Answer:
non-linear
Step-by-step explanation:
sorry if its wrong
Answer:
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. Businesses use inequalities to control inventory, plan production lines, produce pricing models, and for shipping/warehousing goods and materials.
Step-by-step explanation:
Here's an example of a real world problem that's using inequalities.
Virena's Scout troop is trying to raise at least $650 this spring. How many boxes of cookies must they sell at $4.50 per box in order to reach their goal?
Let x = number of boxes sold. Then the inequality describing this problem is 4.50 ≥ 650.
We solve the inequality by dividing both sides by 4.50: x ≥ 144.44.
We round up the answer to 145 since only whole boxes can be sold.
Virena's troop must sell at least 145 boxes.
Then you should Check to make sure its correct:
If we multiply 145 by $4.50 we obtain $652.50, so if Virena's troop sells more than 145 boxes they will raise more than $650. But if they sell 144 boxes, they will only raise $648, which is not enough. So they must indeed sell at least 145 boxes. The answer checks out.
Try drawing the triangles: the original and the dilated one.
If the tangent of x is 4/3, and then all lengths of the original triangle are doubled, then the tangent of x is 8/6 = 4/3. Thus, B is the correct answer.
Write the equations in matrix,
![\left[\begin{array}{ccc}5&-1&1\\1&2&-1\\2&3&-3\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C1%262%26-1%5C%5C2%263%26-3%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using row transformation,
R₂ <---> R₃
![\left[\begin{array}{ccc}5&-1&1\\2&3&-3\\1&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C2%263%26-3%5C%5C1%262%26-1%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using,
R₂ ---> R₂ - 2R₃
![\left[\begin{array}{ccc}5&-1&1\\0&-1&-1\\1&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\-5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%26-1%26-1%5C%5C1%262%26-1%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C-5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using,
R₂ --- > (-1)R₂
![\left[\begin{array}{ccc}5&-1&1\\0&1&1\\1&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%261%261%5C%5C1%262%26-1%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using row transformation,
R₂ <----> R₃
![\left[\begin{array}{ccc}5&-1&1\\1&2&-1\\0&1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C1%262%26-1%5C%5C0%261%261%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using,
R₂ ---> R₂ - R₁/5
![\left[\begin{array}{ccc}5&-1&1\\0&11/5&-6/5\\0&1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\21/5\\5\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%2611%2F5%26-6%2F5%5C%5C0%261%261%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C21%2F5%5C%5C5%5Cend%7Barray%7D%5Cright%5D%20)
Using,
R₃ ---> R₃ - 5R₂/11
![\left[\begin{array}{ccc}5&-1&1\\0&11/5&-6/5\\0&0&17/11\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\21/5\\34/11\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%2611%2F5%26-6%2F5%5C%5C0%260%2617%2F11%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C21%2F5%5C%5C34%2F11%5Cend%7Barray%7D%5Cright%5D%20)
∴ 5x-y+z = 4 ====(i)
11y-6z = 21 === (ii)
17z=34 === (iii)
from iii,
z=2.
Plug z=2 in ii to get y,
∴y=3.
Plug y and z values in i to get x,
∴x=1
Therefore the solution to the system of equations is (1,3,2)
We know how we got 90, since a right angle is 90 degrees,
180 degrees are in a triangle.
180-90=90
Find the pair that equals 90 so you get 180 degrees!
If you have more questions don’t have hesitation to ask!
Or add all number to get 180 degrees!
