Hey there! :)
Answer:
Point V.
Step-by-step explanation:
Given the coordinates of T at (-6.5, 1), U represents T before any reflections. (Helps to visualize this better)
Reflecting across the x-axis results in the sign of the y-coordinate changed. Point T after this reflection becomes (-6.5, -1).
Finally, reflecting across the y-axis will change the sign for the x-coordinate.
(-6.5, -1) becomes (6.5, 1). This is represented by point V.
Answer:
A: adjacent angles: The angle ∠CFD & ∠DFE are directly next to each other, making them <em>adjacent angles</em>.
B: Complementary angles: Note that m∠BFC measures at 90°. m∠BFE is a straight line, with 180°. This means that ∠BFE - ∠BFC = ∠DFE.
180 - 90 = 90 ∴ m∠DFE = 90°
~
Answer:
265 feet to the nearest foot.
Step-by-step explanation:
sin 3 = a / 5072
a = 5072 sin 3
= 265.4479 feet
Answer:
151
Step-by-step explanation:
Hello, let's note A the matrix, we need to find 
such that A= I, where I is the identity matrix, so the determinant is 0, giving us the characteristic equation as
We just need to solve this equation using the discriminant.
And then the eigenvalues are.
To find the basis, we have to solve the system of equations.
![A\lambda_1-\lambda_1 I=\left[\begin{array}{cc}3i&3\\-3&3i\end{array}\right] \\\\=3\left[\begin{array}{cc}i&1\\-1&i\end{array}\right] \\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}ai+b=0\\-a+bi=0\end{cases}\\\\\text{(1,-i) is a base of this space, as i-i=0 and -1-}i^2\text{=-1+1=0.}](https://tex.z-dn.net/?f=A%5Clambda_1-%5Clambda_1%20I%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3i%263%5C%5C-3%263i%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%3D3%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Di%261%5C%5C-1%26i%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5Ctext%7BFor%20a%20vector%20%28a%2Cb%29%2C%20we%20need%20to%20find%20a%20and%20b%20such%20that.%7D%5C%5C%5C%5C%5Cbegin%7Bcases%7Dai%2Bb%3D0%5C%5C-a%2Bbi%3D0%5Cend%7Bcases%7D%5C%5C%5C%5C%5Ctext%7B%281%2C-i%29%20is%20a%20base%20of%20this%20space%2C%20as%20i-i%3D0%20and%20-1-%7Di%5E2%5Ctext%7B%3D-1%2B1%3D0.%7D)
![A\lambda_2-\lambda_2 I=\left[\begin{array}{cc}-3i&3\\-3&-3i\end{array}\right] \\\\=3\left[\begin{array}{cc}-i&1\\-1&-i\end{array}\right]\\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}-ai+b=0\\-a-bi=0\end{cases}\\\\\text{(1,i) is a base of this space as -i+i=0 and -1-i*i=0.}](https://tex.z-dn.net/?f=A%5Clambda_2-%5Clambda_2%20I%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-3i%263%5C%5C-3%26-3i%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%3D3%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-i%261%5C%5C-1%26-i%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Ctext%7BFor%20a%20vector%20%28a%2Cb%29%2C%20we%20need%20to%20find%20a%20and%20b%20such%20that.%7D%5C%5C%5C%5C%5Cbegin%7Bcases%7D-ai%2Bb%3D0%5C%5C-a-bi%3D0%5Cend%7Bcases%7D%5C%5C%5C%5C%5Ctext%7B%281%2Ci%29%20is%20a%20base%20of%20this%20space%20as%20-i%2Bi%3D0%20and%20-1-i%2Ai%3D0.%7D)
Thank you
