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Earning is the flat 350 + $10 for each oil change

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I would plot these two. Both are lines. Then find the area between the lines that satisfies the two inequalities.
Plot the line y = 2x + 6

Now draw another line at y=-5 (horizontal line). The solution is all the area between the two lines, including the top line, that lies above y=-5. So it is a 'wedge' going out from the point (-5.5, -5) toward the right.
Make sense?

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Given
In this case, the first term on the left and the one on the right have the same denominator. So we can simplify them as is




Now we can 'cross multiply' to get rid of the denominators on each side


Now combine like terms

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let x be the number.
Given

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Not quite.
If you multiply your terms, you get 3x^2 -13x -10. Which is not what you want. You are correct in that you need 3&1 and 5&2. Now you need to find the sum of prodcuts that gives you the middle term. Notice that the sign on the constant term (10) is positive. So, the two factor must both have a + or both have a minus, in order to get a positive product.
So, start with this
(3x + A ) (x + B)
The only choices we have that allow the product of A*B to be 10 are 2,5 and 1,10.
We are trying to end up with a sum or products for the middle term that equals 11. Since there is a 3x term in one of the factors, the product can either be 3*10 + 1*1 = 31
OR 3*1 + 1*10 = 13. Neither is 11. So the other pari of factors must be the ones we want. But in which order?
3*2 + 5+1 = 11
3*5 + 2*1 = 17
So the one we want is 3*2 and 5*1
As follows:
(3x+5)(x+2)
Look at this URL --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic

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Given

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Given
To do these 'in your head', you need to look at the coefficients on the x terms. In this case, both are equal to 1. So, the resulting coefficient on the term will be = 1
Now let's do the constant term:
By looking at the two constants (5 and 2), you can see the last term will be the product of = 10.
The hardest part if figuring out what the middle term, the term will be. For that you need to realize that coefficient is a sum or difference of two products. In our case, since both terms have a + sign in them, the resulting x term will be a sum. It is the sum of + = = 7.
So the answer is
If you need a place to verify this type of answer, go here --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=expand&s3=basic
That won;t show you the intermediate steps, but will allow you to verify the accuracy of your result.

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Use this --> http://www.calc101.com/webMathematica/long-divide.jsp#topdoit

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Given
find
f(0)



f(-1)




f(2)

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Given
You are given the volume of a cube and asked to find the length of one side.
Take the cube rott of both sides and then simpify

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Given

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Assuming the first two keys are digits and the last three are letters (that is, assuming we know in advance this is that case), then
The first key is digits - so Alan has 10 choices
The second key is digits, but can't be the same digit used on key 1. So 10-1=9
The third key is letters - 26 possibilities
The fourth key is letters - 26 possibilities
The fifth key is letters - 26 possibilities
So, 10*9*26*26*26 possible permutations
I never thought I would see a mathematics problem that appeals to a thief!
Next question, what is the probability Alan gets caught and goes to jail? :)

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x + w + y = 4300
0.0325x + 0.04w + 0.0575y = 193
3.25x + 4(3x) + 05.75y = 19300
4x + y = 4300
15.25x + 5.75y = 19300
Using substitution:

Solved by pluggable solver: Solving a linear system of equations by subsitution

Lets start with the given system of linear equations Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y. Solve for y for the first equation Subtract from both sides Divide both sides by 1. Which breaks down and reduces to Now we've fully isolated y Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x. Replace y with . Since this eliminates y, we can now solve for x. Distribute 5.75 to Multiply Reduce any fractions Subtract from both sides Combine the terms on the right side Now combine the terms on the left side. Multiply both sides by . This will cancel out and isolate x So when we multiply and (and simplify) we get <---------------------------------One answer Now that we know that , lets substitute that in for x to solve for y Plug in into the 2nd equation Multiply Subtract from both sides Combine the terms on the right side Multiply both sides by . This will cancel out 5.75 on the left side. Multiply the terms on the right side Reduce So this is the other answer <---------------------------------Other answer So our solution is and which can also look like (,) Notice if we graph the equations (if you need help with graphing, check out this solver) we get graph of (red) and (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle. and we can see that the two equations intersect at (,). This verifies our answer. ----------------------------------------------------------------------------------------------- Check: Plug in (,) into the system of equations Let and . Now plug those values into the equation Plug in and Multiply Add Reduce. Since this equation is true the solution works. So the solution (,) satisfies Let and . Now plug those values into the equation Plug in and Multiply Add Reduce. Since this equation is true the solution works. So the solution (,) satisfies Since the solution (,) satisfies the system of equations this verifies our answer.

