Express the complex number in trigonometric form. -2

Answer:

120 floor seats, 80 stadium seats

Step-by-step explanation:

use extreme values

if all were floor seats, then cost would be 32*200, or 6400

6400-5440=960

32-20=12

960/12=80

200-80=120

120 floor seats and 80 stadium seats were sold.

Let's designate F as the number of floor seats and S as the number of stadium seats.

Given :

F + S = 200 (Equation for the total number of tickets)

32F + 20S = 5440 (Equation for the total sales amount)

We can use substitution or elimination to solve this system. If we multiply the first equation by 20 to get

20F + 20S = 4000

and subtract it from the second equation, we get:

12F = 1440

F = 120

We found the number of floor seats sold. We can then substitute F back into the first equation to find the number of stadium seats:

120 + S = 200

S = 80.

So, 120 floor seats and 80 stadium seats were sold.

Answer:

A U B = {x|x is an integer}

Step-by-step explanation:

If A={x|x is an odd integer} then:

A = 1, 3, 5, 7, 9, 11, etc.

(Negative odd integers are also included)

and B= {x|x is an even integer}  

A = 2, 4, 6, 8, 10, 12, 14, etc.

(Negative even integers are also included)

We have that a u b is going to be the set of all integer numbers. That is to say:

A U B = {x|x is an integer}

Answer:

6ft for 30°

8.5ft for 45°

10.4ft for 60°

Step-by-step explanation:

12(sin 30°)=x

x=6

12(sin 45°)=x

x=8.5

12(sin 60°)=x

x=10.4

By using right angle trigonometry and the cosine function (x = L cos θ), we find that a 12-ft ladder reaches 10.4 ft, 8.5 ft and 6 ft up a wall when it is leaned at 30°, 45° and 60° respectively.

The problem described here involves the use of right angle trigonometry, specifically the use of the cosine function. In order to determine how high up the wall the ladder reaches at an angle of 30°, 45° and 60°, we can use the formula: x = L cos θ.

Firstly, let's calculate the height at 30 degrees (θ = 30°). We know that cos 30° = √3/2, so we substitute into the formula: x = 12ft * √3/2 which approximately equals 10.4 ft.

Next, for 45 degrees (θ = 45°), cos 45° = √2/2. Substituting into the formula: x = 12ft * √2/2 = 8.5 ft.

Finally, for 60 degrees (θ = 60°), cos 60° = 1/2. Therefore, x = 12ft * 1/2 = 6ft). So, the ladder reaches 10.4 ft up the wall when the angle is 30°, 8.5 ft when the angle is 45°, and 6 ft when the angle is 60°.

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Answer:

  x = 24

Step-by-step explanation:

The segments on either side of an angle bisector are proportional:

  (x +4)/44.8 = 35/56

  x +4 = 44.8·(35/56) = 28 . . . . multiply by 44.8

  x = 24 . . . . . subtract 4

Answer:

The value of x is 24.

Step-by-step explanation:

Given information: In ΔGHE, ED is angle bisector, EG=44.8 millimeters, GD=(x+4) millimeters, DH=35 millimeters, and EH=56 millimeters.

According to the angle bisector theorem, an angle bisector divide the opposite side into two segments that are proportional to the other two sides of the triangle.

In ΔGHE, ED is angle bisector, By using angle bisector theorem, we get

[tex]\frac{GD}{DH}=\frac{EG}{EH}[/tex]

[tex]\frac{x+4}{35}=\frac{44.8}{56}[/tex]

Multiply both the sides by 35.

[tex]x+4=\frac{44.8}{56}\times 35[/tex]

[tex]x+4=28[/tex]

Subtract 4 from both the sides.

[tex]x=28-4[/tex]

[tex]x=24[/tex]

Therefore the value of x is 24.

Answer:

  about 35.4 yards

Step-by-step explanation:

Make use of the formula for the area of a square and solve for the side length. The area (A) of a square of side length s is given by ...

  A = s²

You are given A and asked to find s. So you have

  1255 yd² = s²

To find s, you take the square root of both sides of the equation.

  √(1255 yd²) = √(s²)

  35.426 yd ≈ s . . . . . the square root of 1255 is irrational, so we have shown an approximation rounded to 3 decimal places.

Each side of the field is about 35.4 yards long.

