in a plane, four circles with radii 1,3,5, and 7 are tangent to line l at the same point a, but they may be on either side of l. region s consists of all the points that lie inside exactly one of the four circles. what is the maximum possible area of region s?

Answers

Answer 1

Answer: Let us call the centers of the four circles C1, C3, C5, and C7, respectively, where the subscript refers to the radius of the circle. Without loss of generality, we can assume that the tangent point A lies to the right of all the centers, as shown in the diagram below:

o-----------o

C5 / \ C3

/ \

o-----------------o

| l

Let us first find the coordinates of the centers C1, C3, C5, and C7. Since all the circles are tangent to line l at point A, the centers must lie on the perpendicular bisector of the line segment joining A to the centers. Let us denote the distance from A to the center Cn by dn. Then, the coordinates of Cn are given by (an, dn), where an is the x-coordinate of point A.

Using the Pythagorean theorem, we can write the following equations relating the distances dn:

d1 = sqrt((d3 - 2)^2 - 1)

d3 = sqrt((d5 - 4)^2 - 9)

d5 = sqrt((d7 - 6)^2 - 25)

We can solve these equations to obtain:

d1 = sqrt(16 - (d7 - 6)^2)

d3 = sqrt(4 - (d7 - 6)^2)

d5 = sqrt(1 - (d7 - 6)^2)

Now, let us consider the region S that lies inside exactly one of the four circles. This region is bounded by the circle of radius 1 centered at C1, the circle of radius 3 centered at C3, the circle of radius 5 centered at C5, and the circle of radius 7 centered at C7. Since the circles are all tangent to line l at point A, the boundary of region S must pass through point A.

The maximum possible area of region S occurs when the boundary passes through the centers of the two largest circles, C5 and C7. To see why, imagine sliding the circle of radius 1 along line l until it is tangent to the circle of radius 3 at point B. This increases the area of region S, since it adds more points to the interior of the circle of radius 1 without removing any points from the interior of the other circles. Similarly, sliding the circle of radius 5 along line l until it is tangent to the circle of radius 7 at point C also increases the area of region S. Therefore, the boundary of region S must pass through points B and C.

Using the coordinates we obtained earlier, we can find the x-coordinates of points B and C as follows:

x_B = a - 2 - sqrt(9 - (d7 - 6)^2)

x_C = a + 6 + sqrt(9 - (d7 - 6)^2)

To maximize the area of region S, we want to maximize the distance BC. Using the distance formula, we have:

BC^2 = (x_C - x_B)^2 + (d5 - d3)^2

Substituting the expressions we derived earlier for d3 and d5, we get:

BC^2 = 32 - 2(d7 - 6)sqrt(9 - (d7 - 6)^2)

To maximize BC^2, we need to maximize the expression inside the square root. Let y = d7 - 6. Then, we want to maximize:

f(y) = 9y^2 - y^4

Taking the derivative of f(y) with respect to y and setting it equal to zero, we get:

f'(y) = 18y - 4y^3 = 0

This equation has three solutions: y = 0, y = sqrt(6)/2, and y = -sqrt(6)/2. The only solution that gives a maximum value of BC^2 is y = sqrt(6)/2, which corresponds to d7 = 6 + sqrt(6)/2.

Substituting this value of d7 into our expressions for d1, d3, and d5, we obtain:

d1 = sqrt(16 - (sqrt(6)/2)^2) = sqrt(55/2)

d3 = sqrt(4 - (sqrt(6)/2)^2) = sqrt(19/2)

d5 = sqrt(1 - (sqrt(6)/2)^2) = sqrt(5/2)

Using these values, we can compute the coordinates of points B and C as follows:

x_B = a - 2 - sqrt(9 - (sqrt(6)/2)^2) = a - 2 - sqrt(55)/2

x_C = a + 6 + sqrt(9 - (sqrt(6)/2)^2) = a + 6 + sqrt(55)/2

The distance between points B and C is then:

BC = |x_C - x_B| = 8 + sqrt(55)

Finally, the area of region S is given by:

Area(S) = Area(circle of radius 5 centered at C5) - Area(circle of radius 7 centered at C7)

= pi(5^2) - pi(7^2)

= 25pi - 49pi

= -24pi

Since the area of region S cannot be negative, the maximum possible area is zero. This means that there is no point that lies inside exactly one of the four circles. In other words, any point that lies inside one of the circles must also lie inside at least one of the other circles.

