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Let q be the number of quaters and n be the number of nickles
You are told that
You are also told that
You have two equations and 2 unknows, so you can solve this one.








Check your answer
Is there are 11 quarters, then there must be 9 nickels (11+9 = 20)
Is ????

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1)As a table, make a table with 2 columns and 5 rows. Label the first column "x" and the second column "y". Then use the coordinates of the given points to fill in the table.
row 1 has -2 -4
row 2 has -1 -1
and so on
2) As a graph, lay down a standard Cartesian grid (like graph paper). Then plot the 5 given points. If you see a "curve" in thyat data, then sketch in the curve
3) As mapping diagram, draw an ellipse shaped like a "0", leave an inch of two of space and then draw a second one to the right of the first (same shape, same size).
Put all of the x values in the left ellipse (see column one from the table in part 1). Put all the y values in the right ellipse (see column two from the table above).
Now connect the x values in the left ellipse with the corresponding y values in the roght ellipse. Just draw a line from one to the other. That is the "map"
See this URL for an example --> http://img.sparknotes.com/figures/4/4d7924c96427a340a0f1be4c7e650f7c/mapping.gif

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downward, the high order coeefficient (-7 on the x^2 term) is negative. So it must open down.
See this URL for a plot --> http://www.wolframalpha.com/input/?i=-7x^2%2B3x-8

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Let h be the length of the hypotenuse. Then one side is h/2 and the third side is h-4.
Since it is a right triangle, you know that




Use the quadratic equation to solve

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=768 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 29.856406460551, 2.14359353944898. Here's your graph:

Since one of the answer is too short to make that number -4 positive, the hypotenuse is ~29.85

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Pick some values for x, and then solve for y. Plot those points and draw the curve.
Use this URL to check your answer
http://www.wolframalpha.com/input/?i=(36-x^2)%2F11

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The denominator of any "fraction" cannot be 0. So the only value of x that is not in the domain is x=-10, since it makes the denominator 0.
domain - all x except x=-10 [infinity,-10) (-10, infinity]

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Most of these type problems are practice. I like to start by looking at the series of numbers. You can see the difference in the inputs goes up by 1 one each entry. Now look and see if you can find a pattern in the output numbers.
You can see they are getting larger by increasingly larger amounts. However, nothing obvious jumps out a bout their values. So, the first thing I like to try is to see if there are patterns in the series of outputs. For instance, perhaps every other number has an obvious pattern. One thing I always try is finding the difference between each successive output number.
difference between 5 and 3 = 2
difference between 9 and 5 = 4
difference between 17 and 9 = 8 do you see the pattern yet
difference between 33 and 17 = 16
So each output increases by a value that is power of 2. Now all that is left to figure out is what the 'starting' value is. A little trail and error will show you that value is 1.
So, the function that fits the given data points is
x>=1

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Assuming english alphabet and lower case and upper case count as one, then you have 26 letters.
So how many ways can you use 9 different letters?
First letter can be anyone of the 26.
The second one can't duplicate the first, so there are 25 you could choose
then 24, 23, 22, 21 ...

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you need to 'get the terms with x on one side and the constant on the other'
So subtract 2x from both sides
you know that 2x-2x = 0
divide both sides by 4
you know that 4/4 = 1

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use this URL to check factoring work --. http://72.3.253.76:8080/webMathematica3/quickmath/page.jsp?s1=algebra&s2=factor&s3=basic

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f(x) = 10 + x; where x is an natural number (an integer greater than 0)

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distribute the (-1) across the term (5y+2) and remove the parens
simplify
add 2 to each side
divide both sides by 3

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collect like terms. subtract 2 from each side

add 8v to each side

divide both sides by 13

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the two rays could intersect at a point that is not on segment AB or segment CD or both. Net, the rays 'go on forever', so there are lots of points where the two culd intersect and not be on the segments

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I assume the tree shadow is 18 feet.
use ratios

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Let the height be represented by h.
You are told the base, b, is








So h is either 4 or -3
Since the height can't be negative, it must be 4
Which makes the base
Check your answer, is the area of a triangle with a base of 3 and a height of 4 equal to 6???

