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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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Answer:

around 73-89%

Step-by-step explanation:

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3 years ago
Simplify the expression 6 + 3(2x - 4(3x - 2)].​
I am Lyosha [343]

Answer:

-30x + 30

Step-by-step explanation:

6 + 3 × [2x - 12x + 8]

6 + (-30x) + 24

-30x + 24

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3 years ago
For the functions f(x)=4x−3 and g(x)=3x2+4x, find (f∘g)(x) and (g∘f)(x).
barxatty [35]

Answer:

(16x + 21) and (16x - 6)

Step-by-step explanation:

f(g(x)) = f(6 + 4x)

Applying the f(x) function on (6 + 4x) gives

4(6 + 4x) - 3

Which equals 16x + 24 - 3

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7 0
3 years ago
A recipe for beef stew calls for 1 pound of beef and 3 potatoes the recipe is doubled to include 2 pounds of beef and 6 potatoes
Lerok [7]

Pounds of beef and potatoes are in ratio or proportion of \frac{1}{3} .

<u>Step-by-step explanation:</u>

Correct Question: A recipe for beef stew calls for 1 pound of beef and 3 potatoes. The recipe is doubled to include 2 pounds of beef and 6 potatoes. Which proportion represents the situation?

We have , A recipe for beef stew calls for 1 pound of beef and 3 potatoes , i.e.

Number of beef stew calls = 1

Number of potatoes = 3

Now , The recipe is doubled to include 2 pounds of beef and 6 potatoes i.e. for every 2 pounds of beef we have 6 potatoes

⇒ 2/6

⇒ \frac{2}{6}

⇒ \frac{2}{2(3)}

⇒ \frac{1}{3}

Therefore , Pounds of beef and potatoes are in ratio or proportion of \frac{1}{3} .

4 0
2 years ago
Read 2 more answers
A soup kitchen makes 15 gallons of soup each day a quarter of the soup is served and the rest is saved for the next day , what i
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Number of ounces left is 1120

Step-by-step explanation:

  • Step 1: Find number of ounces left after each day.

Given total soup prepared each day = 15 gallons

Amount served each day = 1/4 of 15 = 15/4 gallons

Amount left after each day = 15 - 15/4 = 60 - 15/4 = 35/4 gallons

  • Step 2: Convert gallons into ounces. 1 gallon = 128 ounces

35/4 gallons = 35/4 × 128 = 1120 ounces

5 0
3 years ago
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