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Dovator [93]
2 years ago
5

Simplify 5+2i/6+i

Mathematics
1 answer:
nlexa [21]2 years ago
3 0

Given problem is \frac{(5+2i)}{(6+i)}

To simplify that we need to multiply and divide by conjugate of the denominator

conjugate of denominator 6+i will be 6-i as we just need to change sign of the imaginary part

Now multiply and divide by 6-i


=\frac{(5+2i)}{(6+i)}\cdot\frac{(6-i)}{(6-i)}

=\frac{30-5i+12i-2i^2}{36-6i+6i-i^2}

=\frac{30+7i-2i^2}{36-i^2}

=\frac{30+7i-2\left(-1\right)}{36-\left(-1\right)}

=\frac{30+7i+2}{36+1}

=\frac{32+7i}{37}

=\frac{32}{37}+\frac{7}{37}i

Hence final answer is \frac{32}{37}+\frac{7}{37}i

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4 coffees and 12 lattes. Costs $61
Gala2k [10]

Answer:

Cost of a coffee is <u>$2.5</u> and cost of a latte is <u>$4.25.</u>

Step-by-step explanation:

Let cost of 1 coffee be 'c' and cost of 1 latte be 'l' dollars.

Given:

4 coffees and 12 lattes cost $61.

12 coffees and 7 lattes cost $59.75.

∵ 1 coffee cost = c

∴ 4 coffees cost = 4c and 12 coffee cost = 12c

∵ 1 latte cost = l

∴ 12 lattes cost = 12l and 7 lattes cost = 7l

Now, as per question:

4c+12l=61-----1\\12c+7l=59.75----2

Now, multiplying equation (1) by -3 and adding the result to equation (2). This gives,

-3(4c+12l)=-3(61)\\\\-12c-36l=-183\\12c+7l=59.75\\+\\----------\\0-29l=-123.25\\\\l=\frac{-123.25}{-29}=\$4.25

Now, plug in the value of 'l' in equation 1 to solve for 'c'. This gives,

4c+12(4.25)=61\\\\4c+51=61\\\\4c=61-51\\\\4c=10\\\\c=\frac{10}{4}=\$2.5

Therefore, cost of a coffee is $2.5 and cost of a latte is $4.25.

4 0
3 years ago
A high-speed computer printer prints a page in 1/6 second. Using this printer, how long would it take to print 30 pages?
german
30*\frac{1}{6}=\frac{30}{6}=5
6 0
3 years ago
Read 2 more answers
Help me i need it
forsale [732]

Step-by-step explanation:

I just answered that. how often did you put that in ?

7 0
2 years ago
Given △XPS≅△DNF, find the values of x and y.
White raven [17]

Answer:

x = 3

y = 15

Step-by-step explanation:

If △XPS ≅△DNF, their corresponding sides would be congruent. This implies that:

XP ≅ DN

PS ≅ NF

XS ≅ DF

Given that:

XP = 4y - 3

DN = 57

NF = 51

XS = 17x + 3

DF = 54

Therefore:

XP = DN

4y - 3 = 57 (Substitution)

Add 3 to both sides

4y = 57 + 3

4y = 60

Divide both sides by 4

y = 60/4

y = 15

Also,

XS = DF

17x + 3 = 54 (substitution)

Subtract 3 from each side

17x = 54 - 3

17x = 51

Divide both sides by 17

x = 51/17

x = 3

4 0
2 years ago
A cube has a side length of 6 cm. What is the volume of the cube, in cubic centimeters ​
Lady_Fox [76]

Answer:

V=216cm³

Step-by-step explanation:

V=216cm³

3 0
2 years ago
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