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nika2105 [10]
3 years ago
13

Х If 5.3 = 12, what is the value of x? 8 0 ООО 18 o 24

Mathematics
1 answer:
gladu [14]3 years ago
8 0

Answer:18

Step-by-step explanation:

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Rationalize the denominator of sqrt -49 over (7 - 2i) - (4 + 9i)
zubka84 [21]
\sqrt{ \frac{-49}{(7-2i)-(4+9i) } } 


This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:

\frac{ \sqrt{-49}}{7-2i-4-9i}

See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result: 

\frac{ \sqrt{-49} }{3-11i}

Now, the \sqrt{-49} must be respresented as an imaginary number, and using the multiplication of radicals, we can simplify it to \sqrt{49}  \sqrt{-1}
This means that we get the result 7i for the numerator.

\frac{7i}{3-11i}

In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely: x^2 - y^2 =(x+y)(x-y)
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.

\frac{7i (3+11i)}{(3-11i)(3+11i)}

See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how (3-11i)(3+11i)= 3^2 -(11i)^2 therefore, we can finally write:

\frac{7i(3+11i)}{3^2 - (11i)^2 }

I'll let you take it from here, all you have to do is simplify it further.
The simplification is quite straightforward, the numerator distributed the 7i. Namely the product 7i(3+11i) = 21i+77i^2.
You should know from your classes that i^2 = -1, thefore the numerator simplifies to -77+21i
You can do it as a curious thing, but simplifying yields the result:
\frac{-77+21i}{130}
7 0
3 years ago
Help please help me
BARSIC [14]

Step-by-step explanation:

if you're looking for x

x=180-42-51= 87°

and if you're looking for D

D= 180-42= 138°

7 0
3 years ago
What does the number 3.1968e+22 mean?
sattari [20]
You add them and then it would be 30.6898033492
8 0
3 years ago
The cost of three dozen of eggs at thirty pesos per dozen in numerical expression<br>​
evablogger [386]
3 x 30

It cost 30 pesos per dozen and they are buying 3 dozen

3 x 30 = 90
4 0
3 years ago
Graph the line with this equation y = x + 4​
zhannawk [14.2K]

Answer:

Step-by-step explanation:

5 0
3 years ago
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