_____

Any scientific or graphing calculator can compute the square root for you, as can any spreadsheet program or any of a number of on-line calculators. A Google or Bing search box will also compute the square root for you. (see attachment)

Answer: [tex]cos(\pi-x)=-cos(x)[/tex]

Step-by-step explanation:

We need to apply the following identity:

[tex]cos(A - B) = cos A*cos B + sinA*sin B[/tex]

Then, applying this, you know that for [tex]cos(\pi-x)[/tex]:

[tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex]

We need to remember that:

[tex]cos(\pi)=-1[/tex] and [tex]sin(\pi)=0[/tex]

Therefore, we need to substitute these values into [tex]cos(\pi-x)=cos(\pi)*cos(x)+sin(\pi)*sin(x)[/tex].

Then, you get:

[tex]cos(\pi-x)=(-1)*cos(x)+0*sin(x)[/tex]

[tex]cos(\pi-x)=-1cos(x)+0[/tex]

[tex]cos(\pi-x)=-cos(x)[/tex]

Answer:

AE = 3

Step-by-step explanation:

Let Hannah = X and Heather = Y.

The sum of their ages is 30, so you would have x + y = 30

Then Hannah's age is 4 less than 2 times Heather's age so X = 2y-4

The equations are :

X + Y = 30 and X = 2y - 4

The answer is C.

Answer:

recursive: f(0) = 7; f(n) = f(n-1) -8

explicit: f(n) = 7 -8n

Step-by-step explanation:

The sequence is an arithmetic sequence with first term 7 and common difference -8. Since you're numbering the terms starting with n=0, the generic case will be ...

recursive: f(0) = first term; f(n) = f(n-1) + common difference

explicit: f(n) = first term + n·(common difference)

To get the answer above, fill in the first term and common difference values.

1. 7=k

2. 21+w=36

-21 -21

----------------------

w=15

3. -5 =G+3

-3 -3

---------------------

-8=G

4. 2b/2=12/2

b=6

5. 35/5=5R/5

7= R

6. Q/2 (2) = 6 (2)

Q=12

Answer:

Step-by-step explanation:

1) 14-7 = 7 = k

2) 21 + W = 36  →  W = 36 - 21  → W = 25

3) -5 = G + 3.  Add 5 to both sides, obtaining G = 8.

4) 2b = 12.  Div. both sides by 2:  b = 6

5) 35 = 5R.  Div. both sides by 5:  7 = R

6) Q/2 = 6; Mult both sides by 2: Q = 12

Answer:

  y = 90°

Step-by-step explanation:

The angle y subtends an arc of 180°, so its measure is 180°/2 = 90°. (We know the arc is 180° because the end points of it are on a diameter, so it is half a circle.)

Answer:

1/10

Step-by-step explanation:

When Maggie gives a grape treat to her brother, there are 2 grape treats out of 5 total treats.

When Maggie selects another treat, there is 1 grape treat out of 4 treats left.

So the probability that both happen is:

2/5 × 1/4

1/10

The assumption of the inductive step is not correct. If [tex]\mathrm{max}(x,y)=2[/tex], for instance, it's entirely possible that [tex]x=1[/tex] and [tex]y=2[/tex].

Answer:

c ≈ 4.105

Step-by-step explanation:

You want to find c in ...

cos(13°) = 4/c

Multiply the equation by c/cos(13°) and evaluate.

c = 4/cos(13°) ≈ 4.105

Answer:

Solve the equation where the sine of 30 degrees is equal to YZ/50.

Solve 180 – (30 + 90) = 60 to find the measure of angle Z. Then use the cosine of Z to write and solve an equation.

Use the 30°-60°-90° triangle theorem to find that YZ = 50/2.