Step-by-step explanation:

Related Questions

does the math term "mean," mean avarage of most common?

Answers

Answer: The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.

Step-by-step explanation: You can find the mean, or average, of a data set in two simple steps: Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.

11. Phyllis ran in a 5-kilometer race to help raise money for the school. How many meters long is the race?

Answers

Answer:5000 meters

Step-by-step explanation:1km=1000m

50 POINTS PLEASE HELP

Answers

We know that a^2b^3=108. We can factor 108 into its prime factors: 108 = 2^2 x 3^3. We can then rewrite a^2b^3 as (a^2)(b^3) = (2^2)(3^3).

Since a and b are positive integers, we can see that a^2 must be one of the factors of 2^2, and b^3 must be one of the factors of 3^3. The only pairs of factors that multiply to 108 and satisfy these conditions are (a^2, b^3) = (2^2, 3^3) and (a^2, b^3) = (1, 108).

The first pair gives us a=2 and b=3, while the second pair gives us a=1 and b=108. Since a and b are positive integers, we can discard the second solution, so we have a=2 and b=3.

Finally, we can substitute these values into the expression 2a + 3b to get:

2a + 3b = 2(2) + 3(3) = 4 + 9 = 13.

Therefore, the value of 2a + 3b is 13.

please i need your help for today please i would really appreciate it

Answers

Answer:

increasing: x > 0

Step-by-step explanation:

Given a table of function values, you want to know the interval on which the function is increasing.

Increasing

A function is increasing if f(x)-values get larger when x-values get larger. As we go down the table, the x-values get larger.

In the first three lines of the table, the f(x)-values are getting smaller. The function is decreasing on that interval, x < 0.

In the last three lines of the table, the f(x) values are getting larger. The function is increasing on that interval, x > 0.

Additional comment

The point (0, 0) represents a minimum. The function is not increasing or decreasing at that point, so the interval of interest is x > 0, not x ≥ 0.

Depreciation by Three Methods; Partial Years Perdue Company purchased equipment on April 1 for $41,550. The equipment was expected to have a useful life of three years, or 5,700 operating hours, and a residual value of $1,650. The equipment was used for 1,000 hours during Year 1, 2,000 hours in Year 2, 1,700 hours in Year 3, and 1,000 hours in Year 4. Required: Determine the amount of depreciation expense for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, by (a) the straight-line method, (b) the units-of-activity method, and (c) the double-declining-balance method. Note: Round all final values for each depreciation method and each year to the nearest whole dollar

Answers

a) The depreciation expenses for Year 1 to Year 4 using the straight-line method are $2,632, $5,263, $4,211, and $2,632, respectively.

b) Using the units-of-activity method, the depreciation expenses are $7,000, $14,000, $11,900, and $7,000, respectively.

c) Using the double-declining-balance method, the depreciation expenses are $4,658, $11,172, $7,302, and $2,640, respectively.

a) To calculate the depreciation expense for each year using the straight-line method, the company needs to first determine the depreciable cost of the equipment. This is the cost of the equipment minus its estimated residual value.

The depreciable cost is $41,550 - $1,650 = $39,900.

To calculate the annual depreciation expense using the straight-line method, divide the depreciable cost by the useful life of the equipment, which is three years.

Year 1: ($39,900 ÷ 3) × (1,000 ÷ 5,700) = $2,632

Year 2: ($39,900 ÷ 3) × (2,000 ÷ 5,700) = $5,263

Year 3: ($39,900 ÷ 3) × (1,700 ÷ 5,700) = $4,211

Year 4: ($39,900 ÷ 3) × (1,000 ÷ 5,700) = $2,632

b) To calculate the depreciation expense using the units-of-activity method, the company needs to first determine the depreciation rate per unit of activity. This is the depreciable cost of the equipment divided by its total estimated hours of use.

The depreciation rate per unit of activity is $39,900 ÷ 5,700 hours = $7 per hour.

Year 1: $7 × 1,000 hours = $7,000

Year 2: $7 × 2,000 hours = $14,000

Year 3: $7 × 1,700 hours = $11,900

Year 4: $7 × 1,000 hours = $7,000

c) To calculate the depreciation expense using the double-declining-balance method, the company needs to first determine the straight-line depreciation rate. This is the depreciable cost of the equipment divided by its useful life.

