the equation
4x-2y=4
-4x+2y=-3
have the same/different what slopes and the same/different what y-intercepts?​

The roots f the following polynomial function F(x) = x3 - x2 - 5x - 3 are (A) -1 and (B) 3.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

For instance, the polynomial 2x+5 has an exponent of 1.

f(x) = anxn + anxn+1 +... + a2x2 + a1x + a0 is the formula for a polynomial. The greatest power of x in an expression is the polynomial's degree.

Polynomials of degrees 0, 1, 2, 3, and 4 are constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively.

So, there is only one true, positive root, according to Descartes' rule of signs. On the list, 3 is the only real number that is positive.

When dividing x3-x2-5x-3 by (x-3), we may use synthetic division to get the quotient and discover that it is x2+2x+1, which we know as (x+1)2.

As a result, 3 is a root and -1 is a root with multiplicity 2.

A and B are the options that need to be checked.

Therefore, the roots f the following polynomial function F(x) = x3 - x2 - 5x - 3 are (A) -1 and (B) 3.

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Complete question:

Which of the following are the roots of the polynomial function? Check all that apply.

F(x) = x3 - x2 - 5x - 3

Answer:

Step-by-step explanation:

Ethernet LANs are usually arranged in a star topology with computers wired to central switching circuitry that is incorporated in modern routers.

Ethernet is a family of computer networking technologies that is used in LAN, metropolitan area networks (MAN), and wide area networks (WAN). It was first introduced in 1980 by Xerox Corporation, and later standardized by the Institute of Electrical and Electronics Engineers (IEEE) as IEEE 802.3.

Ethernet networks can be implemented in different topologies, such as a bus, star, or mesh topology. However, the most common topology for Ethernet LANs is a star topology, in which computers are wired to a central switching circuitry that is incorporated in modern routers. This allows for efficient communication between the computers on the network.In addition to LANs, Ethernet is also used for other networking applications such as Internet access, wireless networking, and broadband access. Overall, Ethernet is a widely used technology that has become an important component of modern computer networking.

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The statement that is NOT true is (C) The axis of symmetry is y = 4.

Answer:

[tex]\boxed{706.50}[/tex]

Step-by-step explanation:

You can resolve multiple decimals easily. For this, we need to treat them just like any other number. We can follow the next steps:

[tex]\begin{array}{l}314\times225\\ \cline{0-1}\ \ 1570\\\ \ 628\\\ 628 \\ \cline{0-1}70650\end{array}[/tex]

Finally, we apply step 3:

[tex]\therefore 3.14 \times 225= 706.50[/tex]

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

The tree diagram that list all the possible outcomes with their respective probabilities is given below.

It should be noted that to solve this problem, we can use a tree diagram to represent all the possible outcomes at each step of the selection process. The tree diagram below shows the possible outcomes:

            /   B (6/10)            \   Y (4/10)

       B1 /                            \ Y1

         /                              \

    /   B (5/10)    \   Y (4/10)    /   B (6/10)    \   Y (3/10)

B2 /                  \ Y2         B2 /                  \ Y2

  /                    \           /                    \

 |   B (4/10)   \   Y (4/10)  |   B (5/10)   \   Y (3/10)

B3|                  Y3         |                  Y3

 |                     |       |                     |

  \   B (3/10)   /   Y (4/10)  \   B (4/10)   /   Y (3/10)

    \                  \      /                  \

       \                 \   /                     \

            \   B (2/10)   Y4                     B4 \   Y (2/10)

                 |                                      |

                 |                                      |

                  \   B (1/10)                          \   Y (1/10)

                         |                                     |

                         |                                     |

                          \                                    \

                              B5                                    Y5

The branches in the tree diagram represent the possible outcomes at each selection, and the probabilities are shown next to each branch.

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Therefore , the solution of the given problem of  equation comes out to be for 0 brothers, 78°, for 1 brother, 132°, for two brothers, 66°,for 3 brothers, 42° and for 4 brothers, 42°.

A linear recovery model is founded on the formula: y=mx+b. B is the slope, and m is the y-intercept. The phrase "Bivariate logistic formulas have two components" is frequently used, despite the fact that y and y are two separate elements. When it comes to using linear functions, there are no easy solutions. and. Y=mx+b is the expression, where m stands for slopes and b for the y-intercept.

