Consider the set K = (triangle upsidedown triangle square rectangle)


Let inversion be defined on K as a physical act of turning a member of K upside down. What is triangle?

To solve this problem, we can use the trigonometric functions sine, cosine, and tangent.

First, let's draw a diagram:

             A (top of the mountain)

            /|

           / |

         /    |  h (height of mountain)

       /      |

     / θ     |

B /_____|

   d (distance from base)

We are given that the distance from the base of the mountain to point B is 1/2 mile, or 2640 feet (since there are 5280 feet in a mile). We are also given that the angle of elevation from point B to point A is 65 degrees, and that the angle between the ski lift and the ground is 15 degrees.

Let's start by finding the height of the mountain h. We can use the tangent function, since we know the opposite (h) and the adjacent (d) sides of the right triangle formed by points A, B, and the foot of the mountain (call it point C):

tan(65) = h / d

h = d * tan(65)

Plugging in the values, we get:

h = 2640 * tan(65)

h ≈ 7855 feet

Next, let's find the length of the ski lift. We can use the cosine function, since we know the adjacent (d) and hypotenuse (L) sides of the right triangle formed by points B, the foot of the mountain, and the base of the ski lift (call it point D):

cos(15) = d / L

L = d / cos(15)

Plugging in the values, we get:

L = 2640 / cos(15)

L ≈ 2736 feet

Therefore, the length of the ski lift from the beginning to the end is approximately 2736 feet.

Answer:

Step-by-step explanation:

Imaginary Numbers are 21. (5+2i)/ 4i is  -(5/4) + (1/2)i, 22. 3i/(-2+i) is -1.5i + 0.75. 23. (3-2i)/(4-3i) is 4/5 + (1/25)i, 24. 7/(5-2i) is (14/29) + (7/29)i.

In mathematics, imaginary numbers are a type of complex number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

Imaginary numbers were first introduced in the 16th century as a solution to certain polynomial equations that did not have real solutions. They were initially met with skepticism and derision, but eventually became widely accepted as a fundamental part of complex analysis and number theory.

One of the key properties of imaginary numbers is that when they are multiplied by themselves, the result is always a negative real number. For example, i * i = -1. This property is what makes imaginary numbers useful for representing certain physical quantities, such as the amplitude and phase of an oscillating system.

21. (5+2i)/ 4i = -(5/4) + (1/2)i

To divide complex numbers, we can multiply the numerator and denominator by the conjugate of the denominator. Here, the conjugate of 4i is -4i.

(5+2i)/ 4i = (5+2i)/4i * (-4i/-4i)

= -(20i - 8)/(-16)

= -(20i - 8)/16

= -(5/4) + (1/2)i

Therefore, (5+2i)/ 4i = -(5/4) + (1/2)i.

22. 3i/(-2+i) = -1.5i + 0.75

We can again use the conjugate to simplify the division of complex numbers.

3i/(-2+i) = 3i/(-2+i) * (-2-i)/(-2-i)

= (-6i -3)/(-5)

= 3/5 + 1.5i

Therefore, 3i/(-2+i) = -1.5i + 0.75.

23. (3- 2i)/(4-3i) = (18+5i)/25

Using the conjugate:

(3-2i)/(4-3i) = (3-2i)/(4-3i) * (4+3i)/(4+3i)

= (12+9i-8i-6i²)/(16+12i+12i-9i²)

= (20+i)/25

= 20/25 + (1/25)i

= 4/5 + (1/25)i

Therefore, (3-2i)/(4-3i) = (18+5i)/25 = 4/5 + (1/25)i.

24. 7/(5-2i) = (14/29) + (7/29)i

Using the conjugate:

7/(5-2i) = 7/(5-2i) * (5+2i)/(5+2i)

= (35+14i)/(29)

= (14/29) + (7/29)i

Therefore, 7/(5-2i) = (14/29) + (7/29)i.

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A hemisphere over the cone with a radius of 10 cm and a height of 15 cm.

a) volume of the cone: V = 1570.8 cm³

b) volume of the hemisphere: V = 2093.33 cm³

c) voume of the entire figure : V= 3664.13 cm³

a) The formula V = (1/3)r2h, where r is the cone's radius and h is its height, determines the volume of the cone.

