How do I do double transformations
1 answer:
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You need these two basic solutions and facts to find the equation of a line:
- If you know the gradient
and one point
:
- If you know the gradient two points
:
- The slope of a line is the coefficient m when you write it in the
form
- Parallel lines have the same slope
- The slopes of perpendicular lines give -1 when multiplied
We can use this list to solve all the exercises:
b)
Use the first equation to get
c)
Use the second equation to get
d) same as c)
e) We derive the slope of the line by writing it as
So, the slope is -1/5. From here, it's the same as b)
f) same as e)
g) Again we find the slope as
so the slope is -3, and a perpendicular line has slope 1/3. From there, it's the same as b).
Answer:
Option b (4,1)
Step-by-step explanation:
The region given by the system of inequalities is shown in the graph. We must look within this region for the point that minimizes the objective function
The minimum points are found in the lower vertices of the region.
These vertices are found by equating the equations of the lines::
-------------------
---------------------
The lower vertices are:
(4, 1) (2, 4)
Now we substitute both points in the objective function to see which of them we get the lowest value of
Then the value that minimizes f(x, y) is (4,1).
Option b
