ANSWER
![{i}^{31} = - i](https://tex.z-dn.net/?f=%20%7Bi%7D%5E%7B31%7D%20%20%3D%20%20-%20i)
EXPLANATION
We want to evaluate
![{i}^{31}](https://tex.z-dn.net/?f=%20%7Bi%7D%5E%7B31%7D%20)
Use indices to rewrite the expression as:
![= {i}^{30} \times i](https://tex.z-dn.net/?f=%20%3D%20%20%7Bi%7D%5E%7B30%7D%20%20%5Ctimes%20i)
We know that
![{i}^{2} = - 1](https://tex.z-dn.net/?f=%20%7Bi%7D%5E%7B2%7D%20%20%3D%20%20-%201)
So we rewrite the expression to obtain;
![= ({ {i}^{2}) }^{15} \times i](https://tex.z-dn.net/?f=%20%3D%20%20%28%7B%20%7Bi%7D%5E%7B2%7D%29%20%7D%5E%7B15%7D%20%20%5Ctimes%20i)
This gives us;
![= {( - 1) }^{15} \times i](https://tex.z-dn.net/?f=%3D%20%20%20%7B%28%20-%201%29%20%7D%5E%7B15%7D%20%20%5Ctimes%20i)
This simplifies to
![= - 1 \times i](https://tex.z-dn.net/?f=%20%3D%20%20-%201%20%5Ctimes%20i)
![= - i](https://tex.z-dn.net/?f=%20%3D%20%20-%20i)
The steps of the solution into order to solve for x in the equation 6(x-5) = 54 are:
- A. 6x – 30 = 54
- B. 6x = 84
- D. x = 14
Given the expression 6(x-5) = 54
Expand the expression in parenthesis using the distributive law;
6x - 6(5) = 54
6x - 30 = 54
Add 30 to both sides
6x - 30 + 30 = 54 + 30
6x = 84
Divide both sides by 6
6x/6 = 84/6
x = 14
Therefore the steps of the solution into order to solve for x in the equation 6(x-5) = 54 are:
- A. 6x – 30 = 54
- B. 6x = 84
- D. x = 14
Learn more on equations here; brainly.com/question/2972832
Answer:
<h2>y = 4</h2>
Step-by-step explanation:
Put x = 9 to the equation 3x + 4y = 43
(3)(9) + 4y = 43
27 + 4y = 43 <em>subtract 27 from both sides</em>
4y = 16 <em>divide both sides by 4</em>
y = 4
R= 18
d=r(2)
36=r(2)
36/2=r(2)/2
18=r