jboy314

Let's move everything to the left side and distribute the two

x^2 -2x-8>0

(x-4)(x+2)>0

We can see that the two zeroes are at x=4 and x=-2, neither of which are solutions!  They are important because we can use them to determine what segment(s) of the number line contain our solution set.  Let's try testing 3 numbers, one that is greater than our two zeroes, one that is less than our two zeroes, and one that is between our zeroes.  

Greater than: I'll choose x=1000 because it will make it easy to determine if our inequality holds.  Note that when you substitute a large number like this it makes both factors of our quadratic positive, which guarantees our inequality is true. 

Between: I choose x=0 because it is easy to calculate. (0-4)(0+2)>0 is equivalent to -8>0 which is clearly false.

Less than: let's pick a big negative number.  It really does not matter what it is but when we select any large negative number we get two negative facts which result in a positive produce which guarantees our inequality is satisfied

Therefore our solution set is x>4 or x<-2

you'll need to use tan inverse to find theta.

If you go the calculator on the home page of this website press"2nd" then "atan" to bring up arctan which is equivalent to tangent inverse.  Then type in 1.47/1.59 and hit equals and your result will pop right up!

as a first step lets make this look a little more friendly by multiplying both sides of the equation by 100

5x+4=30-20x

Now add 20x to both sides and subtract 4

25x=26

x=26/25

More than likely you mean cosine inverse of (6.4/9.6).  Since cosine and cosine inverse are functions they have no value and cannot be multiplied by things. To compute cos^-1(6.4/9.6) you can go to the calculator on this site and click the "2nd" button, then "acos" which stands for arc cosine with is the same thing as cosine inverse, then type in your fraction in the parentheses and your answer will pop right out!

Inverse trig functions use ratios or function values as their inputs and produce angle measures as their outputs versus a regular trig function that does the exact opposite.  When I teach this in geometry i use the phrase "inverses find angles" as a way to remember which is which.

As an example, if you wanted to know what measure on the unit circle would produce a y value of 1 you would use sin^-1(1)=pi/2  

Glad I saw your post, Alan.  In my inital setup i missed a decimal point accompanied with 39 so my answers were off by a factor of 100!

Focus on the meaning of"percent" as being "out of 100 so 3.5% really means 3.5/100=.035 

we want this much of 50 which means .035(50)=1.75

In this case we cannot subtract 39. In algebra we always need to look for inverses (opposites) to cancel things out.  When we look at the original setup the 39 is connected to the m by multiplication and then 2600 is added.  We have two options: a, cancel out the multiplication with division or b, cancel out addition with subtraction.  We should pause for a moment to see which one is easier.  If we choose division we need to divide by 39, which is possible but not fun particulalry in the middle piece because we end up with "m+2600/39" and now we have all sorts of fractions to deal with.  Its much easier to subtract 2600

6890<39m+2600<8840

4290<39m<6240

From here your idea to divide by 39 is spot on.  Our result is

110<m<160

Am I correct in my assumption that you are talking about this line "-12<-2x<=-9 "

When we subtracted four it killed off the 4 in the 4-2x so what is left over is just the -2x in that middle "chunk"

Ill help you set it up and then you can try to solve it.  We know we are trying to figure out when plan b is cheaper so

B<A

6+.12x<25+.05x