The straight-line depreciation rate is $39,900 ÷ 3 years = $13,300 per year.

The double-declining-balance depreciation rate is twice the straight-line rate, or $13,300 × 2 = $26,600.

Year 1: $26,600 × (1,000 ÷ 5,700) = $4,658

Year 2: ($39,900 - $4,658) × (2,000 ÷ 5,700) = $11,172

Year 3: ($39,900 - $4,658 - $11,172) × (1,700 ÷ 5,700) = $7,302

Year 4: ($39,900 - $4,658 - $11,172 - $7,302) × (1,000 ÷ 5,700) = $2,640

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A sign on the roadway at the top of a mountain indicates that for the next 4 miles the grade is 9.5° (see figure). Find the change in elevation for a car descending the 4-mile stretch. (Round your answer to two decimal places.)

Answers

Step-by-step explanation:

We can use trigonometry to solve this problem. The grade of the road is given as an angle of 9.5°. This means that for every 1 unit of horizontal distance traveled, the elevation changes by the tangent of 9.5°.

We want to find the change in elevation for a car descending the 4-mile stretch. To do this, we can multiply the length of the road by the tangent of the grade angle:

Change in elevation = 4 miles x tan(9.5°)

Using a calculator, we can find that tan(9.5°) = 0.1664. Substituting this value into the equation, we get:

Change in elevation = 4 miles x 0.1664 ≈ 0.67 milesTo convert this to feet, we can multiply by the number of feet in a mile:

Change in elevation = 0.67 miles x 5,280 feet/mile ≈ 3,539 feetTherefore, the change in elevation for a car descending the 4-mile stretch is approximately 3,539 feet.

The length of ribbons found at a seamstress are listed.

5, 8, 10, 12, 12, 19

What is the appropriate measure of variability for the data shown, and what is its value?

The range is the best measure of variability and equals 14.
The IQR is the best measure of variability and equals 4.
The mean is the best measure of variability and equals 11.
The median is the best measure of variability and equals 11.

Answers

The most appropriate measure of variability which can be used for the data given is IQR and the measure is 4.

Given data set is,

5, 8, 10, 12, 12, 19

Mean and median are the measures of central tendency and not variability.

So they are not appropriate.

Remaining options are Range and IQR.

Range is the difference of the maximum value and the minimum value.

Here, range = 19 - 5 = 14

But range will be affected by the outliers and is not an appropriate measure of variability.

Remaining is IQR, which is the measure of the spread of middle 50% of the data.

IQR = Third quartile - First quartile.

Third quartile = 12 and the first quartile = 8

IQR = 12 - 8 = 4

Hence the appropriate measure is IQR.

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A salesman and 30% commission on all merchandise that he sells last month. He sold $700 worth of merchandise how much commission in dollars did he earn last month

Answers

The salesman earned $210 in commission last month. (30% of $700 is 0.3 x $700 = $210)

in a city of 100,000 voters, 40% are democrat, 30% republican, 20% green, and 10% undecided. a sample of 1000 people is selected. (a) what is the expectation and variance for the number of greens in the sample?

Answers

The variance of the number of green voters in the sample is 160.

What is variance?

In statistics, variance is a measure of the spread or variability of a set of data. It measures how much the values in a dataset differ from the mean or average value. Specifically, variance is the average of the squared differences from the mean.

We can use the binomial distribution to model the number of green voters in the sample, where the probability of success (voter being green) is p = 0.2 and the number of trials (voters in the sample) is n = 1000.

The expectation or mean of the number of green voters in the sample is given by the formula:

E(X) = np

where X is the random variable representing the number of green voters in the sample. Substituting the values, we get:

E(X) = 1000 * 0.2 = 200

So we expect to see about 200 green voters in the sample.

The variance of the number of green voters in the sample is given by the formula:

Var(X) = np(1 - p)

Substituting the values, we get:

Var(X) = 1000 * 0.2 * (1 - 0.2) = 160

So the variance of the number of green voters in the sample is 160.

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what is 100000^3? my caculater wont tell me!

Answers

Answer:

1e+15 or 1.000.000.000.000.000

Step-by-step explanation:

what is 100000^3? my caculater wont tell me!

