Answer:
![\left[\begin{array}{cc}2&0\\-2&3\end{array}\right]+\left[\begin{array}{cc}1&5\\0&1\end{array}\right]=\left[\begin{array}{cc}3&5\\-2&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%260%5C%5C-2%263%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%265%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%265%5C%5C-2%264%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
If you have two matrices:
![A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\and\\B=\left[\begin{array}{cc}e&f\\g&h\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D%5C%5Cand%5C%5CB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7De%26f%5C%5Cg%26h%5Cend%7Barray%7D%5Cright%5D)
The sum of the matrices is:
![A+B=\left[\begin{array}{cc}a+e&b+f\\c+g&d+h\end{array}\right]](https://tex.z-dn.net/?f=A%2BB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%2Be%26b%2Bf%5C%5Cc%2Bg%26d%2Bh%5Cend%7Barray%7D%5Cright%5D)
In this case we have:
![A=\left[\begin{array}{cc}2&0\\-2&3\end{array}\right]\\\\\\B=\left[\begin{array}{cc}1&5\\0&1\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%260%5C%5C-2%263%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5CB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%265%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
The <u>sum</u> is:
![A+B=\left[\begin{array}{cc}2+1&0+5\\-2+0&3+1\end{array}\right]\\\\\\A+B=\left[\begin{array}{cc}3&5\\-2&4\end{array}\right]](https://tex.z-dn.net/?f=A%2BB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%2B1%260%2B5%5C%5C-2%2B0%263%2B1%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5CA%2BB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%265%5C%5C-2%264%5Cend%7Barray%7D%5Cright%5D)
The answer is:
Answer:
y + 1 = 4(x - 2)
y = 4x + 11
8x - 2y = 6
Step-by-step explanation:
Following equations are parallel to the graph 4x - y = 6, because their slopes are equal (4).
y + 1 = 4(x - 2)
y = 4x + 11
8x - 2y = 6
Answer:
B
Step-by-step explanation:
Answer:
Carter family = 25 hours
Davis family = 31 hours
Step-by-step explanation:
Let's say the number of hours the Carter family used their sprinkler is x and the number of hours the Davis family used their sprinkler for is y.
So combined:
x + y = 45 hours
and we are also told that:
40x + 15y = 1300 L
So we can do simultaneous equations to solve the problem.
With some rearranging, we can figure out that:
y= 45 - x
and by substituting that into the second equation:
40x + 15 (45 -x) = 40x + 675 - 15x = 1300L
25x = 1300 - 675
25x = 625
x = 25 = hours that the Carter family used their sprinkler
and we can substitute that back into the original equation to find how many hours the Davis family used their sprinkler so:
25 + y = 56
y = 31
The Davis family used their sprinkler for 31 hours whilst the Carter family used their sprinkler for 25 hours.
Answer:
x = 15
Step-by-step explanation:
Create a proportional relationship to solve for x
3/2 = x/10
Cross multiply
2x = 30
Divide both sides by 2
x = 15