Here,

(Frequency  Total Frequency) x 360 equals angle (0).

the aggregate of all frequencies is the total frequency.

We can see from the provided chart that:

13 individuals lack relatives.

22 individuals each have one sibling.

11 individuals have two siblings, and 7 people have three.

7 individuals have 4 brothers.

13 + 22 + 11 + 7 + 7 = 60 is the overall frequency.

Using the aforementioned method, we can now determine the angle for each category:

For 0 siblings: Angle = (13 ÷ 60) x 360 = 78°

For 1 sibling: Angle = (22 ÷ 60) x 360 = 132°

For 2 siblings: Angle = (11 ÷ 60) x 360 = 66°

For 3 siblings: Angle = (7 ÷ 60) x 360 = 42°

For 4 siblings: Angle = (7 ÷ 60) x 360 = 42°

The total of all angles ought to

All the angles should total up to 360 degrees, which we can verify by:

78° + 132° + 66° + 42° + 42° = 360°

Therefore, the angles needed to represent the number of siblings among 60 individuals on a pie chart are:

for 0 brothers, 78°

for 1 brother, 132°

For two brothers, 66°

for 3 brothers, 42°

for 4 brothers, 42°

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Step-by-step explanation:

To find the vertical asymptotes of the function f(x) = (x^2+3x+6)/(x^2-4), we need to find the values of x that make the denominator equal to zero.

The denominator (x^2-4) factors into (x+2)(x-2). Therefore, the denominator is equal to zero when x = -2 or x = 2.

These values of x give us vertical asymptotes since the function becomes unbounded as x approaches these values. Therefore, the vertical asymptotes of the function are x = -2 and x = 2.

please mark brailest

The probability of renting exactly three apartments in a week using poisson distribution is 0.2107.

A Poisson distribution is a probability distribution that is used to evaluate how many times a particular event is likely to occur during a certain period of time.

The formula for calculating the probability of an event in a poisson distribution is as follows:

where e = 2.71828 (Euler's constant), x = the number of occurrences, μ = the expected value/average number of occurrences.In the given problem, the average number of new apartments rented per week is 2.3. Therefore,μ = 2.3Using the formula for Poisson distribution, we get:

P(3) = e^−2.3 * 2.3^3 / 3!

P(3) = 0.2107Therefore, the probability of renting exactly three apartments in a week is 0.2107.

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The probability that the 39 randomly-selected laptops have a mean "replacement-time" as 3.8 years or less is equal to 0.1058.

The distribution of the sample mean follows a normal distribution with mean (μ) = 3.9 years and standard deviation = σ/√n = 0.5/√39 years, where n = 39 is the sample size.

We want to find the probability that the sample mean replacement time is less than or equal to 3.8 years, which is written as : P(x' ≤ 3.8).

By using the z-score formula, we convert this to a standard normal distribution:

⇒ z = (x' - μ)/(σ/√n) = (3.8 - 3.9)/(0.5/√39) = -1.249,

Using a standard normal distribution table, the probability that a standard normal variable is less than or equal to -1.249,is approximately 0.1058,

Therefore, the required probability is approximately 0.1058.

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The given question is incomplete, the complete question is

Assuming that the laptop replacement times have a mean of 3.9 years and a standard deviation of 0.5 years, find the probability that 39 randomly selected laptops will have a mean replacement time of 3.8 years or less.

Answer:

D is correct.

Step-by-step explanation:

[tex](x + y + 2)(y + 1)[/tex]

[tex] xy + x + {y}^{2} + y + 2y + 2[/tex]

[tex] {y}^{2} + xy + x + 3y + 2[/tex]

So D is the correct answer.

Answer:

87.1 degrees

Step-by-step explanation:

First, you know the sum of the angles is 180 degrees. So, 5x+4x+10+10x-5=180.

Then, simplify to 19x+5=180. So, 19x=175. That means by dividing both sides by 19 x is approximately 9.21.

Finally, plug in x into angle 3.

10x9.21-5

=92.1-5

=87.1

So, the third angle is approximately 87.1.