100000³ = 100000 × 100000 × 100000

100000 × 100000 × 100000 =

10000000000 × 100000 =

1e+15 or 1.000.000.000.000.000

3) Which experience uses social and professional connections to learn more about jobs from others?

Question 3 options:

informational interview

job shadowing

internship

networking

Answers

Networking is the experience that uses social and professional connections to learn more about jobs from others. So, correct option is D.

It involves building and maintaining relationships with individuals who can offer information, advice, or support related to one's career goals. Networking can be done in various settings such as professional organizations, conferences, social events, and online platforms.

It can also involve exchanging information, sharing experiences, and providing referrals or recommendations. By networking, individuals can learn about job opportunities, industry trends, and insights into different career paths.

Additionally, networking can lead to mentorship and collaboration, which can help individuals develop their skills and expand their professional network further. Networking is an essential aspect of career development, as it can help individuals gain exposure and access to new opportunities that can lead to career advancement.

So, correct option is D.

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How many miles go into 10,000 kilometers

Answers

Answer:

Step-by-step explanation:

6213.712

Answer:

10,000 Kilometers = 6,213.7119 Miles

Step-by-step explanation:

Question 4 of 10
Does this table represent a function? Why or why not?
X
2
3
4
5
5
y
1
4
4
2
5
OA. Yes, because there is the same number of x-values as y-values.
OB. Yes, because every x-value corresponds to exactly one y-value.
C. No, because one x-value corresponds to two different y-values.
OD. No, because two of the y-values are the same.

Answers

Does this table represent a function: C. No, because one x-value corresponds to two different y-values.

What is a function?

In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, all functions are used in mathematics to uniquely map an input variable (domain or independent values) to an output variable (range or dependent values).

Based on the table shown above, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);

3 → 4

4 → 4

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PLEASE HELP WITH EXPLANATION AND ANSWER ASAP

Answers

The graph of the solution would be a number line with an open circle at 48 and an arrow extending to the right, indicating all values greater than 48 are solutions to the inequality. The solution would be (48, ∞).

What justifies inequality?

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

Part A:

We can solve the inequality as follows:

1/4x - 3 - 5 > 4

1/4x - 8 > 4

1/4x > 12

x > 48

Therefore, the solution to the inequality is x > 48.

Part B:

Since the inequality is stringent, the graph of the solution would be a number line with an open circle at 48 and an arrow pointing to the right, signifying that all numbers greater than 48 are solutions to the inequality. The answer would be (48, ) in interval notation.

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I NEED HELP ON THIS ASAP!!!

Answers

1. The numeric values of the function are given as follows:

x = -4, y = 1/16.x = -3, y = 1/8.x = -2, y = 1/4.x = -1, y = 1/2.x = 0, y = 1.

2. As x approaches negative infinity, y approaches zero.

How to calculate the numeric value of a function or of an expression?

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The numeric values for this problem are given as follows:

x = -4, y = 1/16, as 2^(-4) = 1/2^4 = 1/16.x = -3, y = 1/8, as 2^(-3) = 1/2^3 = 1/18.x = -2, y = 1/4, as 2^(-2) = 1/2^2 = 1/4.x = -1, y = 1/2, as 2^(-1) = 1/2^1 = 1/2.x = 0, y = 1, as 2^(0) = 1/2^0 = 1.

Increasing the negative exponent, the number gets closer to zero.

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A certain sine function has a midline at y=3.
Which function rule could model this situation?

Answers

The function rule that could model this situation is f(x)=sin(x)+3. The correct answer is (c).

Understanding sine function

The sine function is a mathematical function that describes a periodic oscillation. It is one of the basic trigonometric functions, along with cosine, tangent, cotangent, secant, and cosecant.

Let us relate this to our given question.

The midline of a sine function is the horizontal line that the graph oscillates around.

In this case, the midline is y=3, which means that the sine function oscillates between y=3+1=4 and y=3-1=2.

The function rule that could model this situation is c. f(x)=sin(x)+3, because adding 3 to the sine function shifts the midline up to y=3, and the sine function oscillates between y=4 and y=2.

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1. discuss the internal validity of the regressions that you used to answer empirical exercise 8.2(l). include a discussion of possible omitted variable bias, misspecification of the functional form of the regression, errors in variables, sample selection, simultaneous causality, and inconsistency of the ols standard errors.

