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This can't be found... when you get it to work, I will be happy to help!

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Here is another way to put it:

We find the GCF of all of the terms, which is x. That will get us x^2+4>5x

This can be set into a quadratic (ax^2+bx+c). 

In this case, the quadratic will be x^2-5x+4.

We will then factor the quadratic, which will get us (x - 1)(x - 4) > 0

The possible values of x will be x=1 and x=4.

If we write this in interval notation, it will be (-infinity, 1) U (4, infinity) 

Note  that  if we let  g(x)  be  - 2x^5 + x^4  + ax^3

Then....adding  f(x) + g(x) we get

ax^3  + x^2  - 3    =    degree 3

So

g(x)  must also  be  degree 5

I will try but... wow! This is really complicated!!!

LOL!!!!!

Oh yeah!!! Thanks for the explanation, Chris. 

Me to myself: "I didn't realize that this was a polynomial! Read the question, Cal!" LOL!

Anyway, thanks again!

Nice, Chris! We can also look at it like this--

First equation:   3x + 4y  = -14

                          y = (-3/4)x - 7/2   

We know that Line 2  is perpendicular to Line 1.

Therefore, its slope is also -4/3

The question also says that Line 2 passes through (-5, 7).

Second equation: 7 = (4/3)(-5) + b

                             b= 41/3 

Line 2 will have the equation

y = (4/3)x + 41/3

Where 4/3 is the slope and 41/3 is the y-intercept.

Therefore, Slope+y-intercept will give us 4/3) + (41/3)  =  45/3 = 15

Thanks, jfan  and CTG !!!!!

No....not 6

Look at the graph here :  https://www.desmos.com/calculator/b3vbllckme

Note that the roots of this polynomial  are  n = 3  and  n  = 6

So....at  n =6, the polynomial   = 0 

But we need it to  to be  negative......so.....the largest integer value to  make this true is  n   = 5

I agree! This is true. The inverse sin allows the max and minimum x value between the domain.

We know from f(x)=sin^-x that the range is all real numbers since x can be any real number.

Hope this helped!

The slope of the first line  can be found as

3x + 4y  = -14

4y   =  -3x  - 14      divide  both sides by  4

y = (-3/4)x - 14/4

y = (-3/4)x - 7/2   

Since line 2  is perpendicular to this one then its slope =  4/3

And   since line 2 passes through  (-5, 7)   we have that

7 = (4/3)(-5) + b

7 = -20/3 + b

21/3  = -20/3  + b     add 20/3 to both sides

41/3  = b

So.... line 2  has the equation

y = (4/3)x + 41/3

And  m + b  =   (4/3) + (41/3)  =  45/3 =   15

Same. I'm just doing math and video games... gettin' homeschooled... NOT FUN AT ALL!!! I need some sports!!! I like a normal, young and immature life. LOL!

Wait...Chris! I think you meant 6, right?

We can expand \(3(x - 4) + 2(x^2 - x + 7) - 5(x - 1)\)  to find the constant coefficient.

This will get us \(3x-12+2x^2-2x+14-5x+5.\)

Adding and subtracting "like" terms, this will get us \(2x^2-4x+7.\)

This will get us 7 as the constant coefficient, like jfan17 said.

Hope this helped!

We want to solve  this  :

n^2- 9n  +  18   <  0            factor the left side

(n  - 6) ( n - 3)  <  0

Note that this will  be true  when  n is on the interval  (3, 6)

So.....the greatest integer value of  n that makes the function negative is  n  = 5

We can factor this into (n-3)(n-6).

The possible values of n will be 6.

Hope this helped!

Let's look at the squares between 100 and 200.

First is obviously 100, which is equal to 10²

^{\(100 = 10^2\)}

^{\(121 = 11^2\)}

\(144 = 12^2\)

\(169 = 13^2\)

\(196 = 14^2\)

\(15^2 = 225\), which would be too large, making our answer

5 square numbers inclusive between 100-200. 

I think this will be easy to just list the ways.

x can be from 10^2 to 14^2,

Therefore, x can be 5 different integers.

Hope this helped!

n = 4  and  n = 5

The slope   of   Ax + By  =  3   is      -A/B    

And  x + 3y  = - 5  ⇒  3y  =  -x  - 5     divide through by 3  ⇒  y = (-1/3) - 5/3

So....the slope of the second line =  (-1/3)   

And since this is parallel to the first line,  this implies that

-1/3  = -A/B

So  A = 1   and  B    = 3

Then B - A  =   3  -  1   =   2

Thank you very much!!! You are very good at this!!!!

Hey guest! Personally, I've been just grinding some math lol(i know, sounds boring :P). I've also been reading some books on the side and also some work for school(they actually assigned some to us). What about you?  

Let the measure of angle XAY   = x = angle BAC

Then, because AX = XY, then the measure  of angle XYA  also  = x  

And, by the exterior angle theorem , angle BXY  = 2x

And since XY =TB, then angle XBY  also equals 2x

So angle XYB =  180 -  angle BXY - angle XBY =   180 - 2x - 2x  = 180 - 4x

And  the sum  of angle XYA  +  angle XYB  + angle BYC = 180

So        x   + 180 - 4x + angle BYC  =180      (1)

So, rearranging (1).......  we have that    angle BYC  =   3x

And since YB = BC,  then the measure of angle BCY  also  =  3x = angle BCA

And in triangle BAC, the sum of angles  BAC  + angle ABC + angle BCA   =180

So   

x  +  120  +  3x    =180

4x  + 120  =  180

4x =  60

x = 15°  =   angle BAC