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slega [8]
2 years ago
7

Which expression is equivalent to i 233? 1 –1 i –i

Mathematics
1 answer:
worty [1.4K]2 years ago
7 0

Step-by-step explanation:

i¹ = i

i² = i×i = -1

i³ = -1 × i = -i

i⁴ = -i×i = - -1 = 1

i⁵ = 1×i = i

...

so, when the exponent of i modulo 4 (the remainder when dividing by 4) = 0, then the result is 1.

= 1, then the result is i

= 2, then the result is -1

= 3, then the result is -i

233 modulo 4 = 1 (233/4 = 58, remainder 1).

so, the result is i (the third answer option).

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Two brothers have a total age of 28 if one brother is older by 20 years how old is the second brother
svlad2 [7]

Answer:

8

Step-by-step explanation:

Total meaning addition, you would use the opposite operation to find the answer.  

28 - 20 = 8

And to check your work you would add;

20 + 8 = 28

which is the brothers total combined age.  

6 0
3 years ago
Read 2 more answers
Which expression shows (45 + 15) in the form a(b+c) where a is the greatest common factor
4vir4ik [10]

Answer:

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Step-by-step explanation:

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4 0
2 years ago
Please can someone help thank you
aleksley [76]

Answer:

3:1

Step-by-step explanation:

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5 0
3 years ago
Which figure shows a reflection of pre-image DEFG over the x-axis?
Sergio [31]
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3 0
3 years ago
What is the inverse equation of the function, y = 3x - 6?
algol [13]
The best answer (and only correct answer) among the answer choices given is:
________________________________________________
                    [C]:    y⁻¹ = (x+6) / 3  .
_________________________________________________
Explanation:
__________________________________________________
 Given the original function:  y = 3x - 6 ;
_________________________________________________
To find the "inverse equation" of said function; we change the "x" to a y"; and the "y" to an "x"; and rewrite:
_________________________________________________
x = 3y <span>− 6 ; 

Now, rewrite in "slope-intercept form" ; or y = mx + b ;
     that is, with y as "single, isolated" variable on the left-hand side of the equation (with an "implied coefficient of positive one", only);  then an "equal sign, then "mx + b" ; in which: "m" is the coefficient of the variable, "x"; and in which "m" refers to the "slope";  and "b" refers to the 'y-intercept".
_____________________________________
So,we have the inverse function: 
____ </span>_________________________________________________
      x = 3y − 6  ;  we want to write in slope-intercept form; 
__________________________________________________
Add   "6" to each side of the equation:
__________________________________
     x + 6 = 3y − 6 + 6 ; 
__________________________________
 x + 6 = 3y ;  
________________________
 ↔ Rewrite as:   3y = x + 6 ; 
________________________________________
 Divide EACH side of the equation by "3" ; to isolate "y" one side of the equation; specifically, the left-hand side of equation; and to write in "slope-intercept form:
______________________________
              3y / 3 = (x + 6) / 3  ;
______________________________
   to get:
______________________________
                  y = (x + 6) / 3 ; 
_________________________________
                 y = (x/3)  + (6/3) ;
____________________________________
                y = (x/3 ) + 2 ;
___________________________________
or;  write as: y = (1/3)x + 2 ;
________________________________________
Now, let us examine the answer choices given:
__________________________________________
Note that all the answer choices begin with "y-1" ;
    (except "answer choice: [B]" , which begins with "x-1").  This seems confusing; however, in reality, this does not mean, "y minus 1"; or "x minus 1".  Rather, it mean y⁻¹  or x⁻¹  as notation for the "inverse" (not to be confused with the exponent notation.  The confusion stems from the fact that it can be difficult to make such notations on the "Brainly" system.
__________________________________________________
That being said, we can write the aforementioned "rewritten equations" (see above in THIS VERY ANSWER) as:
_____________________________________
y⁻¹ = (x + 6) / 3 ; 
_________________________________
                 y⁻¹ = (x/3)  + (6/3) ;
____________________________________
                y⁻¹ = (x/3 ) + 2 ;
___________________________________
or;  write as: y⁻¹ = (1/3)x + 2 
___________________________________
That being said:
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The best answer (and only correct answer) among the answer choices given is:  Answer choice: [C]:  y⁻¹ = (x+6) / 3  .
____________________________________________________
6 0
3 years ago
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