suppose the weight of coal in 43 cars selected at random had an average x of less than 61.5 tons. would that fact make you suspect that the loader had slipped out of adjustment? why?

The probability of Carlos drawing a blue marble, not replacing it, and then drawing another blue marble is E. 2/15.

The probability of drawing a blue marble on the first draw is 4/10 (since there are 4 blue marbles out of a total of 10 marbles in the bag).

If Carlos does not replace the first blue marble, then there will be 9 marbles left in the bag, of which 3 will be blue. So the probability of drawing another blue marble on the second draw is 3/9.

To find the probability of both events occurring, we multiply the probabilities together:

Probability of drawing a blue marble on the first draw: 4/10

Probability of drawing a blue marble on the second draw, given that the first draw was blue: 3/9

Probability of drawing two blue marbles in a row: (4/10) * (3/9) = 2/15, or approximately 0.133.

Therefore, the probability of Carlos drawing a blue marble, not replacing it, and then drawing another blue marble is approximately 0.133.

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A bag has 6 red and 4 blue marbles. What is the probability Carlos draws a blue marble, does not replace it, and then draws another blue marble?

7/105

6/225

1/35

2/90

2/15

The distance between City A and City B is approximately 2300.55 miles, rounded to the nearest hundredth of a mile.

Let's assume that City A is at latitude 6 degrees north and City B is at latitude 38 degrees north. Since they have the same longitude, we can assume a longitude of 0 degrees for both cities. We also have the radius of the Earth, which is 3960 miles.

Using the Haversine formula, the distance (d) between the two cities can be calculated as:

d = 2r * arcsin( sqrt( sin²((latB - latA)/2) + cos(latA) * cos(latB) * sin²((lonB - lonA)/2)) )

where r is the radius of the Earth, latA and latB are the latitudes of City A and City B in radians, and lonA and lonB are the longitudes of City A and City B in radians.

Converting the latitudes and longitudes to radians, we get:

latA = 6° * pi / 180 = 0.10472 radians

latB = 38° * pi / 180 = 0.66323 radians

lonA = 0° * pi / 180 = 0 radians

lonB = 0° * pi / 180 = 0 radians

Substituting the values in the formula, we get:

d = 2 * 3960 * arcsin( sqrt( sin²((0.66323 - 0.10472)/2) + cos(0.10472) * cos(0.66323) * sin²((0 - 0)/2)) )

Simplifying the expression, we get:

d ≈ 2300.55 miles

Therefore, the distance between City A and City B is approximately 2300.55 miles, rounded to the nearest hundredth of a mile.

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Prolongation of the aPTT test can be caused by a clotting factor level less than 40%, indicating potential bleeding disorder or inadequate anticoagulant therapy.

The actuated incomplete thromboplastin time (aPTT) test estimates the time it takes for blood to clump, and it is utilized to screen the viability of anticoagulant treatment or to distinguish draining problems. Prolongation of aPTT shows a lack in at least one coagulating factors.

The base level of a specific thickening element that will cause the aPTT test to become drawn out changes relying upon the particular coagulating factor being tried. Nonetheless, as a rule, a coagulating factor level under 40% is viewed as related with delayed aPTT. Consequently, in the event that the level of a specific thickening component falls underneath 40%, it can cause prolongation of the aPTT test, showing a potential draining problem or a lacking anticoagulant treatment.

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Answer:

Okay, I think the answer is D (correct me if I'm wrong, first check others' answers before putting it in)

Step-by-step explanation:

How I got this answer is I remembered that the slope is always the coefficient of x. Because 0.75 is the number next to the variable a for arm length you can assume that is the number the arm length increases for how much the height increases.

The minimum number of customers that need to be included in the test is 1492 members to determine if the new plan has more than a 6% point effect on customer retention, with 90% confidence.

