Find x from two right triangles

The rectangle whose width is 5 meters less than its length and whose area is 176 meters has width of 11 meters and length of 16 meters.

Let's use algebra to solve the problem. Let x be the length of the rectangle in meters. Then the width is 5 meters less than the length, so the width is x - 5 meters.

The area of the rectangle is the length times the width, so we have:

area = length × width

176 = x(x - 5)

Expanding the right-hand side gives:

176 = x^2 - 5x

Moving all the terms to the left-hand side gives:

x^2 - 5x - 176 = 0

We can factor this quadratic equation as:

(x - 16)(x + 11) = 0

The solutions to this equation are:

x = 16 or x = -11

Since the length of the rectangle must be a positive number, we can discard the negative solution x = -11.

Therefore, the length of the rectangle is x = 16 meters.

The width of the rectangle is 5 meters less than the length, so the width is:

x - 5 = 16 - 5 = 11 meters.

Therefore, the dimensions of the rectangle are 16 meters by 11 meters.

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The probability of rolling an even number based on Laura's results is 40%.

We can tell from Laura's outcomes that she rolled the die 10 times and recorded the results. There are 4 even outcomes (numbers 2, 4, 6, and 8) and 6 odd results out of a possible 10 results (1, 3, 5, 7, 9, and 10).

We must divide the number of even possibilities by the total number of potential outcomes in order to calculate the chance of rolling an even number. Given that there are four even outcomes out of a possible ten, the likelihood of rolling an even number is as follows:

probability of rolling an even number = number of even outcomes / total number of outcomes

probability of rolling an even number = 4/10

probability of rolling an even number = 2/5

When rolling an even number, the probability = 0.4.

probability of rolling an even number = 40%

As a result, 40% of the time, depending on Laura's results, an even number will be rolled.

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Since CHNY is a parallelogram, HN = CY. Also, since diagonals CH and NY intersect at point A, we have:

HN + NA = AY (1)

Substituting the given values, we get:

(7x + 5) + (2x + 3) = 4x - 7

Simplifying and solving for x, we get:

9x = -15

x = -5/3

Therefore, the value of x is -5/3.

The equation of the line that passes through the points (-6,-1) and (2,5) is y=0.75x+3.5.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given coordinate points are (-6,-1) and (2,5).

Here, the slope (m) =(5+1)/(2+6)

= 6/8

= 3/4

= 0.75

Substitute m=0.75 and (x, y)= (-6, -1) in y=mx+c, we get

-1=0.75(-6)+c

-1=-4.5+c

c=3.5

So, the equation is y=0.75x+3.5

Therefore, the equation of a line is y=0.75x+3.5.

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The polynomial in standard form after expansion is x² - 7x + 12.

Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.

The given expression is (x - 3) (x - 4).

We have to expand this as a polynomial in standard form.

Standard form of a polynomial with degree n is,

a₀ + a₁ x + a₂ x² + ................. + aₙ₋₁ xⁿ⁻¹ + aₙ xⁿ

(x - 3) (x - 4) = x (x - 4) - 3 (x - 4)

Applying the distributive property,

                   = x² - 4x - 3x + 12

                   = x² - 7x + 12

This is a standard form of a second degree polynomial.

Hence x² - 7x + 12 is the expansion of the given expression.

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The surface area of the figure is 56 square units

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Net of right rectangular pyramid

The surface area of the figure is calculated as

Area = sum of individual areas

Using the above as a guide, we have the following:

Area = 4 * 4 + 4 * 1/2 * 4 * 5

Evaluate the expression

Area = 56

Hence, the area is 56 square units

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The limiting value of the population is 1000000, and it will take approximately 49.92 months for the population to be equal to one-half of this limiting value. The correct option is A.

To find the limiting value of the population and the time it will take the population to be equal to one-half of this limiting value, we need to solve the initial-value problem:

dp/dt = 0.1P(1 - P/1000000), P(0) = 10000

To find the limiting value of the population, we need to find the value of P as t approaches infinity. We can do this by finding the equilibrium solutions of the differential equation. An equilibrium solution is a constant population size that does not change over time. It is found by setting dp/dt = 0, and solving for P.

