The mathematical expression of the given complex number above is -5 + 4i. The conjugate of this complex number is that which has an opposite operation. The given is an addition operation. That is -5 - 4i. Therefore, the answer is the third among the choices.
Answer:
![\left[\begin{array}{cccc}-12&-13&13&|15\\7&-10&-3&|11\\7&14&5&\:\:\:|-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-12%26-13%2613%26%7C15%5C%5C7%26-10%26-3%26%7C11%5C%5C7%2614%265%26%5C%3A%5C%3A%5C%3A%7C-5%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The system of equations is;
-12x-13y +13z =15
7x-10y-3z = 11
7x+14y +5z = -5
The coefficient matrix is ![\left[\begin{array}{ccc}-12&-13&13\\7&-10&-3\\7&14&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-12%26-13%2613%5C%5C7%26-10%26-3%5C%5C7%2614%265%5Cend%7Barray%7D%5Cright%5D)
The constant matrix is ![\left[\begin{array}{c}15\\11\\-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D15%5C%5C11%5C%5C-5%5Cend%7Barray%7D%5Cright%5D)
The augmented matrix is
Answer:
The correct statement is:
C. Buying a needle and buying a thread are dependent events.
Explanation:
The first statement is incorrect because the given events are dependent on each other because the probability that a customer buys a needle given that the customer buys thread is 0.25.
The second statement is incorrect because we cannot say all those who buy a thread also buy a needle.
The fourth statement is incorrect because the probability that a customer buys a needle and thread is 
Answer:nnjjj
Step-by-step explanation:
The answer is actually choice A
---------------------------------------------------------
---------------------------------------------------------
If we add up the equations straight down we will have 0a+2b = 6
Note how adding the 'a' terms gives us 3a + (-3a) = 3a-3a = 0a. The 0a term is really 0 since 0 times anything is 0. So the 'a' terms will go away
The equation 0a+2b = 6 turns into 0+2b = 6 and that simplifies to 2b = 6
To isolate b, we divide both sides by 2
2b = 6
2b/2 = 6/2
b = 3
We can stop here since only one answer choice has b = 3, which is choice A. However, let's keep going to find the value of 'a'
Plug b = 3 into any equation with 'a' and 'b', then solve for 'a'
3a+4b = 9
3a+4*3 = 9
3a+12 = 9
3a+12-12 = 9-12
3a = -3
3a/3 = -3/3
a = -1
So a = -1 and b = 3 pair up to form (a,b) = (-1,3)
--------------------------------------
To check, plug this ordered pair back into both equations
Equation 1:
3a+4b = 9
3*(-1)+4*3 = 9
-3+12 = 9
9 = 9
Equation 1 has been checked out
Equation 2:
-3a-2b = -3
-3(-1)-2(3) = -3
3 - 6 = -3
-3 = -3
this is true as well
So this confirms that the final answer is choice A
