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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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3 years ago
Which statement best describes f(x)=
kotegsom [21]

Answer:

D

Step-by-step explanation:

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8 0
2 years ago
What is 7 1/8 times 2 5/6
Otrada [13]

Answer:

20 and 3/16

Step-by-step explanation:

Answer:

578×176=20316

Solution with Steps

578×176=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

57×178×6=96948

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 969 and 48 using

GCF(969,48) = 3

969÷348÷3=32316

The fraction

32316

is the same as

323÷16

Convert to a mixed number using

long division for 323 ÷ 16 = 20R3, so

32316=20316

Therefore:

578×176=20316

Solution by Formulas

Apply the fractions formula for multiplication, to

578×176

and solve

57×178×6

=96948

Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF(969,48) = 3

969÷348÷3=32316

Convert to a mixed number using

long division for 323 ÷ 16 = 20R3, so

32316=20316

Therefore:

578×176=20316

7 0
3 years ago
Help!<br> What would d be?
Oxana [17]

Answer:

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Step-by-step explanation:

find the diagonal line passing through the middle of the bottom rectangle:

a² + b² = c²

10² + 8² = c²

100 + 64 = 164

c² = 164

c = √164

c = 12.8062484729

find d:

a² + b² = c²

12² + 12.80624847298² = c²

144+ 164 = 308

c² = 308

c = √308

c = 17.5499287748

therefore d = 17.5499287748 inches or 17.5 inches to 1 decimal place

6 0
3 years ago
What is the measure of each interior angle of a regular octagon ?
hodyreva [135]

Answer:

135 degrees

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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