What is the equation of the line? Plsss helppp

(√3 - i ) / (√3 + i ) × (√3 - i ) / (√3 - i ) = (√3 - i )² / ((√3)² - i ²)

… = ((√3)² - 2√3 i + i ²) / (3 - i ²)

… = (3 - 2√3 i - 1) / (3 - (-1))

… = (2 - 2√3 i ) / 4

… = 1/2 - √3/2 i

… = √((1/2)² + (-√3/2)²) exp(i arctan((-√3/2)/(1/2))

… = exp(i arctan(-√3))

… = exp(-i arctan(√3))

… = exp(-iπ/3)

By DeMoivre's theorem,

[(√3 - i ) / (√3 + i )]⁶ = exp(-6iπ/3) = exp(-2iπ) = 1

Answer:

NQ : Summary

CodeNQOne-letter codeXMolecule name2-HYDROXYNAPHTHOQUINONESynonyms2-HYDROXY-1,4-NAPHTHOQUINONESystematic namesProgram Version Name ACDLabs 10.04 2-hydroxynaphthalene-1,4-dione OpenEye OEToolkits 1.5.0 2-hydroxynaphthalene-1,4-dione

Mary expects to pay $954 at this rate for 35 calculators

If you have a rate, such as a price per a certain number of things, and the denominator quantity is not 1, you may determine the unit rate or price per unit by dividing the numerator by the denominator.

Five 5 scientific calculators are being sold for $135.

then the per calculator's cost is 135/5= $27.

And Mary needs to buy 35 calculators for her students

then 35 calculators is 35×27 = $954.

Hence she expects to pay $954.

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Answer:

£8520

Step-by-step explanation:

1 Bahraini dinar = £2.13

Multiply both sides of the equation by 4000.

4000 * 1 Bahraini dinar = 4000 * £2.13

4000 Bahraini dinar = £8520

Answer:25

Step-by-step explanation:

Answer:

All real number greater than equal to zero.

Step-by-step explanation:

The function is given by

[tex]f(x) = \frac{4}{5}\sqrt x[/tex]

The domain is defined as the input values so that the function is well defined.

here, the values of x should be all real number and zero also.

So, the correct option is  (d).

Answer:

D

Step-by-step explanation:

Answer:

32%

Step-by-step explanation:

3 girls like biology, 8 like chem and the rest prefer physics. 28 people like chemistry, and 24 boys like physics. This leaves 29 boys and 3 girls liking bio.

Answer:

C(min)  =  277.95 $

Container dimensions:

x = 2.822 m

y = 1.411 m

h = 3.52 m

Step-by-step explanation:

Let´s call x  and  y the sides of the rectangular base.

The surface area for  a rectangular container is:

S = Area of the base (A₁) +  2 * area of a lateral side x (A₂) + 2 * area lateral y (A₃)

Area of the base is :

A₁ =  x*y       we assume, according to problem statement that

x  =  2*y      y  = x/2

A₁  =  x²/2

Area lateral on side x

A₂  = x*h           ( h  is the height of the box )

Area lateral on side y

A₃ = y*h        ( h  is the height of the box )

s = x²/2  + 2*x*h + 2*y*h

Cost  =  Cost of the base + cost of area lateral on x + cost of area lateral on y

C = 10*x²/2  + 8* 2*x*h  + 8*2*y*h

C as function of x is:

The volume of the box is:

V(b) = 14 m³  = (x²/2)*h       28 = x²h      h = 28/x²

C(x) = 10*x²/2  + 16*x*28/x² + 16*(x/2)*28/x²

C(x)  =  5*x²  +  448/x  + 224/x

Taking derivatives on both sides of the equation we get:

C´(x)  =  10*x  -  448/x² - 224/x²

C´(x)  =  0             10x  -  448/x² - 224/x² = 0     ( 10*x³ - 448 - 224 )/x² = 0

10*x³ - 448 - 224 = 0       10*x³ = 224

x³  =22.4

x = ∛ 22.4

x = 2.822 m

y = x/2  =  1.411 m

h = 28/x²  =  28 /7.96

h =  3.52 m

To find out if the container of such dimension is the cheapest container we look to the second derivative of C

C´´(x) = 10 + 224*2*x/x⁴

C´´(x)  =  10 + 448/x³    is positive then C has a minimum for x = 2.82

And the cost of the container is:

C = 10*(x²/2) +  16*x*h + 16*y*h

C = 39.82 +  158.75  + 79.38

C =  277.95 $

Answer:

the first one is 4 and the second one is 0

Answer:

Hence the cost of adult tickets is $8

and the cost of child ticket is $4

Step-by-step explanation:

Given data

Let the cost per adult be x

and the cost per child be y

So

3x+2y= 32------------1

8x+5y= 84------------2

Now solving 1 and 2 simultaneously, we have

3x+2y= 32------------1X  5

8x+5y= 84------------2 X 2

 15x+ 10y= 160

 16x+ 10y= 168

-x+0)=-8

-x= -8

x= 8

Put x= 8 in 1 to find y

3*8+2y= 32

24+2y= 32

2y= 32-24

2y= 8

y= 4

The missing side 'a' of the triangle ABC is 96.80 units.

What is a triangle?

A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.

For the given situation,

Let ABC be the triangle and a,b,c be the respective sides of the triangle.

The diagram below shows that the triangle with their dimensions.

The dimensions are

A=60°, b=50, c=48.

The two sides and one angle of the triangle are given.

The missing side a can be found by using the law of cosines,

[tex]a=\sqrt{b^{2}+c^{2} -2abcosA }[/tex]

Substitute the above values,

⇒ [tex]a=\sqrt{50^{2}+48^{2} -2(50)(48)cos60 }[/tex]

⇒ [tex]a=\sqrt{2500+2304-4800(-0.9524)}[/tex]

⇒ [tex]a=\sqrt{2500+2304+4571.58}[/tex]

⇒ [tex]a=\sqrt{9375.58}[/tex]

⇒ [tex]a=96.82[/tex] ≈ [tex]96.80[/tex]

Hence we can conclude that the missing side 'a' of the triangle ABC is 96.80 units.

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Answer:

hshdjdjdjffhdiosekskskdkcjfiririrotr8tti5tittttit4i5i6i6832wy

Answer:

— Ang salitang entrepreneur ay hango sa salitang French na entrepende na nangangahulugang?

Answer:

Option (3)

Step-by-step explanation:

Track is shaped as a rectangle with a semicircle on either side.

Therefore, length of the track = 2(Length of rectangle) + perimeter of a complete circle formed by joining the semicircles on each side.

= 2(96) + 2πr

= [tex]192+2\pi (\frac{35}{2})[/tex]

= 192 + 35π

= 192 + 109.9

= 301.9 m

Since, Jake plans to run four laps.

Therefore, distance covered by Jake = 4 × 301.9

                                                              = 1207.6 m

Option (3) will be the correct option.

Answer:

C

Step-by-step explanation:

i did the test and got it right :D

[tex]\huge\bold{Given:}[/tex]

Length of the base = 8

Length of the hypotenuse = 17

[tex]\huge\bold{To\:find:}[/tex]

The length of the third side ''[tex]x[/tex]".

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\longrightarrow{\purple{x\:=\: 15}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

Using Pythagoras theorem, we have

(Perpendicular)² + (Base)² = (Hypotenuse)²

[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + (8)² = (17)²

[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + 64 = 289

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = 289 - 64

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = 225

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = [tex]\sqrt{225}[/tex]

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = [tex]15[/tex]

Therefore, the length of the missing side [tex]x[/tex] is [tex]15[/tex].

[tex]\huge\bold{To\:verify :}[/tex]

[tex]\longrightarrow{\green{}}[/tex] (15)² + (8)² = (17)²

[tex]\longrightarrow{\green{}}[/tex] 225 + 64 = 289

[tex]\longrightarrow{\green{}}[/tex] 289 = 289

[tex]\longrightarrow{\green{}}[/tex] L.H.S. = R. H. S.

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]

Answer:

3

Step-by-step explanation:

+2

Answer:

17x+12=12

17x=12-12

17x=0

divide both sides by 17

x=0

rough check

17(0) = 12-12

0=0

I hope this helps

Volume of the sphere = 4/3πr³

905 1/7 = 4/3*22/7*r³

6336/7 = 4/3*22/7*r³

r³ = (6336*7*3)/(4*22*7)

r³ = 133056/616

r³ = 216 

r = ∛216

r = 6 cm 

So, diameter = 6*2 = 12 cm

Surface area of the sphere = 4πr²

= 4*22/7*6*6

= 3168/7

Surface area of the sphere = 452.57 sq cm

Hope it helps.

Answer:

( - infinity, -3 ] [ -2, infinity )

square bracket means it includes the end point.

Step-by-step explanation:

(-∞, -3]U [-2,∞)

Answer:

si si amigo adila

Step-by-step explanation:

Answer:

Answer: 3) R(n) = 1200(1.002)n - 100n

Step-by-step explanation:

After n months, which function represents Chet’s net worth, R(n)?

(1) R(n) = 1200(1.002)n + 100n

(2) R(n) = 1200(1.002)12n + 100n

(3) R(n) = 1200(1.002)n - 100n

(4) R(n) = 1200(1.002)12n - 100n

Answer: 3) R(n) = 1200(1.002)n - 100n

Net worth is the amount of his savings minus his debt,

Everything in the problem is in terms of months, so there is no need to multiply the exponent by 12, which would convert n years into months.

Answer:

B. The distance of an archer's shots from the center of a target

C. The time it takes for an airliner to fly from Los Angeles to New York

Step-by-step explanation:

According to the Question,

B & C should each have a range of values that cover most occurrences with outlying values that decrease in number as they move further away from the dominant value range, which is the definition of a normal distribution.