Step-by-step explanation:

These are the sample answers, use how you would like :)

Answer:

A.  

x + y = 28

1.68x + 2.44y = 54.64

Step-by-step explanation:

Let x = paperback books and y = hardback books

x+y =28

We know that paperbacks cost 1.68 and hardback cost 2.44

1.68x + 2.44y = 54.64

We have 2 equations and 2 unknowns

x+y =28

1.68x + 2.44y = 54.64

Answer:

option b 5√2  

option a 20

option c 4

option d 3/4

option b 3

Step-by-step explanation:

To solve all these questions we will use trigonometry identity which says that

sinΔ = opposite / hypotenuse

1)

sin45 = 5 / KL

Kl = [tex]\frac{5}{\frac{\sqrt{2}}{2} }[/tex]

KL = 5√2  

2)

TanФ = opp / adj

Ф = Tan^-1(5/14)

Ф = 19.65

   ≈ 20

3)

sin(30) = rq / 8

rq = sin(30)(8)

rq = 4

4)

tan(Ф) = 6/8

5)

angle 3

Answer:

Answer: Nolan took 97.75 Seconds

Step-by-step explanation:

85 x .15 = 12.75  

85 + 12.75 = 97.75

Answer:

(8,0)

Step-by-step explanation:

The equation that models the path traced by the ball is

[tex]h(x)=-8x^2+64x[/tex]

To find the point at which the ball hit the ground, we must equate the function to zero.

[tex]-8x^2+64x=0[/tex]

Factor;

[tex]-8x(x-8)=0[/tex]

[tex]-8x=0,(x-8)=0[/tex]

This implies that;

x=0,x=8,

At x=0, the ball was not yet kicked.

So we take x=8, to be the time the ball hit the ground.

We substitute x=8 into the function to get;

[tex]h(8)=-8(8)^2+64(8)=0[/tex]

Hence the point at which the ball hit the ground is (8,0)

Answer:

  50 cm

Step-by-step explanation:

Consider isosceles triangle AEF in the attachment. Point B is the center of the incircle, and it divides altitude AC into segments having the ratio 12:5.

Triangle ABD is similar to triangle AEC by AA similarity. (Angle A is the same for both right triangles. Then the ratio of hypotenuse to short leg will be the same for each. In triangle ABD, that ratio is 12:5, as given by the problem statement. Since we know AE = 60 cm, also from the problem statement, we know that ...

  AB/BD = AE/EC

  12/5 = 60 cm/EC

so ...

  EC = (60 cm)·(5/12) = 25 cm

Base length EF is twice that, or 50 cm.

To find the dimensions of the rectangle, express its length in terms of its width as 'width + 6'. Substitute this in the formula for perimeter and solve to get width = 5 feet and length = 11 feet.

The problem stated relates to the geometric concept of perimeter and involves a bit of algebra. First, remember that the formula for the perimeter of a rectangle is 2(length + width). If the total perimeter is 32 feet, and the length is 6 feet longer than the width, we can describe the length as 'width + 6'.

Substitute these into the perimeter formula: 2((width + 6) + width) = 32. Simplify this to 2(width + width + 6) = 32, then simplify further to 2(2width + 6) = 32. Divide both sides by 2 to get 2width + 6 = 16. Solving for 'width', we get width = 5 feet. Therefore, the length (which is width + 6) would be 5 + 6 = 11 feet.

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Answer:

7.1 miles

Step-by-step explanation:

Consider right triangle HospitalSchoolSupermarket. In this triangle:

The shortest road from the main entrance of the supermarket to the highway that connects the school and hospital will be the height drawn from the point Supermarket to the hypotenuse HospitalSchool.

Let the length of this road be x mi and the distance from School to point A be y mi. Use twice the Pythagorean theorem for right triangles Supermarket SchoolA and SupermarketHospitalA:

[tex]\left\{\begin{array}{l}x^2+y^2=8.82^2\\ \\x^2+(14.7-y)^2=11.76^2\end{array}\right.[/tex]

Subtract from the second equation the first one:

[tex]x^2+(14.7-y)^2-x^2-y^2=11.76^2-8.82^2\\ \\14.7^2-2\cdot 14.7y+y^2-y^2=11.76^2-8.82^2\\ \\-29.4y=11.76^2-8.82^2-14.7^2\\ \\29.4y=155.5848\\ \\y\approx5.24\ mi[/tex]

Thus,

[tex]x^2=8.82^2-5.24^2=50.3348\\ \\x\approx 7.1\ mi.[/tex]

Answer:

Option A. (6,2)

Step-by-step explanation:

We have the following inequality:

[tex]y- x <-3[/tex]

Solving for y we have:

[tex]y<x-3[/tex]

The line that limits the region of inequality is

[tex]y = x-3[/tex]

Then the region of inequality are all values of y that are less than [tex]f (x) = x-3[/tex]

In other words, the points belonging to the inequality are all those that lie below the line.

