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2 years ago

2+6i/2-4i = a + bi What is the value of a? What is the value of b?

1 answer:

6 0

$\dfrac{2+6i}{2-4i}\\\\\\=\dfrac{2(1+3i)}{2(1-2i)}\\\\\\=\dfrac{1+3i}{1-2i}\\\\\\=\dfrac{(1+3i)(1+2i)}{(1-2i)(1+2i)}\\\\\\=\dfrac{1+2i+3i+6i^2}{1-(2i)^2}\\\\\\=\dfrac{1+5i-6}{1+4}~~~~;[i^2=-1]\\\\\\=\dfrac{5i-5}{5}\\\\\\=\dfrac{5(i-1)}5\\\\=i-1\\\\=-1+i\\\\\text{It is in a form of a +bi so,}~ a = -1~ \text{and}~ b = 1$

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Diano4ka-milaya [45]

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2 years ago

Subtract. 3- (-5) - (-2) Plot the solution on the number line.

Whitepunk [10]

Answer:

10. put a dot on the number 10

Step-by-step explanation:

3-(-5)-(-2)

when subtracting negatives, you actually end up adding

3+5+2=10

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2 years ago

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makkiz [27]

Mistake in Line 2 : Was in the determining the values for a ,b,c

Mistake in Line 4 : Not taking the square roots of both sides.

Step-by-step explanation:

${a}^{2} + {b}^{2} = {c}^{2}$

First Mistake : Line 2

$a = x \\ b = 6 \\ c = 10$

Second Mistake : Line 4

$136 = {x}^{2} \\ not \\ 136 = x$

Correct Solution :

${x}^{2} + {6}^{2} = {10}^{2} \\ {x}^{2} = {10}^{2} - {6}^{2} \\ {x}^{2} = 100 - 36 \\$

${x}^{2} = 64 \\ \sqrt{ {x}^{2} } = \sqrt{64} \\ x = 6$

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2 years ago

What is the equaiton of the line that goes through the point (6,-1) and is parallel to the line represented by the equautions y=

mixas84 [53]

parallel lines have the same slope

The slope-intercept form of a linear equatio is y=mx+b, where m stands for the "slope of the line" and b stands for the "y-intercept of the line"

They give you the equation y= -5/6x+3 Notice this is already on the slope-intercept form, so in this case the slope is -5/6 and the y-intercept is 3

You want an equation of the line that is parallel to the given line. The slopes must be the same, so m=-5/6

So far we have y=-5/6x + b

We don't have b yet but that can be found using the given point (6,-1) which tells you that "x is 6 when y is -1"

Replace that on the equation y=-5/6x + b and you get

-1 = (-5/6)(6) + b

-1 = -5 +b

4 = b

b = 4

We found b, or the y-intercept

Go back to the equation y = -5/6 x + b and replace this b with the b we just found

y = -5/6x + 4

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2 years ago

Ashley uses 1/4 package of raisin for a fruit cake. She then uses 1/9 of the remainder for muffins. What fraction of the package

Flura [38]

$\text {Fruit cake = } \dfrac{1}{4}$

$\text {Raisin left = } 1 - \dfrac{1}{4} = \dfrac{4}{4} - \dfrac{1}{4} = \dfrac{3}{4}$

$\text {Muffins = } \dfrac{1}{9} \times \dfrac{3}{4} = \dfrac{3}{36} = \dfrac{1}{12}$

$\text {Raisin left = } \dfrac{3}{4} - \dfrac{1}{12} =\dfrac{9}{12} - \dfrac{1}{12} = \dfrac{8}{12} -= \dfrac{2}{3}$

Answer: She has 2/3 of the package left.

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3 years ago

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