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In this question: we can substitute y from the first equation into the second equation (a special type of substitution called the y=y method).
This gives us:

Now we need to isolate x and solve:




Now we have our x value, we need to substitute this into either of the original equations and solve for y (I will put it inot the y=x-3 equation though either choice will give you the same answer)



So the point of intersection is (-1,-2)

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So she paid 100%-15% of the regular price (85% of the regular price)
Let's call p our regular price. We can make the equation:
0.85*p=64.34
Now all we need to do is solve for p and we have our answer.
Let me know if this helps, or if there is still anything you are unsure about.

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For this question, you can substitute any value for x and solve for the corresponding y:
For example, one order pair would be :
x=1
y=1+8=9
So we get the ordered pair (1,9).
As long as the two numbers satisfy the equation, they are an ordered pair on that line (remember that ordered pairs are written (x,y) )

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Does the question say that these two points lie on a line (that would be what I would guess but just making sure then I can help you further)

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If you have a variable in the exponent, we always want to take logs of both sides:

Now we can bring down the exponent using our log rules:

And isolate for x


I will leave the rest of the isolating up to you. (Don't forget that log of a number is just a number itself, so don't let that fool you)

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These triangles are similar. Since the bases of the two triangles are doubled from the smaller to the larger, similarily, the heights will be doubled (giving us 2*12=24).

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What is the question?

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8n

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ANS: 0

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If I have 5 dogs and take away 1 dog and then add 2 dogs, how many dogs do I have? 6:) It works the same with variables, instead of dogs we have 5 h , ...etc

so 5h-h+2h=6h:)

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For this question that holds not only for that t but for all t.
We know that csct=1/sint from definition of csc
So sint*csct=sint*(1/sint)=1 (assuming that sint does not equal 0, for pi/3 this is true).

Hopefully this helps:)

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If I run a mile at a speed of ten miles per hour, it takes me 1/10 of the hour to run the mile.
Well, in an hour there are 60 minutes and 1/10*60=6
This means it will take me 6 minutes to run the mile.

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The formula for compound interest is :

where FV represents the future value, PV represents the present value (how much you put into the account right now), i represents the interest rate per period and n represents the number of periods (in our case years).
So we have PV=1500
n=3
and i=0.1 (which is the same as 10%)
Substituting this into our formula we have:


You need to solve for FV (I will let you do the rest- let me know if you are unsure about anything:)

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Permutation is when you arrange a set of numbers (things, etc.) and ORDER MATTERS



If you want some more specifics:
http://en.wikipedia.org/wiki/Permutation

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This is just a quadratic with a twist. (I will help you get started, however you will have to try it yourself to get the answer)
Instead of x in our polynomial we have tanx.
We have dealt with solving for x in quadratics before (If you have been given this question- I hope you have- if not check out factoring/quadratic equations)
Instead of solving for x however you are solving for tanx
And finally, once you have solved for tanx, you have tools to solve for x (tan inverse, or perhaps a special triangle).
Try it out and see if this puts you on the right track if you are still confused let me know:)

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For now, let's just look at the following equation:

we can make this into a more familiar line:

and using the slope and y intercept of this line we can graph it (I will let this up to you, remembering that we have the point (0,-4) from the b value and the slope is -4=rise/run=-4/1)

Now, once you have graphed the line you will have broken your plane into two regions. take any point from each region (but not on the line) and test them. By test I mean plug into:

and see if it holds true, if so, shade the region, if not, leave the region unshaded.


Hopefully this helps get you on the right track:)

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We know that the equation of a line can always be written in the form
where m is the slope of the line and b is the y intercept of the line(keep in mind for other questions that the y intercept of a line always has an x value of 0 for it).

Using this we have

and a point that we can use:



Now substituting these points into our line equation we will solve for b:






So we have our equation for our line!

Hopefully this all is clear!(let me know if not:) )

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Pure acid-- this means that we have 100% acid
Using that fact:
we have the following equation:

where x is the amount of pure acid that is added (also note that we will end up with x+5 gallons in the end)
From here it is a matter of algebra and solving for x.
try it yourself from this step, and let me know if you have any difficulties:)

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In general: the circumference of a circle can be found using the following equation:
where r is the radius.
We have r=5 so we have:

=

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For these types of questions, I find it useful to make a table that compares the way there vs the way back (speed, distance and time).
We also need to recall that speed=distance/time
Okay, so for the way there we drove at 24 mph. We do not know the distance so I will call it d. and similarily we do not know the time. I will call the time y.
For the way back we drove at 40 mph a distance of d and a time of y-0.5.
Using our speed equation we know that distance=speed*time (just rearranging it).
Now we can make equations using what we have:
For the trip there:

and the way back:


Now I will let you do the rest. You have two equations with two unknowns (d and y). We just need to find d.

Try it out and if you are still not able to get the answer let me know:)

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This has MANY answers....
We know that the area of a rectangle is

So we have:


But we can substitute in any number for L and get a corresponding W. (If it was a square however, there would only be one answer as we substitute L=W and solve for W.
With the perimeter the same problem remains. Once we have a L and W we have:

But due to the fact that there are many such L and W, there are just as many perimeters.

Hopefully this clears things up a bit, if there was any more specifications with the question Let me know so I can be more clear with my answer.


Okay, using the new information, if we want the smallest rectangle with whole number lengths and widths-- we know that the smallest length we can have is 1 making the width 59 (not that this is smaller perimeter than if we had a square with area 59 and any other rectangles with that area with whole number lengths).
From here, you can use the above formula and find perimeter. :)

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So we started with a salary of 80 000. Since 10.25% was deducted, (and the original amount is 100%), we have
remaining
So that means we have

remaining in the annual salary. Hopefully this helps a bit:) If you are unsure about anything let me know:)

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Due to the fact that there is no right hand side to this equation, we are unable to solve it (for x).

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For this one, you will have to compute the mean of each set of 3 numbers and see which sets have exactly two decimal places (or none or 1 as we can add a 0 onto it eg. 1=1.00)

I will do A for you and let you do the others.
mean of A=
=
So that one is NOT one of the number sets the work.
Try the rest out and let me know if you have any problems:)