Alright, lets get started.
At the beginning of her training, she is able to run 2 miles without stopping means 2 will be in the addition when we will write the equation for her running miles.
Her goal is to increase her distance by three quarters of a mile each week.
Means in first week, she will add the distance = 
miles
Suppose she runs x weeks, so shee will add distance = 
So, suppose she runs total number of miles = d, then
Where d is total numer of miles she runs
x is number of weeks : Answer
Hope it will help :)
The constraints for the problem is the number of tomatoes and cups of oil on hand.
There are only 45 tomatoes and 10 cups of oil on hand to make both the Tuscan sauce and Marinara sauce.
These are identified as constraints because they limit the number of Tuscan sauce and Marinara sauce that Tiffany can make.
In order to solve this, you have to set up a systems of linear equations.
Let's say that children = c and adults = a
30a + 12c = 19,080
a + c = 960
I'm going to show you how to solve this system of linear equations by substitution, the easiest way to solve in my opinion.
a + c = 960
- c - c
---------------------- ⇒ Step 1: Solve for either a or c in either equation.
a = 960 - c
20(960 - c)+ 12c = 19,080
19,200 - 20c + 12c = 19,080
19,200 - 8c = 19,080
- 19,200 - 19,200
---------------------------------- ⇒ Step 2: Substitute in the value you got for a or c
8c = -120 into the opposite equation.
------ ---------
8 8
c = -15
30a + 12(-15) = 19,080
30a - 180 = 19,080
+ 180 + 180
-------------------------------
30a = 19,260
------- -----------
30 30
a = 642
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I just realized that there can't be a negative amount of children, so I'm sorry if these results are all wrong.
Recall that:
sin(A + B) = sinAcosB + cosAsinB
Therefore:
sin11°cos19° + cos11°sin19° = sin(11° + 19°)
= sin30° = 0.5
I hope this explains it.