The equation of a line passing through the points (2,4) and (6,16) is

2) y=3x-2.

What is equation?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.

Here the given two points are [tex](x_1,y_1)=(2,4)[/tex] and [tex](x_2,y_2)=(6,16)[/tex] .

Now using slope formula then,

=> slope m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{16-4}{6-2} =\frac{12}{4} = 3[/tex]

Now using equation formula then [tex]y-y_1=m(x-x_1)[/tex]

=> y-4=3(x-2)

=> y-4 = 3x-6

=> y = 3x-6+4

=> y = 3x-2

Hence the equation is 2) y = 3x-2.

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The expression for the dimensions of the combined park and bike path in terms of x is length= 200+2x ft and  width = 300+ 2x ft.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given rectangle park length is 200ft and width is 300 ft.

Now in the given diagram , path for bike is expended in both sides of the park.

Length of bike path = x + x = 2x

Width of bike path = x + x = 2x

Then combined dimensions for park and bike path is,

=> length = length of park+ length of path

=> length = 200+2x ft

=> width = width of park + width of bike path

=> width = 300+ 2x ft.

Hence the expression for the dimensions of the combined park and bike path in terms of x is length= 200+2x ft and  width = 300+ 2x ft.

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The slope of the line is 8, which represents the rate at which the amount of money in the account is increasing per week.

An equation is a mathematical statement that asserts that two expressions have the same value. It typically consists of two parts: the left-hand side, which contains one expression, and the right-hand side, which contains another expression. The two sides are separated by an equal sign. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.

Here,

The graph is not shown, but based on the given information, we can determine the slope of the line using the slope-intercept form of a linear equation:

y = mx + b

where y is the amount of money in the account, x is the number of weeks, m is the slope (the rate at which the money in the account is changing), and b is the y-intercept (the initial amount of money in the account). We know that Fred starts with 6 dollars in the account (y-intercept), and deposits 8 dollars each week (slope). Therefore, the equation for the line is:

y = 8x + 6

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Complete question:

Fred starts with 6 dollars in a bank account. He deposits exactly 8 dollars each week, and does not take any money out. The graph below represents the relationship between the number of weeks and the amount of dollars in the account. What is the slope of the line?

The average distance between each data value and the data set's mean is represented by the mean absolute deviation of the data set's 3, 7, 10, 12, and 15 values, which is 3.24. It provides a measurement of the variance or departure from the mean of the data values.

The term "absolute" refers to the distance a number is from 0 on a number line. The absolute value of a number is always positive and represents the magnitude of the number regardless of its sign. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.

The distance between two points on number line is always the absolute value of the difference between those points. Hence distance a number is from 0 on a number line is always the absolute value of that number.

To deviate means to differ or vary from a standard or expected value. The mean absolute deviation of a data set is the average (mean) distance from each data value to the mean of the data set. It measures how spread out the data values are from the mean.

For example, consider the data set {3, 7, 10, 12, 15}. The mean of this data set is (3 + 7 + 10 + 12 + 15)/5 = 9.4. To calculate the mean absolute deviation, we need to find the absolute deviation of each data value from the mean, then take the mean of those absolute deviations.

The absolute deviations from the mean are:

|3 - 9.4| = 6.4

|7 - 9.4| = 2.4

|10 - 9.4| = 0.6

|12 - 9.4| = 2.6

|15 - 9.4| = 5.6

The mean absolute deviation is the average of these absolute deviations:

(6.4 + 2.4 + 0.6 + 2.6 + 5.6)/5 = 3.24

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(a) Option A, if its value is a large positive number, statistic A x2 provides strong evidence for the alternative hypothesis.

(b) Option B, the null hypothesis that gender is not related to personal goals and the alternative hypothesis that gender is related to personal goals.

(c) Option B, the variables considered in the chi-square test for the evaluation of contingency table B are categorical variables.

(a) If the x2 statistic is a large positive number, it provides strong evidence for the alternative hypothesis. The x2 statistic is used in hypothesis testing to determine if there is a significant difference between observed and expected frequencies. Large positive values ​​indicate that the observed frequency is significantly different from the expected frequency, supporting the alternative hypothesis.