The z-score corresponding to the desired confidence level of 90% = 1.645

The retention rate under the old plan =  1-p = = 0.7

The margin of error = E = 6 percentage points = 0.06

To calculate the minimum number of customers needed for the test, we can use the following formula:

[tex]n = (Z^2 * p * (1-p)) / E^2[/tex]

[tex]n = (1.645^2 * p * (1-p)) / 0.06^2[/tex]

assuming that p = 0.5

n = (1.645^2 * 0.5 * (1-0.5)) / 0.06^2

n = 1492

Therefore we can conclude that the minimum number of customers that need to be included in the test is 1492 members.

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Therefore, the solutions to the equation are x=-2+√3 and x=-2-√3.

The square root of a number is a value that, when multiplied by itself, gives the original number.

For example, the square root of 25 is 5, because 5 x 5 = 25.

The symbol used to represent square root is √.

If you want to find the square root of a number using a calculator or computer, you can use the square root function. For example, the square root of 64 can be found by typing "sqrt(64)" into a calculator, which would give you the answer of 8.

If you want to find the square root of a number by hand, there are a few methods you can use depending on the number. One common method is called the "long division method", which involves breaking down the number into factors and finding the square root of each factor. Another method is called the "guess and check method", which involves making educated guesses and adjusting until you find the square root.

Actually, the last step in your given solution is incorrect. Here are the correct steps to complete the square for the equation. [tex]\sqrt{(x^2+4x+1)}=2:[/tex]

Move the constant term to the right-hand side:

[tex]\sqrt{(x^2+4x)} = 1[/tex]

Add half of the coefficient of x squared to both sides:

[tex]\sqrt{(x^{2} +4x+4)}= 1+2[/tex]

Simplify the perfect square trinomial on the left-hand side and simplify the right-hand side:

[tex]\sqrt{(x+2)^2} = 3[/tex]

Take the square of both sides to eliminate the radical:

[tex]x+2 = \sqrt3[/tex]

Solve for x by subtracting 2 from both sides and considering both the positive and negative square root:

x = -2 ± √3

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According to the information, the area of the irregular octagon is approximately 111.8 square yards.

To find the area of a figure with 8 sides and given side lengths, we need to first determine what type of figure it is. Based on the side lengths provided, it is not immediately clear what type of figure it is. However, we can calculate the perimeter of the figure to gain some insights.

The perimeter of the figure is 40 yards, which suggests that it might be an octagon (a polygon with 8 sides). To confirm this, we can check if the side lengths satisfy the necessary condition for an octagon, which is that all 8 sides have to be equal or else they should be grouped in pairs of equal lengths. From the given side lengths, we can see that there are no pairs of equal lengths, so it is an irregular octagon.

To find the area of the irregular octagon, we can divide it into smaller shapes such as triangles and rectangles. One way to do this is to draw lines from one vertex to all the other vertices, dividing the octagon into 6 triangles and 2 rectangles. Then we can calculate the area of each individual shape and add them up to get the total area of the octagon.

This process can be tedious and time-consuming, so we can also use a formula to calculate the area of the irregular octagon. One common formula is the Brahmagupta's formula, which states that the area of an irregular quadrilateral (such as an octagon) can be calculated as:

where a, b, c, and d are the lengths of the sides, B and D are the opposite angles, and s is the semiperimeter (half the perimeter):

Using the given side lengths and the formula above, we can calculate the area of the irregular octagon. The calculations can be a bit involved, but using a calculator or spreadsheet can help make it easier.

After plugging in the side lengths and evaluating the formula, we get:

Therefore, the area of the irregular octagon is approximately 111.8 square yards.

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Answer:

Tucker has 2 one-dollar bills, 1 five-dollar bill, and 12 ten-dollar bills.

Step-by-step explanation:

The R-square value represents the correct output for the regression models by 71% of the variability in the number of chairs produced can be explained by whether the shift is in the morning or evening and whether it is a weekday shift or weekend shift

The R-square value in regression analysis tells us the proportion of the variability in the response variable.

That can be explained by the regression model.

In this case, the output states that the R-square value is 0.7059.

This means that 70.59% of the variability in the number of chairs produced.

This can be explained by the independent variables in the model which is whether the shift is in the morning or evening and whether it is a weekday or weekend shift.

Therefore, the correct option for the regression model is 'That 71% of the variability in the number of chairs produced can be explained by whether the shift is in the morning or evening and whether it is a weekday shift or weekend shift.'

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The above question is incomplete, the complete question is:

Below is some output from the regression on the furniture factory data. What does the R-square value tell us?

That we cannot reject the null hypothesis

That there is multicollinearity between the independent variables

That on average, 0.7059 more chairs are produced during weekday shifts than during weekend shifts.

That 71% of the variability in the number of chairs produced can be explained by whether the shift is in the morning or evening and whether it is a weekday shift or weekend shift.

As a result, the sector QPR's area is roughly 60.3 m².

We must apply the following algorithm to determine the sector QPR's area:

Sector QPR area = θ/360°(r²)

where r is the circle's radius, is a constant equal to roughly 3.14, and is the sector's angle in degrees.

We can substitute these numbers into the calculation and simplify it because the angle in this example is provided as 80 degrees and the radius r as 8 meters:

QPR sector area = (108/360)(8)²

QPR sector area = (0.3)(64)

QPR sector area = 19.2

QPR sector area = 19.2

QPR sector area = 60.318°

As a result, the sector QPR's area is roughly 60.3 m².

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Therefore , the solution of the given problem of area comes out to be the picture's revised dimensions are 21 feet long and 15 feet wide.

What is scale factor?

A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.

What exactly does an area mean?

Its total size can be determined by figuring out how much area would be required to completely enclose its exterior. When choosing a comparable product for the rectangular design, the surrounding area is taken into account. The total measurements of something are determined by its surface area. The volume of water a cuboid can contain depends on the number in sides between its four trapezoidal shapes.

Here,

The initial image's length and width must be multiplied by 3 in order to enlarge it by a scale factor of 3.

=>  7 feet in length at first.

=>  5 foot original diameter

=> New length = 7ft x 3 = 21ft

=>  New width = 5ft x 3 = 15ft

As a result, the picture's revised dimensions are 21 feet long and 15 feet wide.

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There are 60 seconds in a minute and 60 minutes in an hour. To find the total number of instructions the computer can perform in an hour, we need to multiply the number of instructions per second by the number of seconds in an hour.

Number of seconds in an hour = 60 seconds/minute × 60 minutes/hour = 3600 seconds/hour

Total number of instructions per hour = instructions per second × seconds per hour

= 4.66 × 10^8 instructions/second × 3600 seconds/hour

= 1.6776 × 10^12 instructions/hour

Therefore, the computer can perform 1.6776 x 10^12 instructions per hour.

Answer: Three of eight sectors do not move the token; this area is 35.9 in2.

To find the radius of the spinner:      A  =  pi · r2

                                                    35.9  =  (3/8) · pi · r2

                                                    35.9  =  1.1781 · r2

                                                   30.73  =  r2

                                                           r  =  5.5 in

Step-by-step explanation:

D) 20 ft.

If the area of a square garden is 25 square feet, it means that the length of each side of the square is the square root of 25, which is 5 feet.

To find the perimeter of the square garden, we need to add up the lengths of all four sides. Since all sides of a square are equal, we can simply multiply the length of one side by 4 to get the perimeter.

Perimeter = 4 x length of one side

Perimeter = 4 x 5 ft

Perimeter = 20 ft

Therefore, the perimeter of the square garden is 20 feet.

The relationship between length and weight can be modeled by a power function.

The fact that the scatterplot of the natural logarithm of weight vs. the natural logarithm of length shows a more linear relationship suggests that the relationship between length and weight can be better modeled by a power function rather than an exponential function. This is because when the logarithms of both variables are taken, an exponential function becomes a linear function, while a power function remains a non-linear function.

In a power function, one variable is raised to a power that is not necessarily an integer, whereas in an exponential function, one variable is raised to a constant power. Therefore, it is more likely that the relationship between length and weight can be modeled by a power function.

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The most relevant answer to this question is researcher conducting a qualitative study knows that saturation of information has occurred when data collected confirms theoretical models.

In qualitative research, data saturation refers to when the collection of new data no longer leads to additional ideas or themes.

In other words, saturation occurs when data has been thoroughly explored and little or no new information or new patterns emerge.

so, the researcher can be sure that he or she has collected enough data to answer the research question, and collecting more data is unlikely for new insights.

Therefore, Using the data provided, we can calculate:  

x = (38.1 + 38.4 + 38.3 + 38.2 + 38.2 + 37.9 + 38.7 + 38.6 + 38.0 + 38.2) / 10 = 38.25

In a t distribution table or calculator, find the t value with 9 (n-1) degrees of freedom and 95% confidence intervals. This is approximately 2.262.

Substituting these values ​​into the formula gives:

therefore, the most relevant answer to this is data collected confirms theoretical models.

This means that the researcher has collected enough data to confirm or disprove their original theoretical models, and collecting more data is unlikely to change those models. 

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The calculated slope of the lot is 25/cos(angle)

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

The figure

The slope of the lot is the length of the hypotenuse

So, we have

cos(angle) = 25/slope

This gives

slope = 25/cos(angle)

Hence, the slope is 25/cos(angle)

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Answer: Let's assume that the zeros of the given quadratic equation are a and 1/a, since they are reciprocals of each other. By the sum-product relationships for zeros of a quadratic equation, we have:

a + 1/a = -b/a1 = -4/(1-3k) (where b = 4 and a1 = 1-3k)

Multiplying both sides by a1, we get:

a1(a + 1/a) = -4

Expanding the left-hand side, we get:

a1a + a1/a = -4

Multiplying both sides by a, we get:

a1a² + a1 = -4a

Substituting a1 = 1-3k, we get:

(1-3k)a² + (1-3k) = -4a

Rearranging, we get:

(1-3k)a² + 4a + (3k-1) = 0

Since a is one of the zeros of the quadratic, we know that the quadratic can be factored as:

(1-3k)(a - r)(a - s) = 0

where r and s are the other two roots of the quadratic. By expanding the left-hand side, we get:

(1-3k)(a² - (r+s)a + rs) = 0

Comparing with the expanded form of the quadratic, we see that:

r + s = -4/(1-3k)

rs = (3k-1)/(1-3k)

By Vieta's formulas, we know that rs = c/a1, where c is the constant term of the quadratic. Substituting c = -5 and a1 = 1-3k, we get:

rs = -5/(1-3k)

Equating this with the expression we obtained earlier for rs, we get:

-5/(1-3k) = (3k-1)/(1-3k)

Multiplying both sides by 1-3k and simplifying, we get:

-5 = (3k-1)(3k-2)

Expanding the right-hand side, we get:

-5 = 9k² - 15k + 2

Simplifying, we get:

9k² - 15k - 7 = 0

Using the quadratic formula, we get:

k = (15 ± sqrt(15² + 497))/18

k = (15 ± sqrt(429))/18

Therefore, the two possible values of k are:

k = (15 + sqrt(429))/18 ≈ 1.57

k = (15 - sqrt(429))/18 ≈ -0.24

Note that both of these values of k satisfy the condition that the zeros of the quadratic are reciprocals of each other.

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

m∠B and m∠D are congruent angles, which means they are equal in measurement.

We can write the following equation to find the value of x:

5x - 7 = 3x + 21

5x - 3x = 21 + 7

2x = 28

x = 14

To find the measure of m∠B, replace x with 14:

5 × 14 - 7 = 63°

63 + m∠C = 180

m∠C = 117°

Thus, the height of the water in the tank is increasing at a rate of approximately 4 / (9π) meters per minute

To solve this problem, we need to find the rate at which the height of the water is increasing. Let's call the height of the water in the tank h(t), and the rate at which it is increasing dh/dt. We know that the volume of a cylinder is given by the formula[tex] V = πr^2h[/tex], where V is the volume, r is the radius, and h is the height.
Given information:
- The radius of the cylindrical tank, r, is 3 m.
- The volume of water, V, is being filled at a rate of 4 m^3/min.
We want to find dh/dt. First, we need to find the expression for the volume of the water in the tank with respect to time, V(t):
V(t) = π(3)^2*h(t)
V(t) = 9π*h(t)
Now, we can find the derivative of V(t) with respect to time:
dV/dt = 9π*dh/dt
We know that dV/dt = 4 m^3/min. Therefore:
4 = 9π*dh/dt
Now, we can solve for dh/dt:
dh/dt = 4 / (9π)

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The amplitude of the sine equation y = 2sin(Θ) - 3 is 6.

What is Graph ?

A graph is a data structure that represents a set of objects and the relationships between them. It consists of a collection of vertices (also known as nodes or points) and a collection of edges (also known as links or arcs) that connect the vertices.

The amplitude of a sine function is the distance between the maximum and minimum values of the function.

From the given graph of y = 2sin(Θ) - 3, we can see that the maximum value of the function is 2 and the minimum value is -4.

Therefore, the amplitude is the absolute value of the difference between the maximum and minimum values:

amplitude = |2 - (-4)| = |2 + 4| = 6

So, the amplitude of the sine equation y = 2sin(Θ) - 3 is 6.

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One of the most notable intellectual achievements of the Maya civilization was their use of the mathematical concept known as the zero decimal system.

The Maya developed a sophisticated numerical system that allowed them to perform complex calculations, which was essential for their advancements in various fields such as astronomy, agriculture, and architecture.
The zero decimal system used by the Maya was a base-20 (vigesimal) system that incorporated the concept of zero as a placeholder. This was a significant breakthrough in mathematics, as it enabled the Maya to perform complex calculations and record large numbers more efficiently.
Here's a step-by-step explanation of how the Maya zero decimal system worked:
1. The Maya used a combination of dots and bars to represent numbers. A dot represented the number 1, and a bar represented the number 5.
2. Numbers from 1 to 19 were written using a combination of dots and bars. For example, the number 7 would be represented as one bar (5) and two dots (1 + 1).
3. To represent the number zero, the Maya used a unique symbol called a shell glyph.
4. The Maya zero decimal system was positional, meaning that the value of a digit depended on its position within a number. For example, in the number 24, the digit 2 is in the 20s position, and the digit 4 is in the ones position.
5. To write numbers larger than 19, the Maya used a vertical arrangement of glyphs, with the ones at the bottom, the 20s above them, the 400s above that, and so on.
The use of the zero decimal system allowed the Maya to excel in various fields, such as creating an accurate calendar system, predicting celestial events, and planning agricultural activities. This mathematical achievement is a testament to the advanced intellectual capabilities of the Maya civilization.

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The patient's systolic pressure will be the lowest during the time interval 5 < t < 8, when they take the medication at 9 a.m.

The given piecewise function for systolic pressure S(t) has two segments, one for the time interval 5 < t < 8 and another for 8 ≤ t ≤ 12.

For 5 < t < 8, the systolic pressure is a constant value of 115. Therefore, the systolic pressure remains the same during this time interval, and it will not be the lowest.

For 8 ≤ t ≤ 12, the systolic pressure increases linearly with time, starting from 140 and increasing by 9 units every hour. Therefore, the systolic pressure at the beginning of this interval is 140, and it increases until it reaches the maximum value of 211 at t=12.

Since the systolic pressure is highest at the end of the second interval, the lowest value of the systolic pressure must occur in the first interval, which is 5 < t < 8. Therefore, the patient's systolic pressure will be lowest during this time interval, and it will be a constant value of 115.

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The given question is incomplete, the complete question is:

When a patient with hypertension takes a particular type of blood pressure medication, the effects on the systolic pressure, S(t), can be (140-5tif Osts 5 measured by the following piecewise defined function: S(t) = 115 if 5<t<8 - where t is the time, in hours, since 43 +9t if 8sts 12 taking the medication. Based on the graph of the piecewise function, if the patient takes the blood pressure medication at 9 a.m., in which interval will their systolic pressure be lowest?

The value of angle RTS is determined as 75⁰.

The value of angle RTS depends on the value of the arc angle SR.

The value of arc angle SR is calculated by finding the value of x, and we will have the following equation.

38x - 2 + 18x - 2 + 34x + 4 = 360 (sum of angles in a circle)

90x = 360

x = 360/90

x = 4

The value of arc angle SR = 38x - 2

= 38(4) - 2

= 150⁰

The value of angle RTS is equal to half of arc angle SR (based on intersecting chord theorem)

∠RTS = ¹/₂ x 150⁰

∠RTS =  75⁰

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Check the picture below.

The answer of the given question is , part 1 - No, a non-complex equation cannot have two horizontal asymptotes , part 2- a non-complex equation cannot have two vertical asymptotes , part 3-  vertical behavior does not apply to complex numbers.

A horizontal asymptote is horizontal line that  function approaches as x goes to positive or negative infinity. In other words, it describes the long-term behavior of the function as x gets very large or very small.

For a function f(x), if the values of f(x) get closer and closer to a specific number L as x approaches infinity or negative infinity, then the line y = L is a horizontal asymptote of the function.

No, a non-complex equation cannot have two horizontal asymptotes. A horizontal asymptote represents the behavior of a function as x approaches positive or negative infinity, and it is determined by the highest power of x in the denominator and numerator of the function. A non-complex equation can only have one horizontal asymptote, which can be a horizontal line or a slant asymptote.

Similarly, a non-complex equation cannot have two vertical asymptotes. A vertical asymptote occurs when the denominator of a function approaches zero and the numerator does not. A non-complex equation can have multiple vertical asymptotes, but they must be distinct values of x.

If a complex number is used as x, an equation could pass through a vertical asymptote because the notion of vertical behavior does not apply to complex numbers. However, the concept of horizontal asymptotes still applies to complex numbers, and an equation cannot have two horizontal asymptotes in the complex plane.

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The constant in the given expression is

C. 9

In a mathematical expression, a constant is a value that does not change and remains the same throughout the expression or equation.

It is a fixed numerical value, coefficient, or term that is independent of the variable(s) in the expression.

For example, in the expression 15x^2 + 2x + 9, the constant is 9, as it remains the same regardless of the value of x.

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For moviegoers who are younger than 12 years old, the ticket price is a fixed amount of $5. This is represented by the first rule of the piecewise function

For moviegoers who are 12 years old or older, but younger than 55, the ticket price is also a fixed amount, but this time it is $9. This is represented by the second rule of the piecewise function

For moviegoers who are 55 years old or older, a special rate is available, and the ticket price is $7. This is represented by the third rule of the piecewise function

So, for a 16 year-old, the ticket price would be $9.

For a 12 year-old, the ticket price would also be $5.

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Answer:

The second one is correct

Step-by-step explanation:

1. Replace x in the equation with the given x (from the table):

y = 2x - 3

x = -1, y = 2 × (-1) - 3 = -2 - 3 = -5

x = 0, y = 2 × 0 - 3 = 0 - 3 = -3

x = 1, y = 2 × 1 - 3 = 2 - 3 = -1

x = 2, y = 2 × 2 - 3 = 4 - 3 = 1

x = 3, y = 2 × 3 - 3 = 6 - 3 = 3

.

2. y = -x + 6

x = -1, y = -(-1) + 6 = 1 + 6 = 7

x = 0, y = -0 + 6 = 6

x = 1, y = -1 + 6 = 5

x = 2, y = -2 + 6 = 4

x = 3, y = -3 + 6 = 3