Answer:
z = 2
Step-by-step explanation:
Given equations are
x - 2y - z = 2
x + 3y - 2z = 4
-x + 2y + 3z = 2
from the given equations the augmented matrix can be written as
![\left[\begin{array}{ccc}1&-2&-1:2\\1&3&-2:4\\-1&2&3:2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-2%26-1%3A2%5C%5C1%263%26-2%3A4%5C%5C-1%262%263%3A2%5Cend%7Barray%7D%5Cright%5D)
![=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&5&-1:2\\0&0&2:4\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-2%26-1%3A2%5C%5C0%265%26-1%3A2%5C%5C0%260%262%3A4%5Cend%7Barray%7D%5Cright%5D)
![=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\0&0&2:4\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-2%26-1%3A2%5C%5C0%261%26%5Cdfrac%7B-1%7D%7B5%7D%3A%5Cdfrac%7B2%7D%7B5%7D%5C%5C0%260%262%3A4%5Cend%7Barray%7D%5Cright%5D)
![=\ \left[\begin{array}{ccc}1&0&-1-\dfrac{2}{5}:2+\dfrac{4}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-1-%5Cdfrac%7B2%7D%7B5%7D%3A2%2B%5Cdfrac%7B4%7D%7B5%7D%5C%5C%5C%5C0%261%26%5Cdfrac%7B-1%7D%7B5%7D%3A%5Cdfrac%7B2%7D%7B5%7D%5C%5C%5C%5C0%260%262%3A4%5Cend%7Barray%7D%5Cright%5D)
![=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26%5Cdfrac%7B-7%7D%7B5%7D%3A%5Cdfrac%7B14%7D%7B5%7D%5C%5C%5C%5C0%261%26%5Cdfrac%7B-1%7D%7B5%7D%3A%5Cdfrac%7B2%7D%7B5%7D%5C%5C%5C%5C0%260%262%3A4%5Cend%7Barray%7D%5Cright%5D)
![=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&1:2\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26%5Cdfrac%7B-7%7D%7B5%7D%3A%5Cdfrac%7B14%7D%7B5%7D%5C%5C%5C%5C0%261%26%5Cdfrac%7B-1%7D%7B5%7D%3A%5Cdfrac%7B2%7D%7B5%7D%5C%5C%5C%5C0%260%261%3A2%5Cend%7Barray%7D%5Cright%5D)
![=\ \left[\begin{array}{ccc}1&0&0:\dfrac{14}{5}+\dfrac{7}{5}\\\\0&1&0:\dfrac{2}{5}+\dfrac{1}{5}\\\\0&0&1:2\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%3A%5Cdfrac%7B14%7D%7B5%7D%2B%5Cdfrac%7B7%7D%7B5%7D%5C%5C%5C%5C0%261%260%3A%5Cdfrac%7B2%7D%7B5%7D%2B%5Cdfrac%7B1%7D%7B5%7D%5C%5C%5C%5C0%260%261%3A2%5Cend%7Barray%7D%5Cright%5D)
So, from the above augmented matrix, we can write
z = 2
any of the 34 cars can finish first
any of the remaining 33 cars can finish second
any of the remaining 32 cars can finish third
Thus, the top 3 finishes can be done in (34)(33)(32) = 35904 ways
To find the correct polynomial, we can use the answers to help us out. The middle variable must be the sum of +2 and another number; the last number in the equation must be the product of +2 and the other number.
Knowing this information, we can use the process of elimination to find the exact polynomial that contains the factor (3x + 2).
A) This can't be it because to get -x as the middle variable, you would need to add -3 and +2. However, -3 x +2 doesn't equal -4.
B) This equation isn't the right one because to get +8 you need to add +6 + 2. However, the product of these two isn't -8.
C) Can't be correct because +2 and -7 = -5, but 2 x -7 = -14...not -9.
D) Is the correct answer because you can add 2 and -1 to get +1. (There is an understood +1 in front of the x in the equation.) The product of 2 and -1 equals -2, which happens to be the last number inside this equation. Therefore, this (D) is the correct answer choice.
Hope I could help you out! If my math is incorrect, or I didn't provide the answer you were looking for, please let me know. However, if the answer was correct and well explained, please consider marking it <em>Brainliest</em>.
Have a good one!
God bless.
Answer:
(B)-16+40
Step-by-step explanation: -8(2x-5)
-8*2=-16
-8*-5=40(positive because a negative multiplied by a negative is postive)
add the x to the answers...Then its -16x+40
Hope This Helps:)
Answer=24.49 I’m not 100% sure but I believe this is the answer :)
Hope it helps
