CPhill

The horse ran 11 (1/8)  =  11/8 miles

And 15 min 30 sec  =  15.5 min

So

Distance /  Time  =     (11/8) miles / (15.5) min  ≈  .089  miles per minute

y = -9x  + 2

In this form, there really isn't any "work" to be done......

The slope is  -9    and the y intercept  is 2

k / (-8)  =  -3      we can write

(-1/8)k  =  - 3     and we can take the multiplicative inverse of (-1/8)  = (-8/1) on both sides to solve

So

(-8/1) (-1/8) k   =  -3 (-8/1) 

k  =  24

Here's a possibility using the graph  of  y  = 20sin(πx / 3  +  π / 2)  + 80

Look at the graph, here :  https://www.desmos.com/calculator/derjhfgw9m

At  x  =  0   (representing year 1999)  we have 100 horses

At x  =  3  ( representing year 2002 )  we have 60 horses

And again, at x = 6 (representing year 2005 )  we're back up to 100 horses

Sorry, I don't understand what "b"  is asking for

c)  In 2000  ( x = 1)  there were 90 horses

d) In 2015  ( x = 16) there were 70  horses

Here's one (but not the only) possibility

Look  at tthe following graph  of   sin (πx/2  + π/2)  : https://www.desmos.com/calculator/bdvsovus1f

Let the max height of the curve represent "all the way to the right"  and the minimum height of the curve be "all the way to the left"  ....note that there are 4 beats from starting  from all the way to the right, swaying all the way to the left and back again to the right

The amplitude  is  1     (this could be changed without affecting the pattern of beats )

The period is 4 radians.....each radian represents a beat...!!!

P.S. -  I don't understand what is meant by "the equation of the axis " 

x^(2/3) * ( 8x)^(1/3)   =

x^(2/3) * 2x^(1/3)  =

x^(2/3) * x^(1/3) * 2  =

x * 2  =

2x

y  + 4  > 0  →   y > - 4

y ≤ x + 1

Look  at the graph here, Adam 

https://www.desmos.com/calculator/th5yusruds

Notice that the point (3,3)  is the only one  that appears in the feasible region......

-10 = -14v+14v

-10  =  0       thus.....no answer is possible

 (-2x^6 + 5x^5 + 9x^2 +2) / x^4  

Write  term by term.....and we have

-2x^6 / x^4   +   5x^5 /x^4  +  9x^2 / x^4   + 2/x^4    =

-2x^2   +  5x   +  9x^-2 +  2x^-4

.5   =  .5 / 1      multiply top/bottom by 10  =

5 /10     =

[5 * 1] / [ 5 * 2 ]  =

5/5   *  1/2   =

1 * 1/2  =

1/2