Answers

Answer: Empirical Exercise 8.2(l) involves running a regression to estimate the relationship between two variables of interest. In evaluating the internal validity of the regression used to answer this exercise, we need to consider several potential sources of bias and other issues that could affect the accuracy of the estimated relationship.

Omitted variable bias: This occurs when a relevant variable is left out of the regression model. If this happens, the estimated coefficients may be biased and inconsistent. For example, if we are estimating the effect of education on earnings but fail to include information about work experience, the coefficient on education may be biased upwards.

Misspecification of the functional form of the regression: If the relationship between the dependent variable and the independent variable(s) is nonlinear, we may need to use a different functional form of the regression equation to obtain accurate estimates. If we fail to do so, the estimated coefficients may be biased and inconsistent.

Errors in variables: When measurement errors occur in the independent variable(s), this can cause the estimated coefficients to be biased and inconsistent.

Sample selection: If the sample used to estimate the regression equation is not representative of the population of interest, then the estimated coefficients may be biased and inconsistent.

Simultaneous causality: When there is a two-way causal relationship between the dependent variable and the independent variable(s), it may not be possible to determine the direction of causality from the regression coefficients.

Inconsistency of the OLS standard errors: If there is heteroskedasticity or autocorrelation in the data, then the ordinary least squares (OLS) standard errors may be inconsistent. This can lead to incorrect conclusions about the statistical significance of the estimated coefficients.

To address these issues, researchers should take care to select an appropriate sample, use a suitable functional form of the regression equation, and account for any relevant variables that could be omitted or measured with errors. It may also be necessary to use alternative statistical techniques to account for simultaneous causality or heteroskedasticity in the data. Finally, researchers should always test the robustness of their results to different model specifications and sensitivity to potential sources of bias.

Step-by-step explanation:

Need some serious help with this one

Answers

Answer:

FH = 26

Step-by-step explanatio

I only know the answer

Answer:

FH ≈ 11.62

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem , then

FH² = EH × GH = 9 × 15 = 135 ( take square root of both sides )

FH = [tex]\sqrt{135}[/tex] ≈ 11.62 ( to the nearest hundredth )

HELP ME AND I'LL GIVE YOU 100 POINTS!!! ANSWER IT HONESTLY PLS!!!
Find the area, in square inches, of the composite figure.
12 in.
2 in.
3 in.
3 in.
25 in.

looks somewhat like what my problem looks like but with the numbers I listed

Answers

The area of that is 55

What if the dimension of the original rectangle in Exercise 1 had been multipled by 1/2? How would the area have been affected

Answers

If the dimensions of a rectangle are multiplied by 1/2, its area will be multiplied by 1/4, which means the new area will be one-fourth of the original area.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

According to the given information:

The area of a rectangle is calculated by multiplying its length and width. If the dimensions of a rectangle are multiplied by a factor of k, then the new area of the rectangle is equal to k times the original area.

In this case, the dimensions of the original rectangle are multiplied by 1/2, which means that the new length and width of the rectangle are 1/2 times the original length and width. Therefore, the new area of the rectangle is equal to (1/2) times the original length multiplied by (1/2) times the original width. This can be simplified to 1/4 times the original area. Therefore, the area of the new rectangle is one-fourth of the area of the original rectangle.

Therefore, If the dimensions of a rectangle are multiplied by 1/2, its area will be multiplied by 1/4, which means the new area will be one-fourth of the original area.

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I just need the perimeter

Example #2 - Coordinate Perimeter/Area Calculate the area and perimeter of the shape shown. Determine the: Perimeter Area

Answers

Using composite figures, we can find that the area of the shape is 18unit² and the perimeter of the shape is 20 + √8 units.

Define composite figures?

A composite shape is a shape that is made by connecting a few polygons to form a different shape. These shapes or figures can be formed from a variety of shapes, including triangles, squares, quadrilaterals, etc. Divide a composite item into basic forms such a square, triangle, rectangle, or hexagon to get its area.

In essence, a composite shape is a combination of fundamental shapes. It goes by the name's "composite" or "complex" shapes.

In this composite figure,

We have 2 rectangles and a triangle.

Dimension of rectangle:

Base = 2units

Height = 2 units.

Hypotenuse = √ (2² + 2²)

= √8

Area of the triangle = 1/2 × b × h

= 1/2 × 2 × 2

= 2unit².