So x = $700
w = 3x = $2100
y = $1500
Verify your answers. Does 0.0325(700 + 0.04(2100) + 0.057(1500) = 193?

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It is hard to tell from this problem to know 'where in algebra' you are. If you are just starting out, I suspect they are asking you to find the value(s) for k that allow simple factoring to work.
In that case, you will be looking for combinations of numbers whose product is 17 (since the coefficient of the x^2 term is 1). In that case, since 17 is prime, only 1 and 17 are possible factors.
(x-17)(x-1) = x^2 -18x + 17
(x+17)(x+1) = x^2 +18 +17
So the only positive k would be 18
However, if you are farther along in algebra, then what you are being asked is "what vaues of k make the determinant of the solution to the quadratic equation greater than or equal to 0". If the term determinant is something you are learning or know, then use that to find the values of k. There are an infinite number; so use an inequality based on the the determinant being >= 0

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Slope intercept form is y = mx + b
Given
Assuming this is a not mistyped,


slope is undefined
there is no y intercept

I figure you had a typo. Let's assume you meant


slope is 2/3
y intercept is -4/3

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divide both sides by 5 to find b

Use this tool to help check your answers --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=equations&s2=solve&s3=basic

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is the given equation.
What is the cost at 2 months? That is asking, what is C(2)?


dollars
Is the client has $90, she can only get 2 months of service. Keep the other $10 for something else.

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The sum of the interior angles of a triangle is 180 degrees.
TAC + CAB = 180 a well since those angles are supplementary (the form a straight angle).
Thus TAC = the sum of the other two angles in ABC
TAC = ABC + BCA

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=

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Let the angle at BAC = a.
Triangle ABC is isosceles, so its base angles are equal. Call those angles b.
We have a+b+b = 180
By extending B to P, with a length equal to BC, we create a second isosceles triangle BPC. The angle at PBC is the supplement of the angle CBA. That angle is b (from above). So angle PBC = 180-b
Since the second triangle also has base angles equal, we know that angle BPC and BCP are the same. Call that angle c.
Then PBC + 2c = 180.
PBC = 180 - 2c
From above PBC = 180-b, so
180-b = 180 - 2c
b/2 = c
The angle at CPB = c = b/2
The angle PCA = c + b = b/2 + b = 3b/2
Which is 3 times CPB

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See this --> http://library.thinkquest.org/2647/algebra/post.htm
Then substitute in 'numbers' or other combinations of letters to create examples.
For instance:
Transitive Property of Equality: if a = b and b = c, then a = c
example If 12 = (9+3) and (9+3) = (13-1) then 12 = (13-1) OR
if x = y and y = 2z then x = 2z

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I know of 6. Perhaps there are more
1) solving by substitution
2) solving by elimination
3) solving by completing the square
4) solving graphically
5) solving using the quadratic equation
6) factoring
See here for some more words --> http://www.purplemath.com/modules/solvquad.htm

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No.
=
=

is not equal to

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Is the polygon regular? see --> http://www.mathwords.com/a/area_regular_polygon.htm
If not, then chop it into triangles and solve that way

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Use this --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic

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Solved by pluggable solver: Finding the slope

Slope of the line through the points (-4, 0) and (-4, 3) Since you CANNOT divide by 0, this means that the slope of the line is undefined. Answer: The slope of the line is undefined.

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Using products of zero rule
x = 0 x = -2

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Not sure what the original equation really is. Look here for a tool --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=simplify&s3=basic

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Use a combination. See http://www.mathagonyaunt.co.uk/STATISTICS/ESP/Perms_combs.html
15P6 = 15!/((15-6)! * 6!)
= (15*14*13*12*11*10)/ (6*5*4*3*2*1)
= (14*13*11*10)/4
= 7*13*11*5
= 5005

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a) Hearts are 13/52 or 1/4. With replacement, diamonds are 13/52 = 1/4
so 1/4* 1/4 = 1/16
b) without replacement
hearts is still the same (13 of 52). But diamonds is then 13/51.
1/4 * 13/51 = 13/204