Substituting r = 10 cm and h = 15 cm, we get:

V = (1/3)π(10 cm)²(15 cm)

V ≈ 1570.8 cm³

The volume of the cone is approximately 1570.8 cm³.

b) The volume of the hemisphere is given by the formula V = (2/3)πr³, where r is the radius of the hemisphere. Since the hemisphere has the same radius as the cone, i.e., r = 10 cm, we get:

V = (2/3)π(10 cm)³

V = 2093.33 cm³

The volume of the hemisphere is approximately 2093.33 cm³.

c) The volume of the entire figure is the sum of the volume of the cone and the volume of the hemisphere. Adding the volumes of the two shapes, we get:

V = 1570.8 cm³ + 2093.33 cm³

V = 3664.13 cm³

The volume of the entire figure is approximately 5759.6 cm³.

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Answer:

u = 2√3;

v = 2

Step-by-step explanation:

Use trigonometry:

[tex] \cos(60°) = \frac{v}{4} [/tex]

Cross-multiply to find v:

[tex]v = 4 \times \cos(60°) = 4 \times 0.5 = 2[/tex]

Use the Pythagorean theorem to find u:

[tex] {u}^{2} = {4}^{2} - {v}^{2} [/tex]

[tex] {u}^{2} = {4}^{2} - {2}^{2} = 16 - 4 = 12[/tex]

[tex]u > 0[/tex]

[tex]u = \sqrt{12} = \sqrt{4 \times 3} = 2 \sqrt{3} [/tex]

Answer:

1 21/29

Step-by-step explanation:

Answer: Approximately $4,176.19 today for an investment that returns $800 each year for 6 years

Step-by-step explanation:

To calculate the present value of an investment that returns $800 each year for 6 years at a discount rate of 4 percent, we can use the formula for the present value of an annuity:

PV = C x [(1 - (1 / (1 + r)^n)) / r]

where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of years.

Plugging in the given values, we get:

PV = 800 x [(1 - (1 / (1 + 0.04)^6)) / 0.04]

PV = $4,176.19 (rounded to the nearest cent)

Therefore, if the discount rate is 4 percent, you would be willing to pay approximately $4,176.19 today for an investment that returns $800 each year for 6 years

Dοnοvan's hοurly wage than his brοther's hοurly wag wοuld be, $7.98/hοur

Average salary is the average amοunt οf mοney earned by wοrkers in a particular industry, ecοnοmy, area, etc.

Tοtal hοurs wοrked by Dοnοvan = 40 hοurs/week x 48 weeks/year = 1,920 hοurs/year

Next, we can calculate Dοnοvan's hοurly wage:

Hοurly wage οf Dοnοvan = Annual salary οf Dοnοvan / Tοtal hοurs wοrked by Dοnοvan

= $55,000 / 1,920 hοurs/year

= $28.65/hοur

Similarly, we can find the tοtal number οf hοurs that his brοther wοrks in a year:

Tοtal hοurs wοrked by Dοnοvan's brοther = 40 hοurs/week x 52 weeks/year = 2,080 hοurs/year

Hοurly wage οf Dοnοvan's brοther = Annual salary οf Dοnοvan's brοther / Tοtal hοurs wοrked by Dοnοvan's brοther

= $43,000 / 2,080 hοurs/year

= $20.67/hοur

Difference in hοurly wages = Hοurly wage οf Dοnοvan - Hοurly wage οf Dοnοvan's brοther

= $28.65/hοur - $20.67/hοur

= $7.98/hοur

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Answer: your originally supposed to use arrows to show end behaviors  

graph one down /up

graph two down/ down

graph three up/ down

Step-by-step explanation:

pretty sure this is the answer if your asking for the end behaviors

Therefore, the second rectangle has a greater area than the first rectangle.

A rectangle is a quadrilateral geometric shape that has four sides and four right angles (90-degree angles). It is characterized by having opposite sides that are equal in length and parallel to each other. The rectangle's other two sides are also equal in length and parallel to each other but different in length than the opposite sides.

The area of a rectangle is calculated by multiplying its length by its width, which gives the total amount of space inside the shape. The perimeter of a rectangle is the sum of all its sides.

To find the area of a rectangle, we multiply its length by its width. Therefore, the area of the first rectangle is:

Area of first rectangle = 12 ft × 1 ft = 12 sq ft

And the area of the second rectangle is:

Area of second rectangle = 16 ft × 1 ft = 16 sq ft

Therefore, the second rectangle has a greater area than the first rectangle.

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Answer:

60°

120°

Step-by-step explanation:

Supplementary angle are those that sum up to a total of 180 degrees.

So, let's have 2 angles, angle A and angle B.

Angle A's measure is α so the measure of angle B is 2α.

The sum of these two angles sum up to 180 degrees, so we can say that:

α + 2α = 180°

3α = 180°

α = 60°

So, one of our angles is 60° and the other is (2*60)° which is 120°.

The number of rows and columns in the specified matrix and the matrix element are; 2 rows and 3 columns, the correct option is therefore;

a. 2 × 3; 1, which is option A

The common form of denoting the elements in a matrix is by using a letter and two subscripts in the form; A[tex]_{ij}[/tex].

The specified matrix can be presented as follows;

[tex]\begin{bmatrix}-4 &1 &-3 \\ 2& 1& 0 \\\end{bmatrix}, a_{12}[/tex]

The size of a matrix is indicated by the number of rows and columns in the matrix. The size of a matrix is usually indicated as m × n where;

m × n = Number of rows × Number of columns

Where;

m = The number of rows

n = The number of columns

The number of rows in the specified matrix are two rows

The number of columns in the matrix are three columns

The size of the specified matrix therefore is; 2 × 3

The position of a matrix element is similarly indicated by two subscripts, the first indicating the row number of the element and the second indicating the column number of the matrix.

Therefore;

a₁₂ is the element in the first row and in the second column, which is the number 1

The correct option is therefore;

a. 2 × 3; 1

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Answer:

then she will have 139.67 left

Answer-

1/8 because their are 8 peices and 1 of them are blue and 2 of them are yellow so it become 1/8

Answer:

ans is 1/6

because its sure spinner not land on the yelow so two pieces neglect

so prob =favourable cases/total cases

blue has one piece only

1/6

The length of side AC of right triangle ABC is 13. So,the option A is correct

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted Δ triangle ABC.

We can use the trigonometric ratios of right triangle ABC to find the value of y. 

 We label the sides of the triangle as follows: 

 Side AB (opposite angle C) is the hypotenuse. 

 The length of side BC (opposite angle A) is 13. 

 Side AC (opposite angle B) is the unknown side called y. 

 Since angl

e A is 45 degrees, we know that the sine and cosine of angle A are equal: 

 sin(A) = cos(A) = 1/√2 

 Using the Pythagorean theorem, we can relate the lengths of the sides of a triangle: 

 AB² = AC² BC² 

 Substituting the known values, we get: 

 AB² = y² 169 

 Taking the square root of both sides gives us: 

 AB = √(y² 169) 

 Now we can use the sine ratio to relate the length of the sides: 

 sin(A) = opposite/hypotenuse 

 Substituting the known values, we get: 

 1/√2 = and/√(y² 169) 

 By cross linking and simplifying, we get: 

 y√2 = √(y² 169) 

 Squaring both sides we get: 

 2y² = y² 169 

 Subtracting y² from both sides, we get: 

 y² = 169/1 

 Taking the square root of both sides gives us: 

 y = ±13 

 Since y represents length, we can reject the negative solution and the value of y is: 

 y = 13 

 Therefore, the length of side AC of right triangle ABC is 13.

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The width of the rectangular rug is 13 feet and the length of the rectangular rug is 26 feet.

Area of a rectangle formula: A = L * W. A

rectangle's length and width are multiplied to produce its area.

A is the area, L is the length, and W is the width or girth, where

A = L * W.

The corresponding sides of the rectangular rug and the rectangular floor must be proportional if they are alike.

Let's use "x" to represent the rug's width. The floor measures 32 feet in length and 26 feet in width, and the length of the rug is 16 feet according to the details provided. Since the rug and the surface are comparable, we can establish the following ratio:

Rug width/floor width = rug length/floor length

x / 26 = rug's length / 32

We can cross-multiply and then solve for "x" to find the answer:

32x = 26 * Rug's length

x =  (26 * Rug Length) / 32

[tex]= \frac{26 * 16}{32} \\= \frac{26}{2} \\= 13[/tex]

Therefore x ( the width of the rug) is = 13 feet.

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Complete question:

The rectangular rug is similar to the rectangular floor. If the floor of the room measures 32 feet in length and 26 feet in width, and the length of the rug is 16 feet, what is the width of the rug?

Answer:

60

Step-by-step explanation:

Since this is a right triangle, the longest side can be solved using the Pythagorean Theorem

x^2 + y^2 = z^2

So

15^2 + 20^2 = 225 + 400 = 625 = 25^2.

So 25 is hypotenuse.

Add them all together : 25+15+20 = 60.

So your answer is 60.

Answer:

60

Step-by-step explanation:

A squared + B squared = C squared

15 squared + 20 squared = C squared

225 + 400 = C squared

625  = C squared

Use radicals to find the square root of 625

Which is 25

C = 25

25 + 15 + 20 =

60

The approximate perimeter of the entire shape is 77.69 inches.

The perimeter of a figure is the sum of the whole sides of the figure.

Therefore, the perimeter of the entire shape can be calculated as follows:

The shape is made of three sides of a square and half a circle.

Therefore,

circumference of the semi circle [tex]= \pi r[/tex]

[tex]r = 17 \div 2 = 8.5 \ \text{inches}[/tex]

circumference of the semi circle [tex]= 8.5\pi[/tex]

Hence,

perimeter of the shape [tex]= 17+17+17+ 8.5\pi[/tex]

perimeter of the shape [tex]= 51 + 8.5(3.14)[/tex]

perimeter of the shape [tex]= 51 + 26.69[/tex]

Therefore,

perimeter of the shape = 77.69 inches

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Answer:

The following statements about Josiah's solution are true:

1. He predicted the number of rock songs on his MP3 player to be 300 songs. (This is stated in the problem description.)

2. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. (This is true, as he should have divided both the numerator and denominator of the first fraction by 2 to simplify it.)

3. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500. (This is true, as he needed to find a common multiple of 20 and 1,500 to set up the proportion correctly.)

The area of the shaded parts are:

1. Area of shaded part = 165.76 cm²

2. Area of shaded part = 736 cm²

3. Area of shaded part = 155.52 cm²

4. Area of shaded part = 169 cm²

From the question, we are to determine the area of the shaded parts

1.

Area of shaded part = Area of triangle - Area of circle

Area of shaded part = (1/2 × base × height) - (πr²)

Area of shaded part = (1/2 × 18 × 24) - (3.14 × 4²)

Area of shaded part = 216 cm² - 50.24 cm²

Area of shaded part = 165.76 cm²

2. Area of shaded part = = (32 × 24) - (8 × 4)

Area of shaded part = = 768 - 32

Area of shaded part = 736 cm²

3.

Area of shaded part = Area of square - Area of semicircle

Area of shaded part = (length)² - (1/2πr²)

Area of shaded part = 16² - (1/2 × 3.14 × 8²)

Area of shaded part = 256 - 100.48

Area of shaded part = 155.52 cm²

4.

Area of shaded part = (1/2 × 26 × 13)

Area of shaded part = 169 cm²

Hence, the area of the shaded part is 169 cm²

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The perimeter of scale drawing of Central Park is 30 centimeter.

The area of scale drawing of Central Park is 31.25 square centimeters.

What is perimeter?

The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.

Given that Central Park is a rectangular park in New York City

The measured length is 12.5 centimeters

The measured width is 2.5 centimeters

The perimeter of scale drawing of Central Park is given as:

Given is a rectangular park

perimeter of rectangular = 2(length + width)

perimeter of rectangular = 2(12.5 + 2.5)

perimeter of rectangular = 2(15) = 30

Thus perimeter is 30 centimeter

The area of scale drawing of Central Park is given as:

area = length x width

area = 12.5 x 2.5 = 31.25 cm²

Thus area of rectangular park is 31.25 square centimeters

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Volume of  6 3/4 cups of water is equal to 54 cups of water.

What is Volume?

One cup is equal to 8 fluid ounces. Therefore, to convert 6 3/4 cups to fluid ounces, we can multiply by 8:

6 3/4 cups = (6 x 8) + (3/4 x 8) cups = 48 + 6 = 54 cups

So, 6 3/4 cups of water is equal to 54 cups of water.

What is fluid?

A fluid is a substance that has the ability to flow and take the shape of its container. Fluids include liquids, gases, and plasmas.

Liquids are a common type of fluid that can flow and take the shape of their container, but have a definite volume. Some examples of liquids include water, oil, and milk.

Gases are another type of fluid that can flow and fill the entire volume of their container, taking on the shape of the container. Some examples of gases include air, oxygen, and nitrogen.

Plasmas are a unique type of fluid that occurs at very high temperatures, in which some or all of the atoms or molecules have been ionized, resulting in the presence of free electrons and positive ions. Some examples of plasmas include lightning, the sun, and neon lights.

Fluids are important in many fields, including physics, engineering, and biology. They play a critical role in many processes, such as the circulation of blood in the body, the flow of water in a river, and the movement of air in the atmosphere.

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1) AC || DF; BC ≅ DE , 2) )Alternate interior angles formed by transversal BC and parallel lines AC and DF are congruent 3) Identity Property of Congruence (Any segment is congruent to itself)

what is Congruence?

In mathematics, congruence is a term used to describe the relationship between two geometric figures that have the same shape and size. Two objects are said to be congruent if they are identical in shape and size.

