Answer:
![AB\Rightarrow \quad \begin{bmatrix}0 & 9\\ 5 & 13\end{bmatrix}\\BA\Rightarrow \quad \begin{bmatrix}15 & 15\\ 1 & -2\end{bmatrix}](https://tex.z-dn.net/?f=AB%5CRightarrow%20%5Cquad%20%5Cbegin%7Bbmatrix%7D0%20%26%209%5C%5C%205%20%26%2013%5Cend%7Bbmatrix%7D%5C%5CBA%5CRightarrow%20%5Cquad%20%5Cbegin%7Bbmatrix%7D15%20%26%2015%5C%5C%201%20%26%20-2%5Cend%7Bbmatrix%7D)
Step-by-step explanation:
For two matrix P and Q, the product, say PQ is defined when:
The number of columns of P = The number of rows of Q
Since A is a 2×2 matrix and B is also a 2×2 matrix
Thus both AB and BA are possible.
So AB is:
![AB\Rightarrow\begin{bmatrix}1 & 3\\ 2 & 1\end{bmatrix}\begin{bmatrix}3 & 6\\ -1 & 1\end{bmatrix}\\AB\Rightarrow\quad \begin{bmatrix}3\times 1+3\times (-1) & 6\times 1+3\times 1\\3\times 2+1\times (-1) & 6\times 2+1\times 1\end{bmatrix}\\AB\Rightarrow \quad \begin{bmatrix}0 & 9\\ 5 & 13\end{bmatrix}](https://tex.z-dn.net/?f=AB%5CRightarrow%5Cbegin%7Bbmatrix%7D1%20%26%203%5C%5C%202%20%26%201%5Cend%7Bbmatrix%7D%5Cbegin%7Bbmatrix%7D3%20%26%206%5C%5C%20-1%20%26%201%5Cend%7Bbmatrix%7D%5C%5CAB%5CRightarrow%5Cquad%20%5Cbegin%7Bbmatrix%7D3%5Ctimes%201%2B3%5Ctimes%20%28-1%29%20%26%206%5Ctimes%201%2B3%5Ctimes%201%5C%5C3%5Ctimes%202%2B1%5Ctimes%20%28-1%29%20%26%206%5Ctimes%202%2B1%5Ctimes%201%5Cend%7Bbmatrix%7D%5C%5CAB%5CRightarrow%20%5Cquad%20%5Cbegin%7Bbmatrix%7D0%20%26%209%5C%5C%205%20%26%2013%5Cend%7Bbmatrix%7D)
BA is:
![BA\Rightarrow\begin{bmatrix}3 & 6\\ -1 & 1\end{bmatrix}\begin{bmatrix}1 & 3\\ 2 & 1\end{bmatrix}\\BA\Rightarrow\quad \begin{bmatrix}3\times 1+6\times 2 & 3\times 3+6\times 1\\(-1)\times 1+1\times 2 & (-1)\times 3+1\times 1\end{bmatrix}\\BA\Rightarrow \quad \begin{bmatrix}15 & 15\\ 1 & -2\end{bmatrix}](https://tex.z-dn.net/?f=BA%5CRightarrow%5Cbegin%7Bbmatrix%7D3%20%26%206%5C%5C%20-1%20%26%201%5Cend%7Bbmatrix%7D%5Cbegin%7Bbmatrix%7D1%20%26%203%5C%5C%202%20%26%201%5Cend%7Bbmatrix%7D%5C%5CBA%5CRightarrow%5Cquad%20%5Cbegin%7Bbmatrix%7D3%5Ctimes%201%2B6%5Ctimes%202%20%26%203%5Ctimes%203%2B6%5Ctimes%201%5C%5C%28-1%29%5Ctimes%201%2B1%5Ctimes%202%20%26%20%28-1%29%5Ctimes%203%2B1%5Ctimes%201%5Cend%7Bbmatrix%7D%5C%5CBA%5CRightarrow%20%5Cquad%20%5Cbegin%7Bbmatrix%7D15%20%26%2015%5C%5C%201%20%26%20-2%5Cend%7Bbmatrix%7D)
$825.61 - It is 37.07 per gram
Answer:
5
Step-by-step explanation:
first, change the fractions to decimals (.7 and 3.5)
then, divide .7 by 3.5 to get 5
3.5 ÷ .7 = 5
Answer:
Trent has 6 quarters and 5 dimes.
Step-by-step explanation:
Consider the provided information.
Let q = Number of quarters
d = Number of dimes.
Trent has 11 quarters and dimes.
![q+d=11](https://tex.z-dn.net/?f=q%2Bd%3D11)
![q=11-d](https://tex.z-dn.net/?f=q%3D11-d)
The worth of a quarter is 25 cents.
The worth of a dimes is 10 cents
![25q+10d=200](https://tex.z-dn.net/?f=25q%2B10d%3D200)
Substitute the value of q in above equation.
![25(11-d)+10d=200](https://tex.z-dn.net/?f=25%2811-d%29%2B10d%3D200)
![275-25d+10d=200](https://tex.z-dn.net/?f=275-25d%2B10d%3D200)
Substitute the value of d in ![q=11-d](https://tex.z-dn.net/?f=q%3D11-d)
![q=11-5](https://tex.z-dn.net/?f=q%3D11-5)
![q=6](https://tex.z-dn.net/?f=q%3D6)
Hence, Trent has 6 quarters and 5 dimes.
Answer:
Step-by-step explanation:
Anything from the center to the edge is the radius. It is one half of what it measures in diameter.