In this case, we have:

dp/dt = 0.1P(1 - P/1000000) = 0

Solving for P, we get:

P = 0 or P = 1000000

The population size cannot be zero, so the limiting value of the population is P = 1000000.

To find the time it will take the population to be equal to one-half of this limiting value, we need to solve for the value of t when P = 500000. Unfortunately, there is no algebraic solution for this equation, so we need to use numerical methods to estimate the value of t.

One way to do this is to use a numerical solver to solve the initial-value problem. Here, we can use a computer software or a graphing calculator to solve the differential equation and find the value of P for different values of t, until we find the time at which P = 500000.

Using a graphing calculator or a computer software, we can solve the differential equation to get:

P(t) = 1000000/(1 + 999e^(-0.1t))

Using this formula, we can find the time it takes for P to reach 500000 by solving for t when P = 500000:

500000 = 1000000/(1 + 999e^(-0.1t))

1 + 999e^(-0.1t) = 2

e^(-0.1t) = 1/999

-0.1t = ln(1/999)

t = -10 ln(1/999) ≈ 49.92

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Complete question is:

A model for the population P(t) in a suburb of a large city is given by the initial-value problem dp = 0.1 P(1 - P/1000,000), P(O) = 10,000 where t is measured in months. The limiting value of the population and the time will take the population be equal to one-half of this limiting value respectively are

a. 1000,000, 49.92

b. 500,000, 58

C. 1000,000 42

d. 1000,000 46

The total cost of downloading 20 songs is $45.

The total cost of downloading ss songs is $11 + $1.0ss.

What does the word "cost" mean?

During the manufacturing or production of a company's goods and services, every expense incurred by the company is referred to as a cost.

                            In simplest terms, it is the amount of money that businesses invest in buying and selling goods.

The total cost of the of downloading songs is the sum of the fee per month and the cost of downloading songs.

Total cost of downloading 45 songs = cost per month x cost of downloading 45 songs

$11 + ($1 x 45)

$11 + $45

$56

Total cost of downloading ss songs = $11 + ($1 x ss)

$11 + $1ss

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(2x+3) (x+2) (x−2) thats the answer

The equation of the line passing through (-2, -4) and (2, 1) in slope-intercept form is y = (5/4)x - 9/4.

An equation is a mathematical statement that shows that two expressions are equal to each other. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

(2, 5) and (6, 2):

The two points are connected by a line that has the following slope:

m = (y2 - y1) / (x2 - x1)

= (2 - 5) / (6 - 2)

= -3/4

We may write the following using the equation of a line in the point-slope form:

y - y1 = m(x - x1)

Choosing point (2, 5) as (x1, y1), we get:

y - 5 = (-3/4)(x - 2)

Simplifying this equation, we get:

y = (-3/4)x + 11/2

So the equation of the line passing through (2, 5) and (6, 2) in slope-intercept form is y = (-3/4)x + 11/2.

(-1, 3) and (0, -2):

The two points are connected by a line that has the following slope:

m = (y2 - y1) / (x2 - x1)

= (-2 - 3) / (0 - (-1))= -5

We may write the following using the equation of a line in the point-slope form:

y - y1 = m(x - x1)

Choosing point (-1, 3) as (x1, y1), we get:

y - 3 = (-5)(x + 1)

Simplifying this equation, we get:

y = -5x - 2

So the equation of the line passing through (-1, 3) and (0, -2) in slope-intercept form is y = -5x - 2.

(-2, -4) and (2, 1):

The two points are connected by a line that has the following slope:

m = (y2 - y1) / (x2 - x1)

= (1 - (-4)) / (2 - (-2))

= 5/4

We may write the following using the equation of a line in the point-form:slope

y - y1 = m(x - x1)

Choosing point (-2, -4) as (x1, y1), we get:

y + 4 = (5/4)(x + 2)

Simplifying this equation, we get:

y = (5/4)x - 9/4

So the equation of the line passing through (-2, -4) and (2, 1) in slope-intercept form is y = (5/4)x - 9/4.