In the given question,

STATEMENTS

AC || DF; BC ≅ DE

<CBE ≅ <DEB

BE ≅ BE

∆DBE ≅ ∆BEC

REASONS

1)Given

2)Alternate interior angles formed by transversal BC and parallel lines AC and DF are congruent

3) Identity Property of Congruence (Any segment is congruent to itself)

4) SAS (Side-Angle-Side) Congruence Postulate (Since BC and BE are congruent and <DBE and <BEC are congruent, and BE is common to both triangles)

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(A). the current sale price of the computer system is $543.20.

Therefore, members of the store's loyalty club pay $488.88 for the computer system with their discount.

Find the current sale price. Round to the nearest cent if necessary.

• Members of the store's loyalty club get an additional 10% off their computer purchases. How much do club members pay for the computer with their discount?

To find the current sale price, we first need to calculate the markdown amount. We know that the markdown is 30% of the original selling price, which is $776, so the markdown amount is:

30% of $776 = 0.30 x $776 = $232.80

The sale price is then the original selling price minus the markdown amount:

Sale price = $776 - $232.80 = $543.20

Therefore, the current sale price of the computer system is $543.20.

Next, we need to calculate the price that club members pay after their discount. We know that club members get an additional 10% off the sale price, which is $543.20, so their discount amount is:

10% of $543.20 = 0.10 x $543.20 = $54.32

The price that club members pay is then the sale price minus their discount amount:

Price for club members = $543.20 - $54.32 = $488.88

Therefore, members of the store's loyalty club pay $488.88 for the computer system with their discount.

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We can start by finding the sum of the given numbers and equating it to the product of 20 and 8 (the number of elements):

6 + 29 + 3 + 14 + q + (q+8) + Q^2 + (q-10) = 20 * 8

Simplifying the left side by combining like terms, we get:

2q^2 + 20q - 100 = 124

Bringing everything to one side, we get:

2q^2 + 20q - 224 = 0

Dividing both sides by 2, we get:

q^2 + 10q - 112 = 0

Now, we can use the quadratic formula to solve for q:

q = (-10 ± √(10^2 - 4(1)(-112))) / (2(1))

q = (-10 ± 18) / 2

So the possible values of q are:

q = 4 or q = -14

To verify, we can substitute these values back into the original equation and see if the mean is indeed 20:

For q = 4:

(6 + 29 + 3 + 14 + 4 + 12 + 16 + -6) / 8 = 20 (checks out)

For q = -14:

(6 + 29 + 3 + 14 - 14 - 6 + 196 + -24) / 8 = 20 (checks out)

Therefore, the possible values of q are 4 and -14.

a) the angular speed of a point on its equator in radians per day is 6 rad/day.

b) the linear speed of a point on the equator in miles per day is 2 ×10² m.

What is angular speed?

Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows: ω = θ t. where θ is the angular displacement, t is the time and ω is the angular speed.

Here, we have

Given: Suppose that Mars rotates on its axis once every hour. The equator lies on a circle with a diameter of miles.

a) The angular velocity is

 W = θ / t

 t = 1 day (24 h / 1 day) (3600s / 1 h) = 86400 s

w = 2π / 86400

w = 7.27 10⁻⁵ rad / s

Reduce to rad/day

 w = 7.27 rad / s (3600s / 1 h) (24 h / 1 day)

w = 6.28 rad/day

w= 6 rad/day

Hence, the angular speed of a point on its equator in radians per day is 6 rad/day.

b) the linear velocity is

v = w r

Mercury radius is

r = 2.43 106 m

v =  7.27 10⁻⁵ 2.43 10⁶

v = 1.76661 10² m / s

v = 2 ×10² m

Hence, the linear speed of a point on the equator in miles per day is 2 ×10² m.

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Answer:

(a) After 9 months, the unpaid balance is $125,874.09.

(b) Over the 9 months, she paid a total of $4,918.56 in interest.

To create the amortization table, we can use the formula for calculating the monthly payment of a loan:

P = (r * A) / (1 - (1 + r)^(-n))

where:

P = monthly payment

r = monthly interest rate

A = loan amount

n = total number of payments

In this case, we have:

A = $128,000.00

n = 25 years * 12 months/year = 300 months

r = 5.3% / 12 = 0.00441666667

Using the formula, we can calculate the monthly payment:

P = (0.00441666667 * $128,000.00) / (1 - (1 + 0.00441666667)^(-300))

P = $770.82

Now, we can create the amortization table: