Answer:
Step-by-step explanation:
Any linear equation can be written as y = mx + b
The point will determine b
The slope (m) is found by this formula for a perpendicular line
m1 * m2 = - 1
m1 = -1/m2
m1 = -1/(-2/3)
m1 = 3/2
So our equation looks like
y = 3/2 x + b
Now we use the point (4,-8)
-8 = 3/2 (4) + b
-8 = 3(2) + b
-8 = 6 + b
b = - 14
The answer is
y = 4/2 - 14
The graph is wrong, the slope is correct but because the sign is less than y that means the line on the graph should be dotted not solid.
Create a right triangle with the the two legs being sides of 9 and 12...then use the Pythagorean theorem to solve
a^2 + b^2 = c^2
9^2 + 12^2 = c^2
81 + 144 = c^2
225 = c^2
Square root both sides to get c = 15 feet.
Answer:
The augmented matrix for each set of linear equations is:
a) 
Augmented matrix:
![\left[\begin{array}{ccc}1&-2&0\\3&4&-1\\2&-1&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-2%260%5C%5C3%264%26-1%5C%5C2%26-1%263%5Cend%7Barray%7D%5Cright%5D)
b) 
Augmented matrix:
![\left[\begin{array}{cccc}1&0&1&1\\-1&2&-1&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%261%261%5C%5C-1%262%26-1%263%5Cend%7Barray%7D%5Cright%5D)
c) 
Augmented matrix:
![\left[\begin{array}{cccccc}1&0&1&0&0&1\\0&2&-1&0&1&2\\0&0&2&1&0&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccccc%7D1%260%261%260%260%261%5C%5C0%262%26-1%260%261%262%5C%5C0%260%262%261%260%263%5Cend%7Barray%7D%5Cright%5D)
d) 
Augmented matrix:
![\left[\begin{array}{ccc}1&0&1\\0&1&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%261%5C%5C0%261%262%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
In order to find the augmented matrix, you have to take the numeric values of each variable and make a matrix with them. For example, in the linear system a) you can make a matrix out of the numeric values accompanying x_1 and x_2, this matrix will be:
![\left[\begin{array}{cc}1&-2\\3&4\\2&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C3%264%5C%5C2%26-1%5Cend%7Barray%7D%5Cright%5D)
Then you have to make a vector with the constants in the linear equations, for the case of system a) the vector will be:
![\left[\begin{array}{c}0&-1&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%26-1%263%5Cend%7Barray%7D%5Cright%5D)
To construct the augmented matrix, you append those matrices together and create a new one:
Answer:
not sure but i think its 29.58 let me know if im right good luck
Step-by-step explanation:
