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marishachu [46]
2 years ago
7

May I know the values of x and y of the following equation?(5-3i)(x-yi) = 3(x+2yi)+1-2i​

Mathematics
1 answer:
gogolik [260]2 years ago
3 0

Answer:

  (x, y) = (17/31, 1/31)

Step-by-step explanation:

Simplify the given equation, then equate real parts and equate imaginary parts. This will give you two equations in the two unknowns.

__

<h3>simplify</h3>

  (5 -3i)(x -yi) = 3(x +2yi) +1 -2i

 5x -5yi -3xi +3yi² = 3x +6yi +1 -2i

  (5x -3y) +i(-5y -3x) = (3x +1) +i(6y -2)

<h3>equate real, imaginary parts</h3>

This resolves to the two equations ...

  • 5x -3y = 3x +1
  • -5y -3x = 6y -2
<h3>solve the system</h3>

Putting these equations into general form gives ...

  2x -3y -1 = 0

  3x +11y -2 = 0

Using the "cross multiplication method" to solve these equations, we get ...

  x = ((-3)(-2) -(11)(-1))/(2(11) -3(-3)) = 17/31

  y = ((-1)(3) -(-2)(2))/31 = 1/31

The values of x and y that satisfy this equation are ...

  (x, y) = (17/31, 1/31)

_____

You can read more about the cross multiplication method here.

brainly.com/question/26397343

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alexandr402 [8]

Answer:

y = x + 3

Step-by-step explanation:

Y in math is usually referred as the output.

X is usually the input.

In other words,

<em>y</em><em> </em><em>is</em><em> </em><em>3</em><em> </em><em>more</em><em> </em><em>greater</em><em> </em><em>than</em><em> </em><em>x</em><em>.</em>

<em>In</em><em> </em><em>other</em><em> </em><em>words</em><em>,</em>

<em>y = x + 3</em>

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3 years ago
How can I tell, when doing synthetic division, if the binomial is<br> a FACTOR of the dividend?
Alecsey [184]

If you get 0 as the last value in the bottom row, then the binomial is a factor of the dividend.

Let's say the binomial is of the form (x-k) and it multiplies with some other polynomial q(x) to get p(x), so,

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If you plug in x = k, then,

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The input x = k leads to the output y = 0. Therefore, if (x-k) is a factor of p(x), then x = k is a root of p(x).

It turns out that the last value in the bottom row of a synthetic division table is the remainder after long division. By the remainder theorem, p(k) = r where r is the remainder after dividing p(x) by (x-k). If r = 0, then (x-k) is a factor, p(k) = 0, and x = k is a root.

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damaskus [11]

Answer:

Step-by-step explanation:

Decrease = 97 - 75 = 22

Percentage of decrease=

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Explanation:

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3) Solve for y:

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