(b) The hypotheses tested in the chi-square test for the contingency table are the null hypothesis that gender is not related to personal goals and the alternative hypothesis that gender is related to personal goals. personal goals. This test determines whether there is a significant relationship between two categorical variables.

(c) The variables considered in the chi-square test used to evaluate the contingency table are categorical variables. These variables cannot be assumed to be mean or normally distributed. The chi-square test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.

Complete Question:

For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. OB. exactly 1.96 c. a large negative number. D. close to o E. close to 1. (b) A study was performed to examine the personal goals of children in elementary school. A random sample of students was selected and the sample was given a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Each student's sex (boy or girl) was also recorded. If a contingency table for the data is evaluated with a chi-squared test, what are the hypotheses being tested? A. The null hypothesis that boys are more likely than girls to desire good grades vs. the alternative that girls are more likely than boys to desire good grades. OB. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. C. The null hypothesis that there is no relationship between personal goals and sex vs. the alternative hypothesis that there is a positive, linear relationship. OD. The null hypothesis that the mean personal goal is the same for boys and girls vs. the alternative hypothesis is that the means differ. O E. None of the above. (C) The variables considered in a chi-squared test used to evaluate a contingency table A. are normally distributed. B. are categorical. C. can be averaged. OD. have small standard deviations. E. have rounding errors.

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the submarine is approximately 2.236 kilometers from its starting point.

Distance is a numerical measurement of the space between two points. It is the length of the path traveled by an object moving from one point to another, regardless of the direction it takes. Distance is typically measured in units such as meters, kilometers, feet, miles, or any other unit of length.

The submarine is essentially moving in a square pattern, with sides of length 1 km. Each time it moves north or west, it changes its distance from the starting point by 1 km.

Since the submarine moves 1 km north and 1 km west in each "leg" of its journey, it will complete 20 legs before traveling a total of 40 km. At this point, it will be 1 km north and 1 km west of its starting point.

The 21st and final leg of the journey brings the submarine 1 km north, so it ends up 2 km north and 1 km west of its starting point. Using the Pythagorean theorem, we can find the distance between the starting point and the final position of the submarine:

d = √((2 km)² + (1 km)²)

=√(5) km

≈ 2.236 km

Therefore, the submarine is approximately 2.236 kilometers from its starting point.

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Answer:

27 cm^2

Step-by-step explanation:

Area of a triangle is B * H / 2

6 * 9 / 2 = 27

I think the budget strategy worked because it brought in the necessary amount of money to Vegas and met everyone's needs for the show.

Money Magic is designed to teach basic budgeting principles. The main character, Enzo, represents the human tendency to focus on short-term gratification. This game challenges students to balance immediate desires with long-term plans.

In this free financial game, help magician Enzo get the show to Las Vegas on budget. The player assumes the role of Lord Enzo the magician and his manager. He's tasked with getting him to Vegas for his big break. Along the way, he will raise $50,000 to pay for the venue when he gets there. And it's not an easy task: On their way to the land of neon lights and slots his machine, they reconcile the cost of the hyped show, pay for upkeep such as Enzo's new tricks, fill the tanks of his magic his mobile with gas Have to. And when you're managing a diva like Enzo, this is no easy task.

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The true statements for a concession sale at a sporting event are:

The following statements are true based on the given data:

7/11 of the people who ordered a hamburger ordered French fries. (252 hamburger orders x 7/11 = 162 orders of French fries with hamburger)

4/11 of the people who ordered French fries ordered a hamburger. (468 French fry orders x 4/11 = 168 orders of hamburgers with French fries)

6/7 of the people who ordered a hot dog ordered French fries. (216 hot dog orders x 6/7 = 186 orders of French fries with hot dog)

2/3 of the people who ordered French fries ordered a hot dog. (468 French fry orders x 2/3 = 312 orders of hot dogs with French fries)

3/7 of the people who ordered a hamburger ordered onion rings. (252 hamburger orders x 3/7 = 108 orders of onion rings with hamburger)

1/3 of the people who ordered a hot dog ordered onion rings. (324 hot dog orders x 1/3 = 108 orders of onion rings with hot dog)

4/7 of the people who ordered onion rings ordered a hamburger. (252 onion ring orders x 4/7 = 144 orders of hamburger with onion rings)

1/2 of the people who ordered onion rings ordered a hot dog. (252 onion ring orders x 1/2 = 126 orders of hot dog with onion rings)

The total number of orders for each item can be calculated by adding up the corresponding row or column totals.

