That's true; the Law of Cosines works with all triangles. With right triangles it simplifies to the Pythagorean Theorem.
Answer:
y=1/2x+5/2
Step-by-step explanation:
expand the point-slope form and rearrange to y=mx+b
y-3=1/2(x-1)
y-3=1/2x-1/2
y=1/2x+5/2
Answer:
-4/151
Step-by-step explanation:
We can find the slope by
m = (y2-y1)/*x2-x1)
= (3.6 - 4.8)/(2.65 - -42.65)
= (3.6 - 4.8)/(2.65 +42.65)
= -1.2 / 45.3
-4/151
Answer:
Yes, it is invertible
Step-by-step explanation:
We need to find in the matrix determinant is different from zero, since iif it is, that the matrix is invertible.
Let's use co-factor expansion to find the determinant of this 4x4 matrix, using the column that has more zeroes in it as the co-factor, so we reduce the number of determinant calculations for the obtained sub-matrices.We pick the first column for that since it has three zeros!
Then the determinant of this matrix becomes:
![4\,*Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] +0+0+0](https://tex.z-dn.net/?f=4%5C%2C%2ADet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%264%266%5C%5C0%263%268%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D%20%2B0%2B0%2B0)
And the determinant of these 3x3 matrix is very simple because most of the cross multiplications render zero:
![Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] =1 \,(3\,*\,1-0)+4\,(0-0)+6\,(0-0)=3](https://tex.z-dn.net/?f=Det%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%264%266%5C%5C0%263%268%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D%20%3D1%20%5C%2C%283%5C%2C%2A%5C%2C1-0%29%2B4%5C%2C%280-0%29%2B6%5C%2C%280-0%29%3D3)
Therefore, the Det of the initial matrix is : 4 * 3 = 12
and then the matrix is invertible
Answer is D. 3000. This is because 1.2*10^3=1200 and 4*10^-1=.04 so using the equation .4x=1200 when x=300 makes the equation true.