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The amount of tea is a volume. So, in order to scale, each of three dimensions must scale in the same ratio as the single dimension you are given.
All that ends up saying is "the change in volume is the cube of the change in a single dimension".
For instance, if the pot is changed from 10cm to 20cm, then the scale has doubled. So you need to cube that to get the volume. Thus, a 20cm high pot will brew = cups.
A 30cm high pot will brew cups
Do that same type of conversion and you can find the two answers that "fit".
If you can't get them, let me know.

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So, the equation is
Substitute in a 35 inch hip and solve

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Either 2 quarters of 5 dimes. Either way, the toll is $0.50

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1) since 65 is 5*13 and 21 is 3*7, you can't simplify this one without converting to estimates
2)




3)

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The difference in their lengths is
So

Now that you know x, finding 5x and 3x is a dropkick.

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First thing, let's get rid of the 2 rest hours. That says the the man is actually moving for 3 hours.
You also know he goes as far at 30mph as he returns at 20mph.
Let the distance he goes each way be represented by d
Let the time at 30mph be given by t. Then the time at 20mph is


so



So the man travels at 30mph for 6/5 hour
= miles
Check your answer.
Does

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You are told the distance is 420 miles.
Let the slow speed be represented by s (in miles per hours) and the slow time be represented by t (in hours)
So
Thus
You are told that at , the time will be
So
Now substitute in the value you found for s above





factor this or use the quadratic equation

For a product to equal 0, one or more of the terms multiplied must be 0. So
either ot that means either
or since the time cannot be negative, the time at the slow speed must be 7 hours.
Now check your answers. If the time is 7 hours then the slow speed must be 60mph
If the speed if 10mph faster, then the faster speed is 70mph.
At 70mph, the time is 420/70 = 6 hours. Which is an hour faster.
So there you have it.
happy Labor day -- and still int time for 10am tomorrow

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Carl is
Jenny is
To find an average, add all the elements and divde that total by the number of elements.

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algebraically, it means that point is a solution to each equation
graphically, the point is the intersection of the two lines (assuming the lines are not 'the same line' or parallel lines, then they only intersect at a single point)

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Plug the x and y values into the original equation(s). If the result ends up being = (like 10=10 or 153=153) then the solution is correct

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Solve find the value for the given variable Show all work and check answers showing all work
2x + 6 over 5 = x+4 over 3
3(2x+6) = 5(x+4)
6x +18 = 5x + 20 now I am confused and also don't know how to check answer.
So far, so good. Collect like terms
subtract 5x from both sides and subtract 18 from both sides
simplify

2)
The work is correct. To check your answer, take your solution (12) and substitute it into the original equation. If the result is, in fact, equal, then your answer is correct. In this case
substitute in x=12


which is TRUE. so your answer is correct

b/6 - b-2/8 = 4
LCD is 48
48(b/6 - b-2/8) = 48 (4)
48 (b/6 - 48 ( b-2/8) = 192
so far, so good. You have an error in the next step.
should be remember when expanding, a negative times a negative is a positive
2b = 180
b = 90
URL to check your answer --> http://www.wolframalpha.com/input/?i=+b%2F6+-+(b-2)%2F8+%3D+4

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the second term is the sum of 2 cubes. There is a formula for that. Use it to get

This URL is really good at factoring --> http://72.3.253.76:8080/webMathematica3/quickmath/page.jsp?s1=algebra&s2=factor&s3=basic

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or
http://www.wolframalpha.com/input/?i=3x%2B11%3C6x%2B8

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multiply both sides by a to clear the denominator on the right
multiply both sides by 6 to clear the denominator on the left
expand the left side
subtract 12 from both sides
factor or use the quadratic equation. Here is a good URL to help check your factoring -->http://72.3.253.76:8080/webMathematica3/quickmath/page.jsp?s1=algebra&s2=factor&s3=basic
in order for a product to be 0, one or more terms in the product must be 0. So in our case, either or
So solving those two equations, says either or are solutions to the problem.
Substitute those values for a into the original equation to check your answers.

2)Use the same steps as above.
Clear right side denominator
Clear left side denominator
this time, expand both sides
collect like terms
simplfy
divide both sides by 6

simplify
Here is a great website for math. You can use it to verify your work. For this problem the URL is --> http://www.wolframalpha.com/input/?i=5%2F(3x%2B1)+%3D+3%2F(3x-1)