Answer:



Step-by-step explanation:
step 1
Find the length side a
Applying the law of cosines

substitute the given values



step 2
Find the measure of angle B
Applying the law of sines

substitute the given values



step 3
Find the measure of angle C
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so

substitute the given values



To do this problem you would first need to factor out a variable, which in this case I would want to do the first equation because it is isolated. Now the equations would look like this:
x = -2y - 1
4x - 4y = 20
Since we know that x is now equal to -2y - 1 we can plug it in to the x value in the second equation:
4 (-2y -1) - 4y = 20
-8y -4 - 4y
-12y - 4 = 20
-12y = 24
y = -2
Now that we know the y value plug the y value to one equation to find the x, I will be using the first equation
x + 2(-2) = -1
x - 4 = -1
x = 3
Solutions:
y = -2
x = 3
Answer:
answer is A
Step-by-step explanation:
Answer:
The image of
through T is ![\left[\begin{array}{c}24&-8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D24%26-8%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
We know that
→
is a linear transformation that maps
into
⇒

And also maps
into
⇒

We need to find the image of the vector ![\left[\begin{array}{c}4&-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%26-4%5Cend%7Barray%7D%5Cright%5D)
We know that exists a matrix A from
(because of how T was defined) such that :
for all x ∈ 
We can find the matrix A by applying T to a base of the domain (
).
Notice that we have that data :
{
}
Being
the cannonic base of 
The following step is to put the images from the vectors of the base into the columns of the new matrix A :
(Data of the problem)
(Data of the problem)
Writing the matrix A :
![A=\left[\begin{array}{cc}4&-2\\5&7\\\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-2%5C%5C5%267%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Now with the matrix A we can find the image of
such as :
⇒
![T(\left[\begin{array}{c}4&-4\end{array}\right])=\left[\begin{array}{cc}4&-2\\5&7\\\end{array}\right]\left[\begin{array}{c}4&-4\end{array}\right]=\left[\begin{array}{c}24&-8\end{array}\right]](https://tex.z-dn.net/?f=T%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%26-4%5Cend%7Barray%7D%5Cright%5D%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-2%5C%5C5%267%5C%5C%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%26-4%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D24%26-8%5Cend%7Barray%7D%5Cright%5D)
We found out that the image of
through T is the vector ![\left[\begin{array}{c}24&-8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D24%26-8%5Cend%7Barray%7D%5Cright%5D)