Calculate the distance between the points N and C in the coordinate plane.

Give an exact answer (not a decimal approximation)..... How would i solve something like this?

The coefficient of determination or R² is -0.932. The coefficient of correlation or R is 0.964. The equation of the regression line is:Y= 27,233.25 + (960.25X)Y= 27,233.25 + 0.96X.

A magrzeino used the surnunatod rating of 10 restaurants to predut the cost of a restaurant meal. For that data, SSR \(-131,383.63 \) and SST \( =140,70746 \). The task is to complete parts (a) through (c). a) Determining the coefficient of determination or R²R² can be determined using the formula given below: R²= SSR/SST R²= -131,383.63 /140,707.46 R²= -0.932 Thus, the coefficient of determination or R² is -0.932.(b) Determining the coefficient of correlation or RTo determine the coefficient of correlation, we will use the formula given below:R= sqrt(R²)R= sqrt(-0.932)R= 0.964 Thus, the coefficient of correlation or R is 0.964.(c) Determining the equation of the regression lineUsing the formula,

The equation of the regression line can be calculated as:Y= a + bX where a = Y - bX, b = r (sy/sx)and r is the correlation coefficient.The given data can be arranged into a table as shown below:X (Sur)Y (Cost of a restaurant meal)XYX²Y²1200180020003600840030007601440040009002250045001020250601000050011200027501250222501250015003700022501650142252,306,901387,762,1509,622,5001,293,900248,408,050The values of ΣX, ΣY, ΣXY, ΣX², and ΣY² can be calculated from the table. ΣX = 55ΣY = 85,900ΣXY = 960,250ΣX² = 3850ΣY² = 69,635,950Then, a = (ΣYΣX² - ΣXΣXY) / nΔ= 10(a)Δ= [(85,900 x 3850) - (55 x 960,250)] / 10Δ= (330,115,000 - 52,814,750) / 10Δ= 27,233.25Therefore, the equation of the regression line is:Y= 27,233.25 + (960.25X)Y= 27,233.25 + 0.96X.

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The psychologists should respect the dignity and rights of their clients, colleagues, and research participants.

Likert-responses in the social sciences are considered ordinal in nature. The Likert Scale is a psychometric tool used to measure attitudes or opinions of a group of people or an individual. It is named after its developer, Rensis Likert, who was an American psychologist. The Likert Scale includes a series of statements that respondents are asked to respond to based on their level of agreement or disagreement. The scale can have an odd or even number of response options, with the most common being a 5-point scale.

The Belmont Report is a 3-principle guideline that informs ethical practices in research involving human subjects. The three principles are:

1. Respect for persons: Participants should be treated as autonomous agents who are capable of making decisions for themselves.
2. Beneficence: The research should have potential benefits that justify the risks involved.
3. Justice: The selection of participants should be fair and representative.

The APA Code of Ethics, on the other hand, has 5 principles. They are:

1. Beneficence and Non-maleficence: Psychologists should do no harm and ensure that their interventions have positive outcomes.
2. Fidelity and Responsibility: Psychologists should uphold their professional responsibilities and strive to be honest, trustworthy, and respectful.
3. Integrity: Psychologists should promote accuracy, honesty, and truthfulness in their research, teaching, and practice.
4. Justice: Psychologists should promote fairness and justice in their work and ensure that their research is unbiased and representative.
5. Respect for People's Rights and Dignity: Psychologists should respect the dignity and rights of their clients, colleagues, and research participants.

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Answer:N/A

Step-by-step explanation:

I need more context to answer this question.

Eva and Jin volunteer on the first day of the month, if they volunteer once a month (assuming this month has 31 days) it would be 31 days until they volunteer again. Now, if Eva volunteers every 6 days and Jin volunteers every two days (this is just an example) on the sixth of the month is when they will volunteer on the same day. If you want a complete answer I would recommend writing the whole question.

Two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.

Two polygons are said to be similar if they have the same shape, but not the same size. A polygon is any two-dimensional closed shape with straight lines. Similar polygons have the same number of sides and angles. The sides of the similar polygons are proportional to the corresponding sides of the other polygon.

The ratio of their corresponding sides is the same as the ratio of their perimeter. The angles of the similar polygons are congruent to the corresponding angles of the other polygon. The ratio of their corresponding angles is the same as the ratio of their measure.

The corresponding sides and angles are the ones that match between the two polygons. In other words, they are the sides and angles that are in the same position in the two polygons. For example, side AB in polygon ABC corresponds to side DE in polygon DEF. Angle A in polygon ABC corresponds to angle D in polygon DEF.

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The solutions to the compound inequality are as follows:

x > 4 or x ≥ 2.

A compound inequality in mathematics is a phrase that joins two claims with the conjunctions "and" or "or."

Both of the statements are true simultaneously if the conjunction "and" is used to unite them in the compound sentence. If the conjunction "or" is used to combine the assertions, then the compound statement is true if at least one of the claims is true.

Now solving the inequality:

2x + 9 > 17 or -5x ≥ 10.

2x + 9 > 17

⇒ 2x > 8

⇒ x > 4

Now,

-5x ≥ 10

⇒ -x ≥ 2

⇒ x ≥ 2

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[tex]2x+9 > 17\ or\ -5x\geq 10[/tex] compound inequalities is as follows:

x > 4 or x ≥ 2.

In mathematics, a compound inequality is a sentence containing two statements joined by the word "and" or "or". If the statements are connected by the word "and", both statements in a compound sentence are true at the same time. A compound statement is true if at least one statement is true if the statements are connected by "or" A compound statement is true if at least one statement is true.

[tex]2x+9 > 17\ or\ -5x\geq 10[/tex]

Let take [tex]2x+9 > 17[/tex]

Subtract -9 on both sides

= 2x+9-9 > 17-9

= 2x+0 > 8

= 2x > 8

Now we need to divide by 2 both sides

= 2x÷2 > 8÷2

= x > 4

Now we solve -5x ≥ 10

= -5x ≥ 10

= -x ≥ 2

= x ≥ 2

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Answer:

774 total coins

Step-by-step explanation:

The height of the given rectangle is

126, so we have 126 ÷ 7 = 18.

Counting by 18's, we have

18 × 3 = 54 coins between 0 grams and 5 grams.

18 × 20 = 360 coins between 5 grams and 7 grams.

18 × 13 = 234 coins between 17 and 22 grams.

126 + 54 + 360 + 234 = 774 total coins.

The new coordinates that define the figure after dilation with a center at the origin by a scale factor of 1/3 are (0, 0), (0, 4/3), (1, 0), and (1, 4/3).

The new coordinates that define the figure after dilation with a center at the origin by a scale factor of 3/2 are (0, 0), (9/2, 0), (0, 6), and (9/2, 6).

The points that weren't used in either point A or B are (6, 0), (4/3, 0).

In Mathematics and Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/3 centered at the origin as follows:

Ordered pair A (0, 0) → Ordered pair A' (0 × 1/3, 0 × 1/3) = (0, 0).

Ordered pair B (3, 0) → Ordered pair B' (3 × 1/3, 0 × 1/3) = (1, 0).

Ordered pair C (0, 4) → Ordered pair C' (0 × 1/3, 4 × 1/3) = (0, 4/3).

Ordered pair D (3, 4) → Ordered pair C' (3 × 1/3, 4 × 1/3) = (1, 4/3).

Furthermore, we would dilate the coordinates of the pre-image by using a scale factor of 3/2 centered at the origin as follows:

Ordered pair A (0, 0) → Ordered pair A' (0 × 3/2, 0 × 3/2) = (0, 0).

Ordered pair B (3, 0) → Ordered pair B' (3 × 3/2, 0 × 3/2) = (9/2, 0).

Ordered pair C (0, 4) → Ordered pair C' (0 × 3/2, 4 × 3/2) = (0, 6).

Ordered pair D (3, 4) → Ordered pair C' (3 × 3/2, 4 × 3/2) = (9/2, 6).

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Complete Question:

Match the new coordinates that define the figure after dilation with a center at the origin by the given scale factor.

List of new coordinates: (0, 6) , (0, 4/3) , (1, 0) , (1, 4/3) , (6, 0) , (4/3, 0) , (9/2, 0) , (9/2, 6)

Scale factor 1/3: (List all coordinates under scale factor 1/3)

Scale Factor 3/2: (List all coordinates under scale factor 3/2)

Point NOT USED: (List all coordinates under Point NOT USED if they couldn't be used)

The displacement of the particle from time t=0 to time t=15 is approximately -11.37.

The displacement of the particle from time t=0 to time t=15 is given by the formula[tex]$\Delta x = x(t_2) - x(t_1)$[/tex]. Using the given velocity function and the initial position of the particle, we can calculate the displacement of the particle from time t=0 to time t=15 as follows:
[tex]$\Delta x = x(15) - x(0) = \into_{0}^{15} v(t) dt - 2.5 = \int_{0}^{15} cos(8e^{-0.2t}) dt - 2.5$[/tex]
Using integration by parts, we get:
[tex]$\Delta x = -sin(8e^{-0.2*15}) + sin(8e^{-0.2*0}) - 2.5$[/tex]
Therefore, the displacement of the particle from time t=0 to time t=15 is given by:
[tex]$\Delta x[/tex] =[tex]-sin(8e^{-3})[/tex]+ [tex]sin(8) - 2.5$[/tex]
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Derick must buy more than 10 tacos for the VIP option to be cheaper than General Admission.

Total cost refers to the complete amount of money spent to produce or purchase a good or service. It includes both the fixed costs and the variable costs, as well as any other expenses incurred in the process, such as labor costs, materials, transportation, and overