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9514 1404 393

Answer:

Step-by-step explanation:

1. de Moivre's theorem (or identity) states that ...

  [tex](\cos(\theta)+i\sin(\theta))^n=\cos(n\theta)+i\sin(n\theta)[/tex]

It is a statement about powers of complex numbers, so is related to the complex plane.

__

2. To graph a parametric equation, you need to know the relationship between the parameter and the coordinates you want to graph.

__

3. Here are the relationships:

  (x, y) = (r·cos(θ), r·sin(θ))

  (r, θ) = (√(x² +y²), arctan(y/x)) . . . with attention to quadrant

Answer:

150 are unoccupied

Step-by-step explanation:

If 75% are occupied, then 100% -75% = 25% are unoccupied

600 *25%

600 *.25

150

150 are unoccupied

Answer:

150

Step-by-step explanation:

100% - 75% = 25%

25% of seats unoccupied

hence,

number of seats unoccupied = 25/100 * 600 = 150

Answer:

-1-5<2x+5-5<4-5

-6<2x<-1

-3<x<-1/2

Answer:

1) No, the sum isn't equal to 180

2) Yes, the sum is equal to 180

3) No, the sum isn't equal to 180

4) Yes, the sides follow the triangle inequality

5) Yes, the sides follow the triangle inequality

6) Yes, it's an equilateral triangle

Answer:

(x + 4)² + (y + 10)² = 9

Step-by-step explanation:

The standard equation of a circle is written as seen below

(x - h)² + (y - k)² = r²

Where (h,k) is at the center and r is the radius

We want to find the standard equation of a circle that has a radius of 3 and a center at (-4,-10)

Remember r = radius so r = 3

and (h,k) is at center so h = -4 and k = -10

Now to find the standard equation of the circle we simply plug in the values of the variables (h,k and r) into the standard equation of a circle formula.

Equation of a circle: (x - h)² + (y - k)² = r²

r = 3, h = -4 and k = -10

Plug in values

(x - (-4))² + (y - (-10))² = 3²

Simplify

(x + 4)² + (y + 10)² = 9

And we are done!

Answer:

Step-by-step explanation:

189² = 215² + 123² - 2(215)(123)cos x°

35,721 = 46,225 + 15,129 - 52,890 cos x°

35,721 = 61,354 - 52,890 cos x°

52,890 (cos x° ) = 25,633

cos x° = 25,633 ÷ 52,890 ≈ 0.4846

x° ≈ 61.01°

Answer:

55°

Step-by-step explanation:

sin(x°) = [tex]\frac{opposite}{hypotenuse}[/tex]

x° = [tex]sin^-1(\frac{9}{11} )=54.90319877[/tex]

Rounded to the nearest degree, the answer is 55°

Answer:

parts of a circle = tangent, chord, arc, segment, sector, diameter, radius, circumference.

A lot of jobs use area and perimeter such as; Surveying, flooring estimates architecture, mechanical engineering,

Typically, a land surveyor conducts and records a perimeter survey and part of this includes the transverse  

Surveyors typically measure positions in series. Starting at control points, they measure angles and distances to new locations and use trigonometry to calculate positions in a plane coordinate system. Measuring a series of positions in this way is known as "running a traverse." A traverse that begins and ends at different locations is called an open traverse.

Here they create segments as seen below attached.

Engineers  Drawing Circles: Begins by defining the radius, diameter and circumference and asking students to draw circles with a given radius, circumference or area. and when requiring they draw two circles with the same centre, one property of each circle being given in example with bridges, or arc of a circle working with calculating precise length for material lists.

The Annulus: the shape formed between two circles. They use the properties of the annulus by completing a table with values of pertaining to the properties of the inner circle, the outer circle and the annulus.

With sectors, engineers, can defining major and minor sector, they calculate the arc length and the area of a sector of a circle. They have learnt how to complete a table of values of properties of a circle and a sector of that circle given different properties from which to start with.

Architecture typically used series of circles in gothic architecture, but also art deco and earlier historic arches, use of semi-circular arches in architecture, and tangents are used as a .function to compute a building's height if they know their distance from the structure and the angle between their eyes and the building's top; clinometers can help them measure those angles.

Metal fabricators and product design workers use spring dividers help them inscribe an arc or create a circle pattern.

I would then write a little more about chords and radius

Answer:

x > - 8

Step-by-step explanation:

4x - 8 > - 40

4x > - 40 + 8

4x > - 32

Divide 4 on both sides,

4x / 4 > - 32 / 4

x > - 8

Answer:

y = 11x - 20

Step-by-step explanation:

y = 4(x - 5) + 7x

y = 4x - 20 + 7x

y = 11x - 20

Answer:

Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities.

Statistics is maths.

Why:-

Statistics is related to maths because we study, use and even consider statistic problems with reference to mathematics.

• It is mostly used to find the census, which is maths.

• It is used to find interest rates and other banking terms using statistics, which is again related to math.

• It is also used to find the average people living in a village or panchayat, which is also math.

Therefore I strongly believe that Statistics is Maths.

Thank You!

9514 1404 393

Answer:

  50

Step-by-step explanation:

The number you choose depends on the location you consider to be zero height.

If we consider the surface of the pool to be zero height, and "up" to be the positive direction for measuring height, then the appropriate number for the original 50-ft height is 50.

Answer:

15

Step-by-step explanation:

15 is the greatest number that divides 45 60 75 without leaving remainder

Answer:

15

Step-by-step explanation:

Let write the factors of each number:

45: (1,3,5,9,15,45)

60:(1,2,3,4,5,6,10,12,15,20,30,60)

75:(1,3,5,15,15,75).

The greatest common factor is 15. So the answer is 15.

Answer:

option D

Step-by-step explanation:

Area of the square is 100 m² so each side is √100 = 10 m and half the area is 50 m²

Area of one quarter of the circle is ¼πr² = ¼π(10²) = 25π

The shaded area is thus (25π - 50) m²

Answer:

A. 671*3

B. 67*13

C. 3*1*7*6

D. 1*80

Answer:

The answer is [tex]1 \frac{4}{7}[/tex]

Step-by-step explanation:

First, you convert [tex]3 \frac{2}{3}[/tex] to an improper fraction. That is [tex]\frac{11}{3}[/tex]. Do the same for the other number.

Next, use KFC, or Keep, Flip, Change.

Keep the first number

Flip the second

Change the operation. Division becomes Multiplication. You should've gotten [tex]\frac{11}{3}[/tex]x[tex]\frac{3}{7}[/tex].

You can simplify now. You would've gotten 11 * [tex]\frac{1}{7}[/tex]. Multiply and you would get [tex]\frac{11}{7}[/tex]. Simplify into a mixed number. The answer is [tex]1 \frac{4}{7}[/tex].

Answer:

Option D, 12

Step-by-step explanation:

4x-8=80/2

or, 4x-8=40

or, 4x=48

or, x=12

Answer:

Given:-  

m∠DEF= (4x-8) °

m DE= 80°

Using a property :- m ∠DEF= 1/2 (m DE)

[tex](4x-8)[/tex] ° [tex]= 1/2 (80)[/tex]

[tex](4x-8)[/tex]° [tex]=(40)[/tex] °

[tex]4x-8=40[/tex]

Add 8 to both sides:-

[tex]4x=48[/tex]

Divide both sides by 4:-

[tex]\frac{4x}{4}=\frac{48}{4}[/tex]

[tex]x=12[/tex]

OAmalOHopeO

5(2x+1)+4=6(3x+2)-7

10x+5+4=18x+12-7

10x-18x=12-7-5-4

-8x=-4 (-1)

8x=4

x=4/8 (/4)

x=1/2

Answer:

x = 1/2

Step-by-step explanation:

5(2x + 1) + 4 = 6 (3x + 2) - 7

~Simplify both sides

10x + 9 = 18x + 5

~Subtract 9 from both sides

10x = 18x - 4

~Subtract 18x to both sides

-8x = -4

~Divide -8 to both sides

x = 1/2

Best of Luck!

Answer:

2016

Step-by-step explanation:

using USA dollars:

$42000 x .072 (7.2%) = 3024 total commission

3024 x 2/3 = 2016 brokers amount

Answer:

length = 8 cm

breadth = 9 cm

height = 9cm

Volume = ?

now,

Volume = l×b×h

= 8cm ×9cm ×9cm

= 648 cm^3.

Answer:

2x[tex]\leq[/tex]14

Step-by-step explanation:

Answer:

2x ≤ 14

Step-by-step explanation:

twice a number   is no more than     14

               2x                     ≤                 14

Answer:

-2(2x-4) = -4x+8 or 2(2x-4) ≠ 4x ; -4x+8 ≠ 4x

Step-by-step explanation:

Did you accidentally write =4x after your expression? If so, then let me explain why my answer is correct. I used distributive property of multiplication, so I multiplied -2 with 2x to get -4x, and -2 multiplied with -4 to get 8. So my final answer was -4x+8. If you did not accidentally put -4x, then my answer would be, 2(2x-4) ≠ 4x or -4x+8 ≠ 4x. Hope this helped.

Answer:

Below.

Step-by-step explanation:

The zeroes are at x = -2, 0, 1 and 3 so the factors are

(x +2)

x

(x - 1)

(x - 3)

Answer:

x= (2+ √ 34) /5 , (2- √ 34) /5

decimal form= 1.566

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

twice her age:

10*2 = 20

24-20 = 4

Answer:

4 i believe that's the answer

Answer:

B.368

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using Pythagorean theorem

[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]

[tex]\\ \sf\longmapsto H^2=5^3+3^2[/tex]

[tex]\\ \sf\longmapsto H^2=25+9[/tex]

[tex]\\ \sf\longmapsto H^2=34[/tex]

[tex]\\ \sf\longmapsto H=\sqrt{34}[/tex]

[tex]\\ \sf\longmapsto H=5.22[/tex]

(n/3) + 5 - 8 = 2

First add the constants (+5 and -8) on LHS.

(n/3) - 3 = 2

Transfer -3 to RHS, by changing its sign.

n/3 = 2 + 3

Now add the constants (2 and 3) on RHS.

n/3 = 5

Transfer 3 to RHS by changing division to multiplication

n = 5 × 3

Finally multiply the constants (5 and 3) on RHS

n = 15