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Image transcribed:

Concession sales at a sporting event are monitored, and the data is recorded in the two-way table below. Which of the following statements are true?

| French fries | Onion rings | Total

Hamburger | 252 | 144 | 396

Hot dog | 216 | 108 | 324

Total | 468 | 252 | 720

7/11 of the people who ordered a hamburger ordered French fries.

4/11 of the people who ordered French fries ordered a hamburger.

6/7 of the people who ordered a hot dog ordered French fries.

2/3 of the people who ordered French fries ordered a hot dog.

3/7 of the people who ordered a hamburger ordered onion rings.

1/3 of the people who ordered a hot dog ordered onion rings.

4/7 of the people who ordered onion rings ordered a hamburger.

1/2 of the people who ordered onion rings ordered a hot dog.

In order to find the area of the given rectangle, we can use square-inch tiles or rulers. the area of the rectangle is 30 square inches. The length of the rectangle is 15 inches, width is 2 inches then  area of 30 square inches.

Using square-inch tiles:

We can cover the rectangle with square-inch tiles and count the total number of tiles to find the area. Each tile represents one square inch, and the area of the rectangle is equal to the number of tiles covering it. We can start by covering one side of the rectangle with tiles, and then count the number of tiles used. The length of the rectangle is 15 inches, so we need to use 15 tiles to cover one side. We can then cover the other side with the same number of tiles, which gives us a total of 30 tiles. Therefore, the area of the rectangle is 30 square inches.

Using a ruler:

We can measure the length and width of the rectangle using a ruler and then multiply the two measurements to find the area. The length of the rectangle is 15 inches, and the width is 2 inches. Multiplying these values gives us an area of 30 square inches.

Using circular counters:

Circular counters are not an appropriate tool to find the area of a rectangle because they are circular in shape and cannot cover the entire surface of the rectangle.

In conclusion, to find the area of a rectangle, we can use appropriate tools such as square-inch tiles or rulers. These tools allow us to accurately measure the length and width of the rectangle and calculate the area by counting or multiplying the measurements.

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Answer: [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

There is a total of 8 + 5 + 7 + 10 = 30 balls. There is 8 + 10 = 18 black or white balls. 18 / 30 simplifies to [tex]\frac{3}{5}[/tex].

Answer:

[tex]y=-4x+7[/tex]

Step-by-step explanation:

According to the formula of the equation of the line passing through two given points

[tex]y-y1=m(x-x1)[/tex]

where m=slope of the line

[tex]m=(y2-y1)/(x2-x1)[/tex]   ---->eq (II)

where [tex]y2=-5 , y1=3 , x2=1 , x1=-1[/tex]

Substituting the

values in eq(II)

[tex]m=(-5-3)/(1-(-1))=-8/2=-4[/tex]

Substituting the value of m in eq(I)

[tex]y-3=-4(x-(-1))\\= > y=-4x+7[/tex]

So the equation of the line passing through the given points is

[tex]y=-4x+7[/tex]

Answer: y+2x−1=0

Step-by-step explanation: Let's say A is the point (−1,3) and B is the point (3,−5)

The equation of a line that passes through two points is

y−y0=m(x−x0)

Replace x,x0,y and y0

by the coordinates of the two points to find your slope

⇒m

.

It doesn't matter which point you choose to replace

x,x0,y and y0 with as long as you pair xwith yand x0 with

y

0

.

m

=

y

−

y

0

x

−

x

0

=

−

5

−

3

3

−

(

−

1

)

=

−

5

−

3

3

+

1

=

−

2

Now, all you have to do is to choose either the coordinates of

A

or

B

to replace in the equation of a line that passes through two points

⇒

y

−

y

0

=

m

(

x

−

x

0

)

. You are only going to replace

x

0

and

y

0

.

