Answer:
1400
Step-by-step explanation:
it will be easier to first do 30 times 60, which is 180, then subtract the parts
the left up part is 100, the left bottom is 150, the top right is 150, added together, is 400
1800-400
<em>Answer:</em>
<em>The right side of the equation is only a different way of writing the left side, so any value of x will solve this equation.
</em>
<em>
</em>
<em>The equation −
2
( x + 3 ) = −
2
x − 6 does not have any specific solutions for the simple reason that the left and rigth sides are two representations of the same equation.
</em>
<em>
We have −
2
( x + 3 ) means that each term inside the parenthesis should be multiplied with −
2
, i.e.</em>
<em>
−
2
( x + 3
) = −
2 ⋅ x − 2 ⋅ ( + 3
) = −
2
x − 6
</em>
<em>
</em>
<em>Which is exactly what the right side says.
</em>
<em>
</em>
<em>Any value of x will, therefore, fulfill this equation.</em>
The coefficient matrix is build with its rows representing each equation, and its columns representing each variable.
So, you may write the matrix as
![\left[\begin{array}{cc}\text{x-coefficient, 1st equation}&\text{y-coefficient, 1st equation}\\\text{x-coefficient, 2nd equation}&\text{y-coefficient, 2nd equation} \end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Ctext%7Bx-coefficient%2C%201st%20equation%7D%26%5Ctext%7By-coefficient%2C%201st%20equation%7D%5C%5C%5Ctext%7Bx-coefficient%2C%202nd%20equation%7D%26%5Ctext%7By-coefficient%2C%202nd%20equation%7D%20%5Cend%7Barray%7D%5Cright%5D%20%20)
which means
![\left[\begin{array}{cc}4&-3\\8&-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-3%5C%5C8%26-3%5Cend%7Barray%7D%5Cright%5D%20%20)
The determinant is computed subtracting diagonals:
![\left | \left[ \begin{array}{cc}a&b\\c&d\end{array}\right]\right | = ad-bc](https://tex.z-dn.net/?f=%20%5Cleft%20%7C%20%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D%5Cright%20%7C%20%3D%20ad-bc%20)
So, we have
![\left | \left[\begin{array}{cc}4&-3\\8&-3\end{array}\right] \right | = 4(-3) - 8(-3) = -4(-3) = 12](https://tex.z-dn.net/?f=%20%5Cleft%20%7C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-3%5C%5C8%26-3%5Cend%7Barray%7D%5Cright%5D%20%5Cright%20%7C%20%3D%204%28-3%29%20-%208%28-3%29%20%3D%20-4%28-3%29%20%3D%2012%20%20)
25 miles and 5 miles because you only multiply two sides to find the area 25•5=125
