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I have posted a good start.

The box starts with x  notes.   (the money value is never important)

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He takes     \(\frac{x}{3}+2 = \frac{x+6}{3}\)

and leaves  \(\frac{2x}{3}-2=\frac{2x-6}{3}\\\)

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from the ones left 

he takes  \(\frac{1}{2}*\frac{2x-6}{3}+2=\frac{x-3}{3}+\frac{6}{3}=\frac{x+3}{3}\\ \)

and leaves   \(\frac{x-3}{3}-\frac{6}{3}=\frac{x-9}{3}\)

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from the ones left 

he takes  \(\frac{1}{2}*\frac{x-9}{3}+2\)

and leaves ...

AND you should be able to take it from there

sqrt(53*106)

sqrt 53 * 2  * 53)

53 sqrt 2

(x-2040) 2/5 = 1/4 x      solve for 'x'

a + b = 13.

B = (3,-7).

1. $i + i^2 + i^3 + \dots + i^{2016} + i^{2017} = -1$.

2. $z = 6 + 7i$ works.

The length of the arc is 14 cm.

The smalest angle works out to 83 degrees.

This is easy if you use coordinates.

log(ab)=2log(a-2b)

log(ab)=log((a-2b)^2)

ab=(a-2b)^2

solve for a/b

no clue

That person spent $5 as well!!! 

 x-y[(x-y)-(x+y)]

x - y [ -2y]

x + 2y²

Let's say the laptop costs 6x. the VR headset costs $y. The laptop cost $2.    So { x + y + z = 3100 1

                      { x - (y+z) = 1900 2

                      {    y = 32             3
3->2     x - 42 = 1900  4

3->1     x + 42 = 3100 5

 4+5      2x = 5000           x = 2500

x - 42 = 1900             z=150

y = 32                      y = 450

450 is the answer

The problem is pretty much asking what is the probability that both numbers are not the same

Using Complementary Probability we could minus the chances that both numbers are the same by 1

The chances of both numbers being the same are \(\frac{1}{6}\)

\(1 - \frac{1}{6} = \frac{5}{6}\)

Let the cost of 1 chair = x

∴ Cost of 3 chairs = 3x

Since Cost of 4 stools = Cost of 3 chairs.

∴ Cost of 4 stools = 3x

∴ Cost of 1 stool = \( {3x\over 4}{}{}\).........(1)

Cost of 2 chairs = 2x

Since the cost of 5 stools is $28 more than 2 chairs.

∴ Cost of 5 stools = 2x + 28

∴ Cost of 1 stool = \({2x+28\over 5}{}{}\)............(2)

From equations  (1) and (2) we have,

Cost of 1 stool = \( {3x \over 4}{}{}\)

Cost of 1 stool = \({2x+28 \over 5}\frac{}{}\)

∴ \( {3x\over 4}{}{} = {2x+28\over5}\)

⇒ 15x = 8x + 112

⇒ 7x = 112
⇒ x = 16
∴ Cost of 1 chair = $16

And Cost of 1 Stool = \( {3x \over 4}{}{} = {3\over4} * 16 = 12\)

Now we have,

Cost of 1 chair = $16

∴ Cost of 2 chairs = 2 × $16 = $32

Cost of 1 stool = $12

∴ Cost of 2 stools = 2 × $12 = $24

Hence the cost of 2 chairs and 2 stools = $32 + $24 = $56

∴ The cost of 2 chairs and 2 stools = $56

You work 9 hours and receive   92 - 20 = 72 dollars

72 dollars / 9 hours = .............   dollars per hour

Let Patrick had 'x' number of Ducks.

Since he had 3 times as many chickens as ducks.

∴ Number of chickens Patrick had = 3x

Since he had a total of 2000 Ducks and chickens,

∴ 3x + x = 2000

⇒ 4x = 2000

⇒ x = 500

∴ Number of Ducks Patrick had = 500

And number of Chickens Patrick had = 3x = 3 × 500 = 1500

Now he sells some chicken and after selling he now has twice as many ducks as chickens.

Let he sells 'y' number of chickens,

∴ Number of chickens left = 1500 - y

And the number of Ducks = 500

he now has twice as many ducks as chickens.

∴ 2 × (1500 - y) = 500

⇒ 3000 - 2y = 500

⇒ 2y = 2500

⇒ y = 1250

this means that he sold 1250 chickens.

ANSWER :

Number of chickens Patrick sold = 1250

CE = 4*sqrt(3).

The sum of the coordinates is 19/2.

d + f = 5.

By DeMoivre's Theorem, the solutions are 1 + sqrt(3)*i, 1 - sqrt(3)*i, -1 + sqrt(3)*i, -1 - sqrt(3)*i.

Thanks