I'm using the point

A

(

−

1

,

3

)

⇒

y

−

y

0

=

m

(

x

−

x

0

)

⇒

y

−

3

=

−

2

(

x

+

1

)

⇒

y

−

3

=

−

2

x

−

2

⇒

y

+

2

x

−

1

=

0

is your line.Let's say

A

is the point

(

−

1

,

3

)

and

B

is the point

(

3

,

−

5

)

The equation of a line that passes through two points is

y

−

y

0

=

m

(

x

−

x

0

)

Replace

x

,

x

0

,

y

and

y

0

by the coordinates of the two points to find your slope

⇒

m

.

It doesn't matter which point you choose to replace

x

,

x

0

,

y

and

y

0

with as long as you pair

x

with

y

and

x

0

with

y

0

.

m

=

y

−

y

0

x

−

x

0

=

−

5

−

3

3

−

(

−

1

)

=

−

5

−

3

3

+

1

=

−

2

Now, all you have to do is to choose either the coordinates of

A

or

B

to replace in the equation of a line that passes through two points

⇒

y

−

y

0

=

m

(

x

−

x

0

)

. You are only going to replace

x

0

and

y

0

.

I'm using the point

A

(

−

1

,

3

)

⇒

y

−

y

0

=

m

(

x

−

x

0

)

⇒

y

−

3

=

−

2

(

x

+

1

)

⇒

y

−

3

=

−

2

x

−

2

⇒

y

+

2

x

−

1

=

0

is your line.

Answer:

54 hours

Step-by-step explanation:

44h=616$

1h=44h divided by 44

=616$ divided by 44

= 14

150% of 14$ = 100% + 50%

= 14$ + 7$

= 21$

826$-616$ = 210$

1h(additional hour rate) =21$

10h= 210$

44h + 10h = 54h = 826$

Answer:

yo moma

Step-by-step explanation:

So, the correct answer is: Major Axis: 12[tex]\sqrt{2}[/tex] units, Minor Axis: 24 units.

An ellipse is a closed curve that is symmetrical about two axes, commonly referred to as the major axis and minor axis. It can be described as a stretched circle or a flattened oval. The shape of an ellipse can be defined by two focal points (also known as foci) and the distance between them. Any point on the ellipse is the sum of the distances between that point and each focus. Ellipses have a wide range of applications in mathematics, physics, astronomy, and engineering. They are used to describe the orbits of planets and other celestial bodies, to design reflectors and lenses for telescopes, and to create art and design elements.

The standard equation of an ellipse centered at the origin is given by:

[tex](x^2/a^2) + (y^2/b^2) = 1,[/tex]

where "a" and "b" are the lengths of the semi-major and semi-minor axes, respectively. To find the lengths of the major and minor axes of the given ellipse, we need to first put it in standard form by dividing both sides by 12:

[tex]x^2/72 + y^2/144 = 1[/tex]

Comparing this with the standard form, we see that.[tex]a^2 = 72[/tex]and b^2 = 144. Thus, the lengths of the semi-major and semi-minor axes are:

a = [tex]\sqrt{72}[/tex] = 6[tex]\sqrt{2}[/tex] units

b = [tex]\sqrt{144}[/tex]= 12 units

Therefore, the lengths of the major and minor axes of the ellipse are:

Major Axis: 2a = 2(6[tex]\sqrt{2}[/tex]) = 12[tex]\sqrt{2}[/tex]units

Minor Axis: 2b = 2(12) = 24 units

So, the correct answer is: Major Axis: 12[tex]\sqrt{2}[/tex] units, Minor Axis: 24 units

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Using some trigonometric relations we can see that x  = 6.72

Here we know that the larger triangle is completely defined, then we can find the angle at X using a trigonometric relation:

Sin(a) = opposite cathetus/hypotenuse

Sin(a) = 7/25

Using the inverse sine function:

a = Asin(7/25) = 16.26°

Now, notice that angle at X is also an angle of the triangle whose x is a side, then we can use the relation:

sin(16.26°) = opposite cathetus/hypotenuse.

This time:

opposite cathetus = x

hypotenuse = 24

Replacing that:

sin(16.26°) = x/24

x = 24*sin(16.26°) = 6.72

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