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kipiarov [429]
3 years ago
5

What is the completely simplified equivalent of 2/(5+i)?

Mathematics
1 answer:
Bezzdna [24]3 years ago
4 0

namely, let's rationalize the denominator in the fraction, for which case we'll be using the <u>conjugate</u> of that denominator, so we'll multiply top and bottom by its <u>conjugate</u>.

so the denominator is 5 + i, simply enough, its conjugate is just 5 - i, recall that same/same = 1, thus (5-i)/(5-i) = 1, and any expression multiplied by 1 is just itself, so we're not really changing the fraction per se.

\bf \cfrac{2}{5+i}\cdot \cfrac{5-i}{5-i}\implies \cfrac{2(5-i)}{\stackrel{\textit{difference of squares}}{(5+i)(5-i)}}\implies \cfrac{2(5-i)}{\stackrel{\textit{recall }i^2=-1}{5^2-i^2}}\implies \cfrac{2(5-i)}{25-(-1)} \\\\\\ \cfrac{2(5-i)}{25+1}\implies \cfrac{2(5-i)}{26}\implies \cfrac{5-i}{13}

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How do you find the selling price for a video game that cost $16 to make and is then marked up 400%?
lisabon 2012 [21]

Answer:

80

Step-by-step explanation:

First find the markup

markup = 16 * 400%

              = 16*4.00

              = 64

Add the markup to the original price

new price = original price + markup

                 =16+64

                  =80

6 0
3 years ago
A container of motor oil is supposed to contain 1000 ml of oil. a quality control engineer is concerned about the variability of
svlad2 [7]

one  hundred millimeters

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4 0
3 years ago
Please help. Thank you.
Marysya12 [62]

The answer would be 24pi inches.

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4 0
3 years ago
A tank is 4 feet long, 6 feet wide and 10 feet<br> tall. How much water can that tank hold?
prohojiy [21]

Answer:

Volume = 240 feet³

Step-by-step explanation:

We'll find it's volume

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4 0
3 years ago
I need help with this!
Viefleur [7K]

Answer:

the answer is option E.

Step-by-step explanation:

it is in the form f/g (x).

we know f and g from the equation;

we can rewrite it as, (√(9-x^2)/(3x-1))

if you notice you cannot put any number less than -3 or greater than 3 in the numeror because if you do you get a negative root which is false. for instance if you put 4 or -4 in the numerator you get 9 - (4 or -4 square ) which is 9- 16 which is a negative number and you cannot take root of a negative number.

on the numerator if you put 1/3 as the value for x you will get zero in the denominator. and any number divided by zero is undefined so that cannot be.

this means that option E is the right one that satisfies the condition. it means the domain is [-3, 1/3) U (1/3, 3] .

4 0
2 years ago
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