Answer:
32
Step-by-step explanation:
1/3x96= 31.999
Answer:
![=\begin{pmatrix}-5&6\\ 1&-4\end{pmatrix}](https://tex.z-dn.net/?f=%3D%5Cbegin%7Bpmatrix%7D-5%266%5C%5C%201%26-4%5Cend%7Bpmatrix%7D)
Step-by-step explanation:
![\begin{pmatrix}-3&4\\2&-5\end{pmatrix}\begin{pmatrix}3&-2\\ 1&0\end{pmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bpmatrix%7D-3%264%5C%5C2%26-5%5Cend%7Bpmatrix%7D%5Cbegin%7Bpmatrix%7D3%26-2%5C%5C%201%260%5Cend%7Bpmatrix%7D)
Multiply the row of the first matrix to the column of the second matrix
![\begin{pmatrix}-3&4\end{pmatrix}\begin{pmatrix}3\\ 1\end{pmatrix}=\left(-3\right)\cdot \:3+4\cdot \:1](https://tex.z-dn.net/?f=%5Cbegin%7Bpmatrix%7D-3%264%5Cend%7Bpmatrix%7D%5Cbegin%7Bpmatrix%7D3%5C%5C%201%5Cend%7Bpmatrix%7D%3D%5Cleft%28-3%5Cright%29%5Ccdot%20%5C%3A3%2B4%5Ccdot%20%5C%3A1)
![\begin{pmatrix}-3&4\end{pmatrix}\begin{pmatrix}-2\\ 0\end{pmatrix}=\left(-3\right)\left(-2\right)+4\cdot \:0](https://tex.z-dn.net/?f=%5Cbegin%7Bpmatrix%7D-3%264%5Cend%7Bpmatrix%7D%5Cbegin%7Bpmatrix%7D-2%5C%5C%200%5Cend%7Bpmatrix%7D%3D%5Cleft%28-3%5Cright%29%5Cleft%28-2%5Cright%29%2B4%5Ccdot%20%5C%3A0)
![\begin{pmatrix}2&-5\end{pmatrix}\begin{pmatrix}3\\ 1\end{pmatrix}=2\cdot \:3+\left(-5\right)\cdot \:1\](https://tex.z-dn.net/?f=%5Cbegin%7Bpmatrix%7D2%26-5%5Cend%7Bpmatrix%7D%5Cbegin%7Bpmatrix%7D3%5C%5C%201%5Cend%7Bpmatrix%7D%3D2%5Ccdot%20%5C%3A3%2B%5Cleft%28-5%5Cright%29%5Ccdot%20%5C%3A1%5C)
![\begin{pmatrix}2&-5\end{pmatrix}\begin{pmatrix}-2\\ 0\end{pmatrix}=2\left(-2\right)+\left(-5\right)\cdot \:0\](https://tex.z-dn.net/?f=%5Cbegin%7Bpmatrix%7D2%26-5%5Cend%7Bpmatrix%7D%5Cbegin%7Bpmatrix%7D-2%5C%5C%200%5Cend%7Bpmatrix%7D%3D2%5Cleft%28-2%5Cright%29%2B%5Cleft%28-5%5Cright%29%5Ccdot%20%5C%3A0%5C)
![=\begin{pmatrix}\left(-3\right)\cdot \:3+4\cdot \:1&\left(-3\right)\left(-2\right)+4\cdot \:0\\ 2\cdot \:3+\left(-5\right)\cdot \:1&2\left(-2\right)+\left(-5\right)\cdot \:0\end{pmatrix}](https://tex.z-dn.net/?f=%3D%5Cbegin%7Bpmatrix%7D%5Cleft%28-3%5Cright%29%5Ccdot%20%5C%3A3%2B4%5Ccdot%20%5C%3A1%26%5Cleft%28-3%5Cright%29%5Cleft%28-2%5Cright%29%2B4%5Ccdot%20%5C%3A0%5C%5C%202%5Ccdot%20%5C%3A3%2B%5Cleft%28-5%5Cright%29%5Ccdot%20%5C%3A1%262%5Cleft%28-2%5Cright%29%2B%5Cleft%28-5%5Cright%29%5Ccdot%20%5C%3A0%5Cend%7Bpmatrix%7D)
simplifying them we get
![=\begin{pmatrix}-5&6\\ 1&-4\end{pmatrix}](https://tex.z-dn.net/?f=%3D%5Cbegin%7Bpmatrix%7D-5%266%5C%5C%201%26-4%5Cend%7Bpmatrix%7D)
Answer as a compound inequality: ![-4 \le y < 2](https://tex.z-dn.net/?f=-4%20%5Cle%20y%20%3C%202)
Answer in interval notation: [-4, 2)
=============================================
Explanation:
The range is the set of all possible y outputs of a function. When dealing with a graph like this, we just look at the highest and lowest points to determine which y values are possible.
The lowest point occurs when y = -4. We include this value. So far we have
which is the same as ![-4 \le y](https://tex.z-dn.net/?f=-4%20%5Cle%20y)
The upper ceiling for the y value is y = 2. We can't actually reach this value because of the open hole at (-3,2). So we say that ![y < 2](https://tex.z-dn.net/?f=y%20%3C%202)
Combine
and
to get the compound inequality ![-4 \le y < 2](https://tex.z-dn.net/?f=-4%20%5Cle%20y%20%3C%202)
This says y is between -4 and 2, including -4 but excluding 2.
To convert this to interval notation, we write [-4, 2) where the square bracket says to include the endpoint and the curved parenthesis says to exclude the endpoint.
Solution
Part 3
For this case we have 6 different terms
Part 4
We can do the following:
![5a^2+a^2+6b-3b+4c-2](https://tex.z-dn.net/?f=5a%5E2%2Ba%5E2%2B6b-3b%2B4c-2)
Part 5
And we can simplify on this way:
![6a^2+3b+4c-2](https://tex.z-dn.net/?f=6a%5E2%2B3b%2B4c-2)