To find out which point belongs to this region substitute inequality and observe if it is satisfied

A. (6,2)

[tex]2<6-3[/tex]

[tex]2<3[/tex]   is satisfied

B. (2, 6)

[tex]6<2-3[/tex]

[tex]6<-1[/tex]   it is not satisfied

C. (2, -1)

[tex]-1<2-3[/tex]

[tex]-1<-1[/tex] it is not satisfied

The answer is the option A

Answer:

As we can see in the picture, we already knew 4 out of 6 sides of the figure so we need to find the other sides.

So the first missing side (the one near the 3 m one) should be:

7 - 4 = 3 (m)

The second missing side (the one near the 4m one) should be:

6 - 3 = 3 (m)

Now that we know all of the side lengths of the figure, the perimeter of the figure will be:

7 + 3 + 3 + 3 + 4 + 6 = 26 (m)

Answer:

Its value in 2006 would be $99, 183, 639, 920

Step-by-step explanation:

Use the compounding interest formula for this one, which looks like this in its standard form:

[tex]A(t)=P(1+r)^t[/tex]

Our P is the initial amount of $24, the r in decimal form is .06, and the time between 2006 and 1626 in years is 380.  Fitting this into our formula we get:

[tex]A(t)=24(1+.06)^{380}[/tex] or

[tex]A(t)=24(1.06)^{380}[/tex]

First raise the 1.06 to the power of 380 on your calculator and then multiply in 24.

As for the second part of the question, I'm not quite sure how it's supposed to be answered. But maybe you can figure that out according to what the unit normally asks you to do.

Answer:

A.  The two triangles.

Step-by-step explanation:

Isometry can be divided into two words: iso = same and metry = measure

So, isometry means "same measure".

In this case, that means the transformation didn't change the measures of the object.

In B, they kept the same shape, but not the same side.

In C, you can see the figure has been transformed,.

A bit if not A them it’s C (sorry I tried)

Answer:

C

Step-by-step explanation:

When you have the radius of a circle, you find the circumference by multiplying the radius by 2PI.

The answer is C.

Answer:

0.74 m

Step-by-step explanation:

The distance around a circle on the other hand is called the circumference (c).

A line that is drawn straight through the midpoint of a circle and that has its end points on the circle border is called the diameter (d) .

Half of the diameter, or the distance from the midpoint to the circle border, is called the radius of the circle (r).

The circumference of a circle is found using this formula:

C=π⋅d

or

C=2π⋅r

Given r = 119.3 mm

So, C = 2 * 3.14 * 119.3 = 749.2 mm = 0.74 m

Answer:

13

Step-by-step explanation:

The longest side must be less than the sum of the shorter sides:

c < a + b

c < 6 + 8

c < 14

So the largest whole number length is 13.

6.

Intersecting chords:

RT x ST = PT x TQ

2 x 6 = 3 x TQ

12 = 3TQ

TQ = 12/3

TQ = 4

7.

AD = 90 -BE = 90-18 = 72

ADE = 180. DE = 180 - AD = 180-72 = 108

AE = 180.  AB = 180-18 = 162

DE = 108

BD = BE +DE = 18 + 108 = 126

DAB = 72 +   162 = 234

ADE = 90 degrees

8.

AB^2 = BC* (BC +x)

8^2 = 2 * (2 +x)

64 = 4 + 2x

60 = 2x

X = 60/2

X = 30

Answer:

1. 37

2. 25

Step-by-step explanation:

In order to find a percentile of a given number set, you must first put the values in ascending order:

18, 20, 22, 25, 26, 36, 37, 41, 45, 50

70% = 0.7

Since there are 10 numbers in the set, we'll multiply 10 by 0.7

10 × 0.7 = 7

So we are going to look at the seventh number in the set.

18, 20, 22, 25, 26, 36, 37, 41, 45, 50

1     2     3    4    5    6    7    8    9   10

The seventh number in the set is 37.

We're going to do the same for finding the 40th percentile:

40% = 0.4

10 × 0.4 = 4

Finding the fourth number in the set...

18, 20, 22, 25, 26, 36, 37, 41, 45, 50

1     2     3    4    5    6    7    8    9   10

... We get 25

And those are you answers, 37 and 25.