" = "x+4", the sixth number would be "1" added to the fifth number "x+4" = "x+5", you get the idea)(If you were solving for consecutive odd or even numbers, you would add "2" every time, consecutive even/odd number = ( x, x + 2, x + 4, x + 6, x + 8, ...)
(examples of consecutive even/odd number: 3, 5, 7, 9 : 16, 18, 20, 22))
.
Since we are solving for just consecutive numbers, our numbers are
.
1st number = ""
2nd number = ""
3rd number = ""
4th number = ""
.
Now we can replace these variables with the problem, and solve for the numbers
.
Find four consecutive integers such that twice the first subtracted from the sum of the other three integers is sixteen.
.
If we replace the variables in the problem, and put the word problem in an equation, the equation =
.
Now we just solve for "x"
.

.
We will remove the first set of parentheses,we will multiply 2(x)
.
=
.
We will remove the other sets of parentheses
.
=
.
We will rearrange the equation, so we can add/subtract like terms
.
=
.
We will add/subtract like terms
.
=, (x+x+x-2x)(+1+2+3) = 16, =
.
To solve for "x" we will move "6" to the right side
.
= = =
.
"x" = "10" , we can check by replacing "x" with our equation
.
=
.
=
.
=
.
= = = = (True)
.
Here is our number variables again (To find the numbers, replace "x" with "10")
.
1st number = "", ""
2nd number = "", "", "", ""
3rd number = "", "", "", ""
4th number = "", "", "", ""
.
Find four consecutive integers such that twice the first subtracted from the sum of the other three integers is sixteen. ( = = = (True))
.
1st number =
2nd number =
3rd number =
4th number =
.
Hope I helped, Levi

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Hi, Hope I can help
.
write an equation in slope-intercept form for the line that satisfies the following condition. slope and passes through (3,9)
.
The slope intercept form of an equation is equal to , where "m" is the slope, "b" is the y intercept.
.
We know the slope is , so we can replace "m" with in our equation
.
, becomes , now we have to find "b"
.
We now a point on the line, point (3,9), and because points are given as (x,y), we can use the point to solve for "b"
.
If the point is (3,9)(x,y), all we need to do is replace "x" and "y" in our equation, with the numbers(replace "x" with "3", replace "y" with "9")
.
, becomes
.
=
.
= , to find "b" we will move "1" to the left side
.
=
.
= =
.
We found that "b" = "8", we can replace "b" with "8" in our equation
.
=
.
is the slope-intercept form/equation of the line
.
We can check our answer by replacing "x" and "y" with (3,9)(x,y) in our equation
.
=
.
=
.
= = (True)
.
We can also find that the y intercept(where the line hits the y-axis) is (0,8), another point on the line,
.
We can check by replacing "x" and "y" with (0,8)(x,y),
.
=
.
=
.
= = (True)
.
The slope-intercept form/equation of the line is
.
Hope I helped, Levi

You can put this solution on YOUR website!
Hi, Hope I can help,
.
the problem says to graph these two equations on the same graph & then find where they intercept. There are more questions to the problem, but I think I can figure them out if I first get the graph correct.
Equations: 1) y=5x
2) y=3x + 100
.
Here are the graphs of the two lines together
.
(brown line)
.
( green line)
.

.
Here is the graph but smaller
.

.
The two lines intersect at point (50,250)
.
You can check by replacing "x" with "50", "y" with "250" in our two equations
.
= = (True)
.
= = = (True)
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The lines intersect at point (50,250)(There are other ways of solving the intersection of two lines)(we knew the answer by the graph)
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Hope I helped, Levi