Y = 40 when x = 16, so 40 = k/16
Therefore, k = 640
So, y = 640/x
Answer:
x=-7, y=2
Step-by-step explanation:
You are given the matrix equation
![\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right] \cdot \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-18\\13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-2%5C%5C-1%263%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-18%5C%5C13%5Cend%7Barray%7D%5Cright%5D)
Find the inverse matrix for the matrix
![\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-2%5C%5C-1%263%5Cend%7Barray%7D%5Cright%5D)
1. The determinant is
![\left|\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right]\right|=2\cdot 3-(-1)\cdot (-2)=6-2=4](https://tex.z-dn.net/?f=%5Cleft%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-2%5C%5C-1%263%5Cend%7Barray%7D%5Cright%5D%5Cright%7C%3D2%5Ccdot%203-%28-1%29%5Ccdot%20%28-2%29%3D6-2%3D4)
2.
3. Inverse matrix is
![\dfrac{1}{4}\left[\begin{array}{cc}3&1\\2&2\end{array}\right]^T=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%261%5C%5C2%262%5Cend%7Barray%7D%5Cright%5D%5ET%3D%5Cdfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%262%5C%5C1%262%5Cend%7Barray%7D%5Cright%5D)
So, the solution of the equation is
![\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right]\cdot \left[\begin{array}{c}-18\\13\end{array}\right]=\\ \\=\dfrac{1}{4}\left[\begin{array}{cc}3\cdot(-18)+2\cdot 13\\1\cdot (-18)+2\cdot 13\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{c}-28\\8\end{array}\right]=\left[\begin{array}{c}-7\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%5Cdfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%262%5C%5C1%262%5Cend%7Barray%7D%5Cright%5D%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-18%5C%5C13%5Cend%7Barray%7D%5Cright%5D%3D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%5Ccdot%28-18%29%2B2%5Ccdot%2013%5C%5C1%5Ccdot%20%28-18%29%2B2%5Ccdot%2013%5Cend%7Barray%7D%5Cright%5D%3D%5Cdfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-28%5C%5C8%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-7%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
1/6(12z-18)=2z-3
12/6z-18/6 =2z-3
2z-3=2z-3
there are infinite solutions for this equation or all real numbers
Answer:
Carla's suitcase was a better purchase.
Step-by-step explanation:
The complete question is:
Carla and Daniel bought identical suitcases at different stores. Carla's suitcase originally cost $75 and was discounted 19% Daniel's suitcase original cost $85 and was on sale for 20% off the original price. Which suitcase was the cheaper?
Solution:
Cost Price of Carla's suitcase = $75
Discount% for Carla = 19%
The amount paid by Carla is,
So, the amount paid by Carla was, $60.75.
Cost Price of Jeana's suitcase = $85
Discount% for Jeana = 20%
The amount paid by Jeana is,
So, the amount paid by Jeana was, $68.
Carla's suitcase was a better purchase.
30043——————3.0043 x 10^4
30.043—————— 3.0043 x10^1
0.0030043—————-3.0043 x 10^-3
0.30043—————-3.0043 x 10^-1
3.0043————-3.0043 x 10^0
Hope this helps please mark brainiest
