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antiseptic1488 [7]
2 years ago
12

Evaluate (6 + 2i) / (3 –i ). 5/4 + 6/4i 8/5 + 6/5i 20/8 + 12/8i 16/9 + 12/9i

Mathematics
1 answer:
Yuki888 [10]2 years ago
7 0

We are given with a complex no. and need to simplify it , so let's start !!!

Let's assume that :

{:\implies \quad z=\sf \dfrac{6+2\iota}{3-\iota}}

Now , Rationalizing the denominator or in other words multiplying and dividing {z} by the <em>conjugate</em> of the denominator

{:\implies \quad z=\sf \dfrac{6+2\iota}{3-\iota}\times \dfrac{3+\iota}{3+\iota}}

{:\implies \quad z=\sf \dfrac{(6+2\iota)(3+\iota)}{(3-\iota)(3+\iota)}}

{:\implies \quad z=\sf \dfrac{6(3+\iota)+2\iota (3+\iota)}{(3)^{2}-(\iota)^{2}}\quad \qquad \{\because (a-b)(a+b)=a^{2}-b^{2}\}}

{:\implies \quad z=\sf \dfrac{18+6\iota +6\iota +2(\iota)^{2}}{9-(-1)}\quad \qquad \{\because (\iota)^{2}=-1\}}

{:\implies \quad z=\sf \dfrac{18+12\iota -2}{10}}

{:\implies \quad z=\sf \dfrac{16+12\iota}{10}}

{:\implies \quad z=\sf \dfrac{16}{10}+\dfrac{12\iota}{10}}

{:\implies \quad {\bf \therefore}\quad \underline{\underline{z=\bf \dfrac{8}{5}+\dfrac{6}{5}\iota}}}

Hence , Option B) <em>(8/5) + (6/5)i</em> is correct :D

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Kelly needs to order lunch for orders 6 people at a business meeting. Her menu choices are chicken salad for a cost of $5 per pe
nirvana33 [79]
Ok , with that information we can write the equations
x + y = 6
5x + 4y = 28

Where x = how many people ordered chicken
and y = how many people ordered egg salad

Through elimination , we can set one of the variables in both equations equal so we can eliminate it :

(4)x + (4)y = (4)6
5x + 4y = 28

4x + 4y = 24. equation 1
5x + 4y = 28. equation 2

Now we can subtract the second equation by the first equation and isolate one variable:
equation 2 - equation 1

5x - 4x + 4y - 4y = 28 - 24

x = 4

Now that we discovered our x value ( How many people ordered chicken salad ) , we can apply it to one of the equations and discover y ( how many people ordered egg salad)

x + y = 6
x= 4
4 + y = 6

We can shift 4 to the other side of the equation by subtracting 4 from both sides of the equation:
4 - 4 + y = 6 - 4
y = 2

x=4 and y=2

So the awnser is :
4 people ordered chicken salad and 2 people ordered egg salad!

I hope you understood my brief explanation!!

p.s if you want to know how to use another method to solve these problems ( Substition) , just let me know in a comentary down here
5 0
3 years ago
HELP! ASAP! Am I correct!?!?
LenKa [72]
It isn't because, it isn't consistent, and it doesn't follow any of the other answer choices. :)

3 0
3 years ago
3-2i/5+i<br><img src="https://tex.z-dn.net/?f=3%20-%202i%20%5Cdiv%205%20%20%2B%20i%20%20" id="TexFormula1" title="3 - 2i \div 5
hammer [34]

3-2i/5+i

\frac{3*5+(-2)*1)+(-2*5-3*1)i}{5^2+1^2}

\frac{13-13i}{26}=\frac{1-i}{2}

=\frac{1}{2}-\frac{1}{2}i

Hope this helps!

Thank you for posting your question at here on Brainly.

-Charlie

3 0
3 years ago
A square pyramid. The square base has side lengths of 6 inches. The 4 triangular sides have a base of 6 inches and height of 9 i
Marrrta [24]

Answer:

The area of the pyramid’s base is 36 in².

The pyramid has 4 lateral faces.  

The surface area of each lateral face is 27 in².

Step-by-step explanation:

"<u>Lateral</u>" means side, so the lateral faces are <u>triangles</u>.

The <u>base</u> is the bottom, which is a <u>square</u>.

To calculate the <u>area of the base</u>, use the formula for area of a square.

A_{base} = s^{2}

A_{base} = (6 in)^{2}

A_{base} = 36 in^{2}

To calculate the <u>area of a lateral face</u>, find the area of a triangle.

A_{lateral} = \frac{bh}{2}

A_{lateral} = \frac{(6 in)(9 in)}{2}

A_{lateral} = \frac{54 in^{2}}{2}

A_{lateral} = 27 in^{2}

In a pyramid, the number of lateral faces is the same as the number of sides in the base. <u>The square base as 4 sides, so there are 4 lateral faces</u>.

3 0
3 years ago
If f(x) = 0, what is x?<br><br> 0 only<br> –6 only<br> –2, 1, or 3 only<br> –6, –2, 1, or 3 only
Angelina_Jolie [31]

Answer:

answer will be 0

plz mark me as brainliest

8 0
3 years ago
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