Graph the polygon with the given vertices and its image after a reflection in the line y=x.
A(2, -1), B(-1, 2), C(2, 3), D(4,2)

Answer:

33cm

Step-by-step explanation:

385 / 35 = 11

11 times 3 = 33

The first four terms of the geometric sequence with a first term of 3 and a common ratio of 2 are 3, 6, 12, and 24.

To find the first four terms of a geometric sequence with a first term (a1) of 3 and a common ratio (r) of 2, we can use the formula for the nth term of a geometric sequence:

\(an = a1 * r^(n-1)\)

Substituting the given values, we have:

a1 = 3

r = 2

Let's calculate the first four terms (n = 1, 2, 3, 4) using the formula:

\(a1 = 3 * 2^(1-1) = 3 * 2^0 = 3 * 1 = 3\\a2 = 3 * 2^(2-1) = 3 * 2^1 = 3 * 2 = 6\\a3 = 3 * 2^(3-1) = 3 * 2^2 = 3 * 4 = 12\\a4 = 3 * 2^(4-1) = 3 * 2^3 = 3 * 8 = 24\)

Therefore, the first four terms of the geometric sequence with a first term of 3 and a common ratio of 2 are 3, 6, 12, and 24.

In summary, the terms of the sequence are obtained by multiplying the first term (a1) by the common ratio (r) raised to the power of (n-1), where n represents the term number.

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Answer:

5, 6

Step-by-step explanation:

Answer:

Los números son:

6 y 5

Step-by-step explanation:

Planteamiento:

a * b = 30

a + b = 11

Desarrollo:

De la segunda ecuación del planteamiento:

a = 11-b    

Sustituyendo esta última ecuación en la primer ecuación del planteamiento:

(11-b)*b = 30

11*b + b*-b = 30

11b - b² - 30 = 0

-b² + 11b - 30 = 0

b = {-11±√((11²)-(4*-1*-30))} / (2*-1)

b = {-11±√(121-120)} /-2

b = {-11±√1} / -2

b = {-11±1} / -2

b₁ = {-11-1} / -2 = -12/-2 = 6

b₂ = {-11+1} / -2 = -10/-2 = 5

Comprobación:

6*5 = 30

6+5 = 11

Solution:

1) Rose:

Rose curve equations have two forms: r = a cos(nθ) and r = a sin(nθ) where a ≠ 0 and n is a positive integers. Petals have length determined by a. If n is odd, the number of petals is n. However, if n is even, the number of petals is 2n.

The equation of a rose has two forms which are

The graph of a polar rose is given below as

2)Limacon:

The polar equation is in the form of a limaçon, r = a – b cos θ. Since the equation passes the test for symmetry to the polar axis, we only need to evaluate the equation over the interval [0, π] and then reflect the graph about the polar axis.

3)A circle:

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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Answer:

duuuuuuude if its easy then why do you need help huh answer me

Step-by-step explanation:

The equation of the image of the line  y = (3/2)x - 4 after a dilation of a scale factor of 3/4 centered at the origin.

What is line equation ?

A line equation is a mathematical expression that describes a line in a two-dimensional coordinate system. There are different ways to write a line equation, but one of the most common is the slope-intercept form:  

y = mx + b.

Apply the dilation to the equation of the line to get the equation of the dilated line in terms of the new coordinates.

Simplify the equation by solving for y in terms of x.

Step 1: Applying the dilation

A dilation of a scale factor of 3/4 centered at the origin will shrink the line by a factor of 3/4. This means that the x and y coordinates of any point on the line will be multiplied by 3/4.

So, we can write the equation of the dilated line in terms of the new coordinates (x', y') as follows:

y' = (3/2) * (3/4) * x' - 4 * (3/4)

y' = (9/8) * x' - 3

Step 2: Solving for y

To simplify the equation, we can solve for y in terms of x by replacing x' with x/3 and y' with y/3:

y/3 = (9/8) * (x/3) - 3

y/3 = (3/8) * x - 3

y = (9/8) * x - 9

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Answer:

  y = 3/2x -3

Step-by-step explanation:

You want the equation of the line y = 3/2x -4 after it has been dilated by a factor of 3/4 about the origin.

Dilation is a transformation that preserves angles and orientation, but changes the distance of each point from the center of dilation. This means the slope of the line is not changed, but the y-intercept is multiplied by the dilation factor:

  y = 3/2x -(3/4)(4)

  y = 3/2x -3 . . . . . . . . dilated line

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The area of the shaded region is  104 cm²

First, we need to know that the area of a circle is calculated using the formula;

A = πr²

Such that the parameters of the formula are;

First, let us find the area of the small circle

Area = 3.14 × 4²

Find the square value and multiply, we have;

Area = 50.24cm²

Area of the large circle = 3.14 × 7²

Find the square value and multiply

Area = 153. 86cm²

Area of the shaded region = Area of large circle - area of small circle

= 153.86 - 50.24

= 104 cm²

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As a result, at the start of year 16, Franklin's sign will for the first time display a larger number than Chester's sign.

An arrangement of things in a particular order is known as a permutation in mathematics. It is an organised collection of items drawn from a bigger set. The product of all positive numbers up to n yields n!, which is the number of permutations of a set of n items. Permutations are used in probability theory to determine the probabilities of specific outcomes occurring in a series of occurrences as well as in combinatorics to count the number of possible arrangements of objects in a collection.

given

Let F stand for Franklin's population in thousands and C for Chester's population in thousands. Next, we have:

At the start of the first year, F and C are both 20.

F grows by 5% year, while C grows by 0.5 annually.

We are looking for the first year that F > C occurred.

Let's construct the following equation for F and C at year n's end:

C(n) = 25 + 0.5n F(n) = 20(1.05)n

The smallest integer n for which 20(1.05)n > 25 + 0.5n is the one we are looking for.

Using a graphing calculator or trial and error, we can get the solution to this problem. The answer is that n = 15.

As a result, at the start of year 16, Franklin's sign will for the first time display a larger number than Chester's sign.

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Answer:

hundredths’ value in 12.984

hundredths’ value in 7.38

My response: In arithmetic, a hundredth is a single part of something that has been divided equally into a hundred parts. For example, a hundredth of 675 is 6.75. In this manner it is used with the prefix "centi" such as in centimeter. A hundredth is the reciprocal of 100.

The ratio of the volume of water in Jug B to the volume of water in Jug C is 35:18.

Let's assume the volume of water in Jug B is x.

According to the given information, Jug A contains 6/7 as much water as Jug B. Therefore, the volume of water in Jug A can be calculated as (6/7) * x.

Similarly, Jug C contains 3/5 as much water as Jug A. Hence, the volume of water in Jug C can be expressed as (3/5) * [(6/7) * x].

To find the ratio of the volume of water in Jug B to the volume of water in Jug C, we divide the volume of water in Jug B by the volume of water in Jug C:

(x) / [(3/5) * (6/7) * x]

Simplifying the expression, we get:

x / (18/35 * x)

The x values cancel out, leaving us with:

1 / (18/35)

To simplify further, we multiply the numerator and denominator by the reciprocal of the denominator:

1 * (35/18)

The final ratio is:

35/18

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The company must sell 400 radios to break even, i.e, when the revenue function and cost function is same.

The sum of the units sold times the price per unit is the revenue. Multiply the output level by the pricing function to get the revenue function.

The cost function is the total cost of production of the item which includes the cost of raw materials, labor, transport and establishment costs.

The cost function and the revenue function is given as:

Cost function is C(x) =5000 + 7.5x

And the revenue function is R(x) = 20x

a)In the break even point cost will be equal to revenue

so, C(x)=R(x)

or,5000+7.5x=20x

or,12.5x=5000

or, x=5000÷12.5

or, x=400

The number of radios produced to break even is 400.

(b)When the company breaks even then x=400

∴R(200)=200×20=8000

So the amount of money is dollars that is coming in or going out is given by 8000.

(c)We know that the profit=Revenue - cost

So the required profit function is given by:

p(x)=R(x)-C(x)

or, p(x)=20x-5000-7.5x

or,p(x)=12.5x-5000

(d)The company sells 500 radios

Therefore profit will be given by

p(500)=12.5×500-5000

or,p(500)=6250-5000

or, p(500)=1250

So on selling 500 radios the company will earn $1875.

Disclaimer: The revenue and cost function of the equation are  

C(x) =5000 + 7.5x and  R(x) = 20x .

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Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.

When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.

Increased employment opportunities result in more individuals having access to income and improved standards of living.

Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.

Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.

Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.

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Answer:

A) 3450, B) November to December

Answer:

True, When the clock transitions from 11:59am to 12:00pm, it is the first hour of noon.

Step-by-step explanation:

Answer:

15 pieces

Step-by-step explanation:

a ratio of 1:3 has 4 total parts, meaning that each part is 5.

20/3 = 15 so that means he has 5 pieces of chocolate and 15 of hard candy.

Answer:

15

Step-by-step explanation:

Answer: \(700\pi \text{ cm}^{2}\)

Step-by-step explanation:

\(V=\pi r^{2} h\\\\V=\pi(10)^{2}(7)\\\\ \boxed{V=700\pi \text{ cm}^{2}}\)

a. Expenses: Books and supplies, Housing and food, Tuition and fees, Transportation and Personal expenses. Funding: Savings,

Scholarships, Grants and Student loans.

b. Total estimated expenses are $29,400

(a) Below is an estimate of all her expenses and sources of funding for her 2-year college education.

Expense:

Books and supplies: $1700

Housing and food: $14,020

Tuition and fees: $11,660

Transportation: $2040

Personal expenses: $2980

Funding:

Savings: $7800

Scholarships: $10,240

Grants: $11,600

Student loans: $6200

(b) What is the total of her estimated expenses?

To find the total estimated expenses, we need to add up all the expenses mentioned:

$1700 + $14,020 + $11,660 + $2040 + $2980 = $29,400

Therefore, the total estimated expenses for Nicole's 2-year college education is $29,400.

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Answer:

A.4

Step-by-step explanation:

Using the sine rule

sin(α)/A equals sin(β)/B

From the question & inserting values,

sin(90°)/8 equals sin(30°)/x

∴x equals\(\frac{sin(30)}{sin(90)}\)×8

∴x equals 4

You can learn more on the sine rule in case you get confused.

Answer:

A

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = \(\frac{1}{2}\) , then

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{8}\) = \(\frac{1}{2}\) ( cross- multiply )

2x = 8 ( divide both sides by 2 )

x = 4

Answer:

A

Step-by-step explanation:

TAMa dahil kung wala ang graph of a relationship ano pa ba?

The operation manager is responsible to identify whether there are errors in quality of the tires manufactured.

There are three different shifts and each shift has different team of workers who manufacture tires. For this we test hypothesis as;

H0 ; Quality of tire manufactured is independent on shifts

Ha ; Quality of tires manufactured is dependent on shifts.

The p value of chi squared test is greater than the significance level therefore we reject the null hypothesis.

This hypothesis reach to conclusion that quality of tires is dependent on shifts, which means there are differences in quality among the three shifts.

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

\(W=31T+500\),

903 liters

Step-by-step explanation:

Multiply the total number of minutes, T, with 31 liters per minute, to get 31T liters. Then add the initial 500 liters. So \(W=31T+500.\)

Substituting T=13 in the equation above results in

\(\begin{aligned}\\W&=31T+500\\&=31(13)+500\\&=403+500\\&=903.\end{aligned}\)

Hence, there are 903 liters after 13 minutes.