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Answers by David F.

There's no x in your function.  I take it you mean as H goes to 0?  That's generally how you use the difference quotient for a particular function.  Does it make more sense that way, then?

3(x-4)-5=-2+5x-9 (answer)

The main problem with this equation is that the x's are on different sides of the equal sign.  Your overall strategy is to put all the x's on one side, and everything else on the other side.  You will end up with something * x = everythingelse, and you'll divide both sides by the 'something'...

Um, Helen, this is a single variable, a number line would be right, wouldn't it? So, draw your numberline. Now consider the geometric properties of the absolute value.  Your statement says (and watch this carefully!) "The distance between x and 4 on the number line is greater...

I would have one of my own students, when encountering this problem, take a few minutes to write things like "2x + 3x = 5x, 4x - x = 3x, etc." and then have them do "x * 3x = 3x^2".  You know, pick 20 or so random things to write where you're first adding, then multiplying...

It helps to know that these "properties" of which we speak are basically traits of operations.  For example, if I sautee some onions in butter, I have to put the butter in the pan first so it will melt.  If I put the onions in first, I will not get the same result that I would...

x^2+60x+500=0 (answer)

Two choices:  Factor the trinomial into two binomials, set each one equal to 0, and then solve each one.  Or, what I'd probably do, toss it into the quadratic formula. In the first case, you'd end up with something like (x + anumber)(x + anothernumber) = 0 and break it into...

First I'd rewrite it.  :)  (I know, you have it written out already and had to type it in here somehow) 12x22y33z4 - 2x3yz2 So, you have two terms here and there's a GCF for the the two.  Start with the coefficients 12 and 2.  What's the greatest common factor for those...

counterexample (answer)

I take it you're supposed to provide a rectangle with a perimeter of 14 inches but an area that is not 10 inches? Easy enough.  What are the side lengths that would make the perimeter 14 inches?  You're only going to have two lengths, because for each side, there is one side that is...

Well, if range is all the y values that exist in the function, then the domain would be the x values that correspond to those y values, right?  So, your domain will be a set of three numbers the same way your range is a set of three numbers. Does that help you to finish the problem...

Well, let's see, the diameter is twice the radius, right?  So to get the radius, you just divide the diameter in half, giving you 6 inches.

When you raise an exponent to an exponent, you multiply them together.  So your answer is x4

Which one of these things is not like the other?  Yes, I'd totally refer to the Cookie Monster for it.  Anybody can see that the x=4y part is the same in both of them, and both have a 1, but the symbol that joins those two pieces together is different between them.  If the pictures...

Break it down piece by piece and write as you do.  Here, like this: "Fifteen times a number" Ok, I'll call my number Q, just because I'm tired of X.  So, I write 15Q, because that's "fifteen times a number".  Next: "decreased by fifteen." ...

Is there a context involved, like an equation?  I'm not seeing how this can be factored either, unless you break up the -9x and find yourself with something like (x - 2)2 + 5x.  You *can* do that, by making it -4x - 5x, move the -5x off to the side and then factor what's left....

Answering this one also answers your other question.  Simply substitute -8 wherever there is an x and simplify. f(-8) = (-8)2 - 3(-8) -82 is 64, and -3 * -8 is 24, so your answer is: f(-8) = 88 With this information, you should be able to work your other problem on your own...

This question has a lot of boring algebra that's easy to get caught up in, so I'll let you work that part out.  Basically, what they're wanting you to do is to break up this ellipse into two parametric equations.  They give you one, x = 4 + 5cost.  You plug that in for x and...