Answer:
100, because 180 - 50 - 90 = 40
The vertical angles theorem is applied, so now angle DCE is 40
And since CE = ED, its isosceles triangle, so base angles are equal, so 40 and 40.
180 - 80 = 100 = Angle E.
Answer:
![\left[\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%260%260%5C%5C0%263%260%5C%5C0%260%263%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
In order to find out the resulting matrix, we will have to multiply the identity matric and the scalar 3:
The 3x3 identity matrix is:
![\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D)
Multiplying with scalar 3:
![3\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]](https://tex.z-dn.net/?f=3%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D)
The scalar will be multiplied by each element of the matrix.
Multiplying zeros with scalar 3 will give us zero. So the resulting matrix will be:
![\left[\begin{array}{ccc}3*1&0&0\\0&3*1&0\\0&0&3*1\end{array}\right] = \left[\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%2A1%260%260%5C%5C0%263%2A1%260%5C%5C0%260%263%2A1%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%260%260%5C%5C0%263%260%5C%5C0%260%263%5Cend%7Barray%7D%5Cright%5D)
So the resultant matrix will be a scalar matrix with 3 at diagonal positions..
a) -3g +35
b)-12m+6
The solution is on the picture
The average has to be at least 120 and at most 130
To calculate the average we need the sum of all values divided by the number of values, in this case, three (135, 145 and the third result).
120 ≤ (135 + 145 + n)/3 ≤ 130
In inequalities like this, what we change in one side, must be changed in the othe rside as well.
360 ≤ 280 + n ≤ 390
80 ≤ n ≤ 110