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The fraction of ballots that were cast for someone other than Candidate A or Candidate B  is given by the equation q = 3/50

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction of ballots that were cast for someone other than Candidate A or Candidate B be represented as q

Now , the equation will be

The fraction of ballots cast for Candidate A = 12/25 = 24/50

The fraction of ballots cast for Candidate B = 23/50

So , the total fraction of ballots casts for Candidate A and Candidate B = fraction of ballots cast for Candidate A + fraction of ballots cast for Candidate B

Substituting the values in the equation , we get

The total fraction of ballots casts for Candidate A and Candidate B is given by p = ( 24 + 23 ) / 50

p = 47/50

Now , fraction of ballots that were cast for someone other than Candidate A or Candidate B = 1 - p

The value of q = 1 - p

q = 1 - ( 47/50 )

q = 3/50

Hence , the fraction is 3/50

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Answer:

  A.  AC = BC because of the perpendicular bisector theorem

Step-by-step explanation:

You want the next step in the proof that ∆ABC is isosceles.

The correct answer choice is the only one that is a true statement:

  A.  AC = BC because of the perpendicular bisector theorem

__

Additional comment

We're not clear on how this proof starts, because the converse of the perpendicular bisector theorem tells you that CD is a perpendicular bisector of AB if and only if every point on CD is equidistant from A and B. That is, you have to assume that ABC is isosceles before the converse of the perpendicular bisector theorem can apply.

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Answer:

Step-by-step explanation:

The equation 1/2 x 3/3 = 3/6 illustrates the property of the Commutative Property of Multiplication.

The Commutative Property of Multiplication states that changing the order of the factors in a multiplication operation does not affect the product. In other words, for any two real numbers a and b, we have:

a x b = b x a

So, in the equation 1/2 x 3/3 = 3/6, we see that the product is the same regardless of the order in which the factors are multiplied.

To determine how many cases of printer paper Jacinta should order, we first need to calculate the number of sheets in one case:

The volume of one ream of paper is: (0.216 m) x (0.279 m) x (0.045 m) = 0.00239 cubic meters

Since there are 500 sheets in a ream, the volume of one sheet of paper is 0.00239 / 500 = 4.78 x 10^-6 cubic meters

The volume of one case is: (0.216 m) x (0.279 m) x (0.27 m) = 0.0161 cubic meters

The number of sheets in one case is therefore: 0.0161 / 4.78 x 10^-6 = 3360 sheets

Since Jacinta needs 7,000 sheets and can only order full cases, she will need to order at least 2 cases:

2 cases would contain 2 x 3360 = 6720 sheets, which is more than Jacinta needs

1 case would only contain 3360 sheets, which is not enough for Jacinta's needs

Therefore, Jacinta should order 2 cases of printer paper.

Answer:

21

Step-by-step explanation:

The buses meet up with one another 2 hours after the first bus's departure.

The first bus travels at 30 mph for 2 hours, so it travels a distance of 30 * 2 = 60 miles.

The second bus starts moving at 50 mph, so it travels at a relative speed of 50 + 30 = 80 mph.

Let x be the number of hours after the first bus's departure that the buses meet up.

The total distance traveled by the two buses is 60 + 80x.

Since the distance traveled by the two buses is equal, we have 60 + 80x = 60 + 80x.

Solving for x, we get x = 2 hours.

Here is the solution in steps:

The first bus travels at 30 mph for 2 hours, so it travels a distance of 30 * 2 = 60 miles.

The second bus starts moving at 50 mph, so it travels at a relative speed of 50 + 30 = 80 mph.

Let x be the number of hours after the first bus's departure that the buses meet up.

The total distance traveled by the two buses is 60 + 80x.

Since the distance traveled by the two buses is equal, we have 60 + 80x = 60 + 80x.

Solving for x, we get x = 2 hours.

Therefore, the buses meet up with one another 2 hours after the first bus's departure.

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A) Rank = 2, Nullspace: (1, -2, 0), Dimension = 1. B) Rank = 2, Nullspace: (1, -2, 0), Dimension = 1. C) Rank = 2, Nullspace: (-3, 1, -2, 0), Dimension = 2. Yes, the rank of the matrix is equal to the dimension of the nullspace.

A) To find the nullspace and rank of the matrix, the matrix must first be reduced to its reduced row echelon form. After reducing the matrix, it is in the form [1 0 1; 0 0 0]. From this, the rank of the matrix can be determined as 2 since there are two non-zero rows in the reduced form. To find the nullspace, the equation of the form of the matrix in the reduced row echelon form must be solved. This gives the nullspace of the matrix as (1, -2, 0). From Theorem 1.12, the dimension of the nullspace is equal to the rank of the matrix, which is 2.

B) To find the nullspace and rank of the matrix, the matrix must first be reduced to its reduced row echelon form. After reducing the matrix, it is in the form [1 0 1 0; 0 0 0 0; 0 0 0 0]. From this, the rank of the matrix can be determined as 2 since there are two non-zero rows in the reduced form. To find the nullspace, the equation of the form of the matrix in the reduced row echelon form must be solved. This gives the nullspace of the matrix as (1, -2, 0, 0). From Theorem 1.12, the dimension of the nullspace is equal to the rank of the matrix, which is 2.

C) To find the nullspace and rank of the matrix, the matrix must first be reduced to its reduced row echelon form. After reducing the matrix, it is in the form [1 0 0 1; 0 0 0 0; 0 0 0 0]. From this, the rank of the matrix can be determined as 2 since there are two non-zero rows in the reduced form. To find the nullspace, the equation of the form of the matrix in the reduced row echelon form must be solved. This gives the nullspace of the matrix as (-3, 1, -2, 0). From Theorem 1.12, the dimension of the nullspace is equal to the rank of the matrix, which is 2.

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The statement can be true under certain conditions. The probability that a particular bucket contains more than 5 elements will depend on the size of the bucket and the distribution of the elements.

However, if we assume that the distribution is uniform and the number of elements is much larger than the number of buckets, we can estimate the probability using the following formula:

P(bucket > 5) = 1 - P(bucket <= 5) = 1 - (5/n)

Where n is the number of elements to be sorted, and 5 is the maximum number of elements that can fit in a bucket. If we assume that there are 16 buckets, then the probability that a particular bucket contains more than 5 elements is at most 1/16 if:

1 - (5/n) <= 1/16

Solving for n, we get:

n >= 80

This means that if we have at least 80 elements to be sorted, and we distribute them uniformly among 16 buckets, then the probability that a particular bucket contains more than 5 elements is at most 1/16. Therefore, the statement can be true under certain conditions.

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The main purpose of this paragraph is to inform the reader of a subject.

Reading paragraph is the ability to process text, understand its meaning, and to integrate with what the reader already knows.

Given is a passage, about an  American Screenwriter and author, Emest Cline,

The paragraph is telling about life of the author, telling about his works, the latest, first, the most successful works, his birthplace, etc. but every thing about him.

Simply, if we see, this tell us the information related to the subject who is Emest Cline,

Hence, the main purpose of this paragraph is to inform the reader of a subject.

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Answer:

Using the slope-intercept form, the y-intercept is −3 .

Since Stephanie carries a 100/300/100 liability policy, Stephanie's insurance can cover up to $100,000, therefore Stephanie have enough coverage to cover the property damages.

Property damage is any harm or destruction to real or tangible personal property that is brought on by carelessness, intentional obliteration, or a natural disaster.

A more serious form of property damage known as destruction of property involves physical harm to items that are either beyond repair or would be very expensive to replace.

We see that Stephanie has an insurance policy and because she has a 100/300/100 liability policy, she can cover for the damage because it is less than $100,000

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The number of pints of water left in the cooler will be 28 pints

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A water cooler contains 5 gallons of water there are 24 students who drink one cup each from the Jug.

In 5 gallons of water, there are 40 pints of water. And in 1 cup of water, there are 0.50 pints.

Then the number of pints of water left in the cooler is given as,

⇒ 40 - 24 x 0.5

⇒ 40 - 12

⇒ 28 pints

The number of pints of water left in the cooler will be 28 pints

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The domain of the function f(x)= -long(5-x)+b is all real numbers except for x = 5.

Function is the process or state of instruction that text inputs performance is specific task and produce an output functional key components of programming language allowing the quarter to create complex commands with simple instruction for example a function can be used to add two numbers together or to generate a random number function can also be combined to create more complex sequence of instruction.

The range of this function is all real numbers as the long function will never return a negative value. The value of b determines the exact range of the function, as it shifts the graph up or down.

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The complete question is: Will changing two or more objective function coefficients simultaneously affect the optimal solution?

The formula for calculating the value of an investment with continuous compounding is:

A = Pe^(rt)

where A is the resulting amount, P is the principal amount, e is the mathematical constant e (approximately equal to 2.71828), r is the annual interest rate, and t is the time in years.

Substituting the given values, we get:

A = 20000 * e^(0.045 * 5)

≈ 26,088.19

Therefore, the value of the account after 5 years is approximately $26,088.19. Rounded to the nearest cent/penny, the answer is $26,088.19.

The correct answer is: The use of logic causes Macbeth to ponder the consequences of murder, and the use of emotion leads him to recommit to the promise he made to his wife.

Probability is a branch of mathematics that deals with the likelihood or chance of an event happening. It is a numerical measure of the uncertainty of an event, represented as a fraction, decimal, or percentage between 0 and 1. An event with a probability of 0 means that it is impossible for the event to occur, while an event with a probability of 1 means that it is certain to occur. In probability theory, events can be independent or dependent. Independent events have no effect on each other, so their probabilities are multiplied to find the probability of both events happening. Dependent events are those in which the outcome of one event affects the outcome of another event, so their probabilities must be multiplied differently to find the probability of both events happening.

Here,

The use of both logic and emotion in this scene highlights Macbeth's internal conflict and the struggle between his moral and immoral desires.

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The expression 9w√2 - 4x² is a polynomial and the degree is 2

From the question, we have the following parameters that can be used in our computation:

9w√2 - 4x²

The above is a polynomial, and the presence of the radical √2 does not make the expression not a polynomial

This is so because √2 is a factor and not an exponent

Next, we have

Highest power = 2

This means that the degree of the polynomial is 2

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The moment about A of the force exerted by the cable at b is 4704 lb-ft. To find the moment, we need to first find the perpendicular distance between the force vector and point A.

We can use the trigonometric relationship sin(theta) = opposite/hypotenuse to find this distance, where theta is the angle between the boom and the cable.

The force exerted by the cable can be broken down into horizontal and vertical components. The horizontal component is equal to the tension in the cable, which is 392 lb. The vertical component is equal to

To find the moment about A, we can multiply the horizontal component by the perpendicular distance between the force vector and point A:

We also need to consider the moment due to the vertical component. Since this force passes through point A, it does not create any moment about A.

Therefore, the total moment about A is:

However, we need to take into account the direction of the moment. Since the horizontal component of the force is in the opposite direction to the rotation of the boom, the moment is negative. Therefore, the final answer is:

Moment about A = -3,763.2 lb-ft = 4,704 lb-ft (rounded to the nearest whole number)

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The distribution of a quantitative trait in a population can have important implications for the size and composition of the population over time.

Quantitative traits are characteristics that can be measured and quantified, such as height or weight. These traits often have a normal distribution pattern in large populations, meaning that most individuals fall within a certain range and there are fewer individuals at the extremes.

The normal distribution of a quantitative trait is often represented by a bell curve. This curve shows the frequency of individuals at different values of the trait, with the majority of individuals falling near the middle of the curve and fewer individuals at the extremes. The mean, or average, of the trait is located at the peak of the curve, and the standard deviation determines the width of the curve.

If the distribution shifts to the left, this means that there are fewer individuals with high values of the trait and more individuals with low values. This could occur if there is selective pressure against individuals with high values, or if there is a genetic mutation that affects the trait in a negative way.

As a result, the population size may increase, as individuals with low values of the trait are more likely to survive and reproduce.

Conversely, if the distribution shifts to the right, this means that there are fewer individuals with low values of the trait and more individuals with high values.

This could occur if there is selective pressure in favor of individuals with high values, or if there is a genetic mutation that affects the trait in a positive way.

As a result, the population size may also increase, as individuals with high values of the trait are more likely to survive and reproduce.

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The given statement "The bureau of justice statistics reported that in 2018, gang-related homicides accounted for 16% of all homicides in the united states, with the highest rates in the west and south." is True.

The Bureau of Justice Statistics (BJS) is a statistical agency within the U.S. Department of Justice that collects, analyzes, and disseminates data on crime, criminal offenders, and the justice system in the United States.

In 2018, the BJS reported that there were an estimated 16,214 homicides in the United States, and 2,641 of those homicides were gang-related. This means that gang-related homicides accounted for approximately 16% of all homicides in the United States in 2018.

The BJS also reported that the highest rates of gang-related homicides were in the Western and Southern regions of the United States. In the West, the rate of gang-related homicides was 6.9 per 100,000 residents, while in the South, the rate was 4.5 per 100,000 residents.

The Northeast and Midwest regions had lower rates of gang-related homicides, with rates of 1.4 and 2.5 per 100,000 residents, respectively.

The BJS defines gang-related homicides as "the killing of a person or people, where the victim(s) and offender(s) are known to be members of a gang." Gang-related homicides can be the result of conflicts between rival gangs, intra-gang violence, or violence directed at non-gang members.

The BJS notes that gang-related violence can have a significant impact on communities, including increased fear, reduced quality of life, and higher rates of property crime.

Overall, the BJS data on gang-related homicides in the United States highlights the need for continued efforts to prevent and address gang violence, and to improve public safety in communities affected by gang-related crime.

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The critical points of the function t(x,y) are:

(0,0)

(4,16)

To find the critical points of the function t(x,y), we need to find the points where the gradient is equal to zero or undefined.

Let's begin by computing the partial derivatives of t(x,y):

t_x = 3x^2 - 12y

t_y = 3y^2 - 12x

Now, we can set these partial derivatives equal to zero and solve for x and y:

3x^2 - 12y = 0

3y^2 - 12x = 0

Simplifying these equations, we get:

x^2 - 4y = 0

y^2 - 4x = 0

Multiplying the first equation by 4x and the second equation by 4y, we get:

4x^3 - 16xy = 0

4y^3 - 16xy = 0

Adding these equations together, we obtain:

4x^3 + 4y^3 - 32xy = 0

Dividing by 4, we get:

x^3 + y^3 - 8xy = 0

This is the equation of a curve known as the "folium of Descartes". It has a cusp at the origin and two other branches that intersect the x-axis and y-axis, respectively.

To find the critical points, we need to solve the system of equations:

x^2 - 4y = 0

y^2 - 4x = 0

x^3 + y^3 - 8xy = 0

From the first equation, we get:

x^2 = 4y

Substituting this into the second equation, we get:

y^2 - 16y = 0

This gives us two possible values for y: y = 0 or y = 16.

If y = 0, then x = 0 from the first equation. Substituting into the third equation, we get:

x^3 = 0

So the critical point is (0,0).

If y = 16, then x = 4 from the first equation. Substituting into the third equation, we get:

64 + 16^3 - 8(4)(16) = 0

Simplifying, we get:

64 + 4096 - 512 = 3648

So the critical point is (4,16).

We can classify these critical points by computing the Hessian matrix of t(x,y) and evaluating it at each critical point:

H = [t_xx t_xy]

[t_xy t_yy]

where t_xx, t_xy, and t_yy are the second partial derivatives of t(x,y).

At (0,0), we have:

t_xx = 6x = 0

t_xy = -12

t_yy = 6y = 0

So the Hessian matrix is:

H = [-12 0]

[ 0 -12]

The determinant of H is 144, which is positive, and the trace of H is -24, which is negative. Therefore, the critical point (0,0) is a saddle point.

At (4,16), we have:

t_xx = 6x = 24

t_xy = -12

t_yy = 6y = 96

So the Hessian matrix is:

H = [ 24 -12]

[-12 96]

The determinant of H is 2112, which is positive.

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