Using pythagorean identities,tan(sin^-1(-5/13))= tan(arcsin(-5/13))
Let A = arcsin(-5/13) = -arcsin(5/13)
Thus, sin A = -5/13 and cos A = sqrt(1 - (5/13)^2) = 12/13.= tan(A)= sin(A) / cos(A)= -5/13 / (12/13)= -5/12
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Answer:
Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario?
First, calculate the rate of change (Slope, once it is a linear function):
I will take the points:
and 

Let's understand the graph!
This linear graph is about songs being downloaded in a period of 5 weeks.
In the beginning, we have 100 songs to be downloaded. As the weeks past, the number of songs remaining decreases, that's why the graph's slope is negative. In week 5, all songs were downloaded.
The initial value (100) represents the number of songs.
Part B: Write an equation in slope-intercept form to model the relationship between x and y.
The Slope-intercept form of linear equations is 
where, m is the slope and b is the y-intercept.
In this case, we have

There are a total of 900 students at Molly’s school. 810 is 90% of 900. 90% of students did not wear a silly hat.
Answer:
For the column "Slope Intercept", the graph is displaying y = -7/2x + 3. Because the line is going down 7 units and to the right 2 units, and the 3 is the point in which the line crosses the y-axis.
For the "Standard" column, it will be
7x + 2y = 6, because that's what it would look like in standard form. (To turn it from standard to slope intercept form, remember you must first subtract 7x on both sides to get 2y = -7x + 6, and then divide by 2 on both sides to get
y = -7/2x + 3.)
For column "Point Slope", I just realized you are supposed to pick a point on the line and plug the coordinates into this formula:⤵⤵⤵
<em>This is the point-slope formula.⤵⤵⤵</em>

For example we'll use point (2,-4). Also, remember that coordinates are written as (x,y), and that m represents slope.
So we have: y - (-4) = -7/2(x-2).
In other words, "Point Slope" would be
y + 4 = -7/2(x-2).
By the way, sorry this is a bit long, and took a while to complete. I had to re-educate myself on point-slope. Anyways hope this helps, I tried :)
d = r · t ⇒ t = d/r
going
t = 54/(r + 4)
coming
t = 30/(r - 4)
54/(r + 4) = 30/(r - 4) times are equal
54(r - 4) = 30(r + 4) product means/extremes
54r - 216 = 30r + 120 distribute
24r - 216 = 120 subtract 30r from both sides
24r = 336 add 216 to both sides
r = 14 divide both sides by 24
Alfonso bikes at 24 mph.