Given:

A fair die is rolled.

It pays off $10 for 6, $7 for a 5, $4  for a 4 and no payoff otherwise.

To find:

The expected winning for this game.

Solution:

If a die is rolled then the possible outcomes are 1, 2, 3, 4, 5, 6.

The probability of getting a 6 is:

[tex]P(6)=\dfrac{1}{6}[/tex]

The probability of getting a 5 is:

[tex]P(5)=\dfrac{1}{6}[/tex]

The probability of getting a 4 is:

[tex]P(4)=\dfrac{1}{6}[/tex]

The probability of getting other numbers (1,2,3) is:

[tex]P(\text{Otherwise})=\dfrac{3}{6}[/tex]

[tex]P(\text{Otherwise})=\dfrac{1}{2}[/tex]

We need to find the sum of product of payoff and their corresponding probabilities to find the expected winning for this game.

[tex]E(x)=10\times P(6)+7\times P(5)+4\times P(4)+0\times P(\text{Otherwise})[/tex]

[tex]E(x)=10\times \dfrac{1}{6}+7\times \dfrac{1}{6}+4\times \dfrac{1}{6}+0\times \dfrac{1}{2}[/tex]

[tex]E(x)=\dfrac{10}{6}+\dfrac{7}{6}+\dfrac{4}{6}+0[/tex]

[tex]E(x)=\dfrac{10+7+4}{6}[/tex]

[tex]E(x)=\dfrac{21}{6}[/tex]

[tex]E(x)=3.5[/tex]

Therefore, the expected winnings for this game are $3.50.

Answer:

You have 500 marbles.

The longest side of the biggest equalateral triangle that you can make with your marbles is 31

Step-by-step explanation:

28 + 4 = 32

So our equation is:

TR(32) - 28

Now find Triangular Number 32: (32 *33)/2=528

528 - 28 = 500

So, we have 500 marbles

Now we need to find the longest side of the biggest equalateral triangle that you can make make with your marbles

Let's go back to 28 + 4 = 32

One row above 32 is 31

So the longest side of the biggest equalateral triangle that you can make with your marbles is 31

Hope this helps!

Answer:

The agency makes 23855

The agent makes 5963.75

Step-by-step explanation:

First find the commission for the agency

367000 * 6.5%

367000*.065

23855

Now the agent gets 25% of this amount

23855 *25%

23855 *.25

5963.75

Answer:

Step-by-step explanation:

The agency made $24,440.00

The Agent made $6,110.00

Answer:

[tex]L =21.945[/tex] --- Length

[tex]W = 7.9725[/tex] --- Width

Step-by-step explanation:

Given

Let

[tex]L \to Length[/tex]

[tex]W \to Width[/tex]

So:

[tex]Area = 175[/tex]

[tex]L = 6 + 2W[/tex]

Required

The dimension of the rectangle

The area is calculated as:

[tex]Area =L*W[/tex]

This gives:

[tex]175 =L*W[/tex]

Substitute: [tex]L = 6 + 2W[/tex]

[tex]175 =(6 + 2W)*W[/tex]

Open bracket

[tex]175 =6W + 2W^2[/tex]

Rewrite as:

[tex]2W^2+ 6W -175 = 0[/tex]

Using quadratic formula:

[tex]W = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

This gives:

[tex]W = \frac{-6 \± \sqrt{6^2 - 4*2*-175}}{2*2}[/tex]

[tex]W = \frac{-6 \± \sqrt{1436}}{2*2}[/tex]

[tex]W = \frac{-6 \± 37.89}{4}[/tex]

Split

[tex]W = \frac{-6+ 37.89}{4}, W = \frac{-6- 37.89}{4}[/tex]

[tex]W = \frac{31.89}{4}, W = \frac{-43.89}{4}[/tex]

The width cannot be negative;

So:

[tex]W = \frac{31.89}{4}[/tex]

[tex]W = 7.9725[/tex]

Recall that:

[tex]L = 6 + 2W[/tex]

[tex]L =6 + 2 * 7.9725[/tex]

[tex]L =21.945[/tex]

Answer:

Interest Earned ₹ 1,800

Principal Amount ₹ 10,000

Total Value ₹ 11,800

The cost of the loan for Mandy will be $11800 and the total interest for 3 years will be $1800.

Simple interest is a predetermined proportion of the principal amount borrowed or lent that is paid or received over a set period of time.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

In another word, if the principle amount is the same in each time period then the interest will also same for every time period.

Given that

Principle amount = $ 10000

Time period = 3 years

Rate of interest = 6%

Rate of interest at the end of 1st year

10000 × 6/100 ⇒ $600

Since in simple interest rate of interest remain same so

Rate of interest for 3 years

3 × 600 = $ 1800 hence rate of interest will be $1800.

Cost of the loan = principle amount + total interest

Cost of the loan = 10000 + 1800 ⇒ $11800 will be the cost of the loan.

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