Answer:
5-46i
Step-by-step explanation:
1. Multiply (10-4i) and (4-5i), I recomnd using foil:
40-50i-16+20i^2 + (-15+20i)
2. Remove the parenthesis around -15+20i
*we can do this since there is a "+":
40-50i-16+20i^2 + (-15)+20
3. Simplify i^2
* i^2 is -1 by textbook defination:
40-50i-16+20(-1) + (-15)+20
4. Simplify
40-50i-16-20 + (-15)+20
6. Combine like terms:
-5-50i-16i+20i
5-46i
And the problem is done
Answer:
(0, 1).
Method 1 (Substitution):
Substituting our two y's, we get the following:

Thus, the only set of solutions is (0, 1). A quick sketch (either by hand or on Desmos) can confirm this.
Method 2 (Elimination):
We have two equations. We'll let the top one be equation 1 and the bottom one be equation 2. Eliminating as many variables as we can, we subtract (2) from (1) to get:
0 = 3x => x = 0.
So the only set of solutions is (0, 1).
Method 3 (Gaussian elimination):
We can place this in an augmented matrix and row reduce.
![\left[\begin{array}{cccc}1&5&1 & 1\\1&2&1 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%261%20%26%201%5C%5C1%262%261%20%26%201%5Cend%7Barray%7D%5Cright%5D)
Row reducing this gives us:
![\left[\begin{array}{cccc}1&5&1 & 1\\0&3&0 & 0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%265%261%20%26%201%5C%5C0%263%260%20%26%200%5Cend%7Barray%7D%5Cright%5D)
This tells us that the only solution for x is x = 0 (since we read this as "3x = 0") and thus, the only solution we get is (0, 1).
Answer:
( -3/2 , 3)
Step-by-step explanation:
midpoint of segment: (x , y) : ((x + x') / 2 , (y + y') /2)
x = (3 + (-6)) / 2 = -3/2
y = (5 + 1) / 2 = 3
Answer:

Step-by-step explanation:

As the answer can be more simplified, divide both numerator and denominator by 5.

Answer:39
Hope it helps :)