Answer:
3rd answer down
Step-by-step explanation:
ok so you take the median of all the #'s which turns out to be 126.5 and that is where your bar should point to in the box, then you should start with 105, and your last bit of the line should end at 150, the start of your box should start at the median of 105 and 117, and the end of your box should stop at the median of 145 and 150.
1)
![(-2+\sqrt{-5})^2\implies (-2+\sqrt{-1\cdot 5})^2\implies (-2+\sqrt{-1}\sqrt{5})^2\implies (-2+i\sqrt{5})^2 \\\\\\ (-2+i\sqrt{5})(-2+i\sqrt{5})\implies +4-2i\sqrt{5}-2i\sqrt{5}+(i\sqrt{5})^2 \\\\\\ 4-4i\sqrt{5}+[i^2(\sqrt{5})^2]\implies 4-4i\sqrt{5}+[-1\cdot 5] \\\\\\ 4-4i\sqrt{5}-5\implies -1-4i\sqrt{5}](https://tex.z-dn.net/?f=%28-2%2B%5Csqrt%7B-5%7D%29%5E2%5Cimplies%20%28-2%2B%5Csqrt%7B-1%5Ccdot%205%7D%29%5E2%5Cimplies%20%28-2%2B%5Csqrt%7B-1%7D%5Csqrt%7B5%7D%29%5E2%5Cimplies%20%28-2%2Bi%5Csqrt%7B5%7D%29%5E2%20%5C%5C%5C%5C%5C%5C%20%28-2%2Bi%5Csqrt%7B5%7D%29%28-2%2Bi%5Csqrt%7B5%7D%29%5Cimplies%20%2B4-2i%5Csqrt%7B5%7D-2i%5Csqrt%7B5%7D%2B%28i%5Csqrt%7B5%7D%29%5E2%20%5C%5C%5C%5C%5C%5C%204-4i%5Csqrt%7B5%7D%2B%5Bi%5E2%28%5Csqrt%7B5%7D%29%5E2%5D%5Cimplies%204-4i%5Csqrt%7B5%7D%2B%5B-1%5Ccdot%205%5D%20%5C%5C%5C%5C%5C%5C%204-4i%5Csqrt%7B5%7D-5%5Cimplies%20-1-4i%5Csqrt%7B5%7D)
3)
let's recall that the conjugate of any pair a + b is simply the same pair with a different sign, namely a - b and the reverse is also true, let's also recall that i² = -1.
![\cfrac{6-7i}{1-2i}\implies \stackrel{\textit{multiplying both sides by the denominator's conjugate}}{\cfrac{6-7i}{1-2i}\cdot \cfrac{1+2i}{1+2i}\implies \cfrac{(6-7i)(1+2i)}{\underset{\textit{difference of squares}}{(1-2i)(1+2i)}}} \\\\\\ \cfrac{(6-7i)(1+2i)}{1^2-(2i)^2}\implies \cfrac{6-12i-7i-14i^2}{1-(2^2i^2)}\implies \cfrac{6-19i-14(-1)}{1-[4(-1)]} \\\\\\ \cfrac{6-19i+14}{1-(-4)}\implies \cfrac{20-19i}{1+4}\implies \cfrac{20-19i}{5}\implies \cfrac{20}{5}-\cfrac{19i}{5}\implies 4-\cfrac{19i}{5}](https://tex.z-dn.net/?f=%5Ccfrac%7B6-7i%7D%7B1-2i%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20the%20denominator%27s%20conjugate%7D%7D%7B%5Ccfrac%7B6-7i%7D%7B1-2i%7D%5Ccdot%20%5Ccfrac%7B1%2B2i%7D%7B1%2B2i%7D%5Cimplies%20%5Ccfrac%7B%286-7i%29%281%2B2i%29%7D%7B%5Cunderset%7B%5Ctextit%7Bdifference%20of%20squares%7D%7D%7B%281-2i%29%281%2B2i%29%7D%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B%286-7i%29%281%2B2i%29%7D%7B1%5E2-%282i%29%5E2%7D%5Cimplies%20%5Ccfrac%7B6-12i-7i-14i%5E2%7D%7B1-%282%5E2i%5E2%29%7D%5Cimplies%20%5Ccfrac%7B6-19i-14%28-1%29%7D%7B1-%5B4%28-1%29%5D%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B6-19i%2B14%7D%7B1-%28-4%29%7D%5Cimplies%20%5Ccfrac%7B20-19i%7D%7B1%2B4%7D%5Cimplies%20%5Ccfrac%7B20-19i%7D%7B5%7D%5Cimplies%20%5Ccfrac%7B20%7D%7B5%7D-%5Ccfrac%7B19i%7D%7B5%7D%5Cimplies%204-%5Ccfrac%7B19i%7D%7B5%7D)
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
"THIS MESSAGE IS TOP SECRET."
We need to use the Caesar cipher.
As in general we always take a shift of 3 keys in Caesar cipher.
so, According to shift of 3 keys it becomes,
T→W
H→K
I→L
S→V
M→P
E→H
A→D
G→J
O→R
C→F
R→U
P→S
So, it can be written as
"THIS MESSAGE IS TOP SECRET."
WKLVP HVVDJ HLVWR SVHFU HW.
we make a set of 5 letters in a word after Caesar cypher.
Hence, Option 'a' is correct.
The answer is c 14 I think
Answer:
x = 7 ± 
Step-by-step explanation:
Given
4(x - 7)² - 48 = 12 ( add 48 to both sides )
4(x - 7)² = 60 ( divide both sides by 4 )
(x - 7)² = 15 ( take the square root of both sides )
x - 7 = ± ( add 7 to both sides )
x = 7 ±