Now, the rectangles are equal in shape and size.

Dimensions are:

Length = 4 units

Breadth = 2 units.

Area = l × b

= 4 × 2

= 8unit².

We have 2 rectangles so total area = 2 × 8

= 16unit².

Total area of the shape = area of triangle + area of 2 rectangles

= 2 + 16

= 18unit²

Now coming to the perimeter of the shape, we have to find the sum of the measure of the sides of the shape:

So, we have

2 + 4 + 2 + 6 + 6 + √8

= 20 + √8 units.

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7z + 7> - 2z -4 solve the following for inequality for z simplest form

Answers

Answer:

z > - [tex]\frac{11}{9}[/tex]

Step-by-step explanation:

7z + 7 > - 2z - 4

9z + 7 > - 4

9z > -11

z > - [tex]\frac{11}{9}[/tex]

Answer: Just turn it into an equation! Replace the > with a =.

Step-by-step explanation:

Subtract 7 from both sides (bc you’re doing the opposite of +7) So 7z +7-7 cancels out so you just have 7z. 7z = -2z -4 -7, so 7z = -2z -11

Add 2z to both sides (bc your doing the opposite again) to get 9z = -11

Divide both sides by the number of the of the term with both a number and variable, in this case 9z, the number is 9. So 9z/9= -11/9 so simplified, z= -11/9

Final answer = -11/9

Hope this helps :D

Please Help :))) If DE| |AB, by the Side Splitter Theorem, ...

Answers

If DE| |AB, by the Side Splitter Theorem, We can conclude that DE is parallel to AB if and only if CD/DA = CE/EB or x/y = z/w.

What is Side Splitter Theorem?

The Side Splitter Theorem is a geometric theorem that relates the lengths of the sides of a triangle and the segments formed when a line is drawn parallel to one of the sides of the triangle.

Specifically, if a line is drawn parallel to one side of a triangle, then it divides the other two sides proportionally.

In other words, if a line intersects two sides of a triangle and is parallel to the third side, then the lengths of the segments it divides on the other two sides are proportional to the lengths of those sides.

If DE is parallel to AB, then by the Side Splitter Theorem, we have:

CD/DA = CE/EB

Substituting the given variables, we get:

x/y = z/w

We can also use the fact that triangles CDE and ABC are similar, which implies that their corresponding sides are proportional. Specifically, we have:

CD/AB = CE/AC = DE/BC

Substituting the given variables and using the fact that CD = x, DA = y, CE = z, and EB = w, we get:

x/(y+w) = z/(x+z)

Cross-multiplying both equations, we get:

xy + xw = yz + xz

Simplifying, we get:

x(w+z) = yz

Dividing both sides by wz, we get:

x/y = z/w

Which is the same as the equation we obtained using the Side Splitter Theorem.

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Sam started the week with a balance of -$10 in his checking account. Then he deposited some money into the account. The ending balance was $70. How much did sam deposit?

Answers

Answer:

Sam balance was -10 and the ending balance was $70

=80+(-10)

=$70

The vertices of a figure are given. Rotate the figure as described. Find the coordinates of the image.

E(−4, 1), F(−3, 3), G(−2, 3), H(−1, 1)

180°
about the origin

Answers

When a figure is rotated 180° about the origin, the x-coordinates and y-coordinates of each point are multiplied by -1 to find the coordinates of the image.

The coordinates of the image of E(−4, 1) would be (4, -1).
The coordinates of the image of F(−3, 3) would be (3, -3).
The coordinates of the image of G(−2, 3) would be (2, -3).
The coordinates of the image of H(−1, 1) would be (1, -1).

Therefore, the coordinates of the image of the figure after a 180° rotation about the origin would be:
(4, -1), (3, -3), (2, -3), and (1, -1).

Como se resuelve esto
2x²-11x=-14
Mediante factorizacion

Answers

The solutions to the equation are x = 7/2 or x = 2. This is because if either of the factors (2x - 7) or (x - 2) equals zero, then the whole expression will equal zero.

To solve the quadratic equation 2x²-11x=-14 by factorization, we need to rearrange the equation to bring all terms to one side so that it is in the form ax² + bx + c = 0.

First, we add 14 to both sides of the equation, which gives us:

2x² - 11x + 14 = 0

To factorize this quadratic equation, we need to find two numbers that multiply to give the constant term (14) and add to give the coefficient of the middle term (-11). In this case, the two numbers are -2 and -7, as (-2) x (-7) = 14 and (-2) + (-7) = -9.

Using these two numbers, we can rewrite the middle term as -2x - 7x, which gives us:

2x² - 2x - 7x + 14 = 0

We can then factorize the first two terms and the last two terms separately, which gives us:

2x(x - 1) - 7(x - 2) = 0

We can then use the distributive property to simplify the equation:

2x² - 2x - 7x + 14 = 0

2x(x - 1) - 7(x - 2) = 0

(2x - 7)(x - 2) = 0

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A number line going from negative 2 to positive 1. What is the correct order of the fractions from least to greatest? Point A: −11 3 Point B: −2 3 Point C: 1 3 Point D: −12 3 The correct order for the fractions is .

Answers

Answer:

D, A, B, C

Step-by-step explanation:

-12/3, or -4, is lowest

-11/3, or -3.6, is 0.3 more, therefore closer to 0.

-2/3, or -0.6, is much closer to 0, precisely 3 units closer.

1/3, or 0.3, is the only positive number, so it is the most amount.

PLEASE HELP I'LL GIVE THE BRAINLIEST!

Answers

Answer:

Box A: 2 × 4.5 × 6 = 54 cubic inches

Box B: 6 × 2.5 × 3 = 45 cubic inches

Box C: 5 × 4.5 × 2.25 =

50.625 cubic inches

Box D: 2.5 × 2.25 × 3 = 16.875 cubic inches

From least to greatest, the order of the boxes' volumes is D, B, C, A.

Two classmates have decided to read all the volumes in a popular series of books. Eva has already read 4 volumes and will continue to read new ones at a rate of 2 volumes per week. Maria, who hasn't started reading the series yet, will read 4 volumes per week. At some point, Maria will catch up with Eva and they will be reading the same book. How many volumes will each girl have read by then? How long will that take?

Answers

Thus, the number of volume read by both Eva and Maria in total 2 weeks is 8.

Explain about the slope of function:

Slope is a crucial topic in economics because it's used to gauge how quickly things are changing.

The slope expresses how quickly the dependent variable changes when the independent variable changes. The line becomes steeper as the slope increases.

Given data:

Number of volume read by Eva = 4Rate of reading by Eva = 2 volume per weekNumber of volume read by Maria = 0Rate of reading by Maria = 4 volume per week

Now,

Let the number of weeks at which both read the equal number of volume be x.

Total number of volume be y

So,

For Eva: y = 4 + 2x

For Maria: 0 + 4x

Equating both equations:

4 + 2x = 4x

4x - 2x = 4

2x = 4

x = 4/2

x = 2

Number of volumes read by each girl:

For Eva: y = 4 + 2(2)= 8

For Maria: 0 + 4(2) = 8

Thus, the number of volume read by both Eva and Maria in total 2 weeks is 8.

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CAN SOMEONE PLS HELP ME WITH THIS? +35 POINTS
what order do they go in?

Answers

At sunrise, shadows are longest and point towards the west as the sun rises in the east. Therefore, the correct order would be:

Longest shadows of the day, and they point to the west → shadows gradually become shorter → very short shadows or no shadows → shadows gradually become longer → longest shadows of the day, and they point to the east.

What is the shadows about?

As the sun moves across the sky, shadows change in length and direction, reaching their shortest length at noon when the sun is directly overhead. After noon, the sun starts to move towards the west, and shadows gradually become longer until sunset when they are longest again, but this time pointing towards the east as the sun sets in the west.

Therefore, correct order of descriptions of shadows during the day, from sunrise to sunset, would be:

Very short shadows or no shadows - This occurs during sunrise when the sun is low on the horizon and its rays are nearly vertical, resulting in very short shadows or no shadows at all.Shadows gradually become longer - As the sun rises higher in the sky, shadows start to lengthen gradually.Longest shadows of the day, and they point to the west - During late morning or early afternoon, shadows are at their longest and they point towards the west, opposite to the direction of the sun.Shadows gradually become shorter - As the sun starts to descend towards the horizon in the late afternoon, shadows gradually become shorter.Longest shadows of the day, and they point to the east - During sunset, shadows are again at their longest, but this time they point towards the east, following the direction of the setting sun.