Answer:
30
Step-by-step explanation:
To find the determinant of a parallelogram given points (a, b), (c, d), and (e, f), we can use
![\left[\begin{array}{ccc}a&b&1\\c&d&1\\e&f&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%261%5C%5Cc%26d%261%5C%5Ce%26f%261%5Cend%7Barray%7D%5Cright%5D)
and calculate the determinant of that. Three points on the parallelogram are (-1,1), (-1, -5), and (4, 5). Plugging these into the matrix, we get
![\left[\begin{array}{ccc}-1&1&1\\-1&-5&1\\4&5&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%261%261%5C%5C-1%26-5%261%5C%5C4%265%261%5Cend%7Barray%7D%5Cright%5D)
. The determinant is equal to
![-1 *det \left[\begin{array}{ccc}-5&1\\5&1\end{array}\right] \\- 1 * det \left[\begin{array}{ccc}-1&1\\4&1\end{array}\right] \\\\+ 1 * det \left[\begin{array}{ccc}-1&-5\\4&5\end{array}\right] \\= -1 * (-5*1 - (1*5))- 1 * (-1 * 1 - (4*1)) + 1 * (-1 * 5 - (-5*4)) \\= -1 *(-5-5) -1 * (-1 - 4) + 1 * (-5 - (-20))\\= -1 * (-10) -1 * (-5) +1 * (15)\\= 10 + 5 + 15\\=30](https://tex.z-dn.net/?f=-1%20%2Adet%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%261%5C%5C5%261%5Cend%7Barray%7D%5Cright%5D%20%5C%5C-%201%20%2A%20det%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%261%5C%5C4%261%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%2B%201%20%2A%20det%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-5%5C%5C4%265%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D%20-1%20%2A%20%28-5%2A1%20-%20%281%2A5%29%29-%201%20%2A%20%28-1%20%2A%201%20-%20%284%2A1%29%29%20%2B%201%20%2A%20%28-1%20%2A%205%20-%20%28-5%2A4%29%29%20%5C%5C%3D%20-1%20%2A%28-5-5%29%20-1%20%2A%20%28-1%20-%204%29%20%2B%201%20%2A%20%28-5%20-%20%28-20%29%29%5C%5C%3D%20-1%20%2A%20%28-10%29%20-1%20%2A%20%28-5%29%20%2B1%20%2A%20%2815%29%5C%5C%3D%2010%20%2B%205%20%2B%2015%5C%5C%3D30)
Answer:
-2
Step-by-step explanation:
x + 3 = 2x + 5
-2 = x
D
Radius of the circle is the length of rectangle divided by 2 (7cm)
Area of circle: pi*r²
Pi= 22/7
(22/7)*7²
=154
Since its a half circle, divide 154 by 2 =77
Area of rectangle:14*9=126
Subtract the circle from the rectangle: 126-77=49
Answer:
100 per deposit
Step-by-step explanation:
