JonathanB

\((x^2 +5x-6 )\over(x^2+x-6)\)

\((x+6)(x-1)\over(x-3)(x+2)\)

From this factoring, it can be deduced that the function has vertical asymptotes (when the denominator equals 0) at x=3 and x=-2. Also, it can be determined that the function has x-intercepts (when the numerator is zero and the denominator isn't) at x=-6 and x=1. 

From this data, it can be concluded that the correct answer is the second graph.

P.s. You can never cross a vertical asymptote. 

The second to last one. It has the correct x-intercept (1,0) and has the correct slope.

A.)

Think of this problem as an interest problem. After a certain amount of time, your money (cells) will double.

The standard equation for simple compounding interest is y = P(R)^x

where

P is the principal/ initial amount 

R is the rate at which your principle will increase  

x is the time interval (seconds, days, year, etc.)

y is the final amount after x time

Knowing that we can make an equation

N= 1000(2)^(h)  

where h is (t/14)

t is in hours so every fourteen hours the expression h increases by 1 and so the equation N doubles.

B.)

There are 24 hours in a day so in 2 days that is 48 hours

h will then be 48/14 

plug this into the equation and you get

N= 1000(2)^(48/14) = 10767 cells (rounding down because you can't have a portion of a cell)

when you are doing the same operation across an expression like the one above you can work from left to right. (except if there are parentheses do them first)

 so then

6/-7 is -6/7 -->

-6/7 / 3 is -6/7 * 1/3 which is -6/21 -->

-6/21 / 11 is -6/21 * 1/11 which is  -6/231 or -2/77 when simplified.

Both of these solutions are essentially doing the same thing 

15% is .15 and as a fraction that 15/100 or 3/20 so by dividing by .15 you are basically multiplying by 20 and dividing by 3.

Arithmetically:

99 - 2*11 = 99 - 2*11 = 77

77/2 = 38.5

Algebraically:

Perimeter of Rectangle = 2x + 2y where x is the width and y is the length

99 = 2x +2y

99 =  2(11) + 2y

99 - 2(11) = 2y 

77/2 = 38.5 = y 

You can do the compare and contrast part. 

And as you can see they are in fact the same value.

The equation for the perimeter of a square is P=4d where d is the length of one side

To find the distance between two points on a cartesian plane you use the distance formula

\(d = \sqrt((x2-x1)^2+(y2-y1)^2)\)

\(d = \sqrt((5-1)^2+(-1-4)^2)\)Where B is (x2,y2) and A is (x1,y1)

sqrt(41) is about  6.4

so we plug that into the perimeter equation and get P=25.6 

I'm assuming you want to solve for b.

\(18sinb = 8 sin110\)

\(sin b = \frac{8}{18}sin110\)

\(sinb = \frac{4}{9} sin110\)

\(arcsin (sin b) = arc sin( \frac{4}{9}sin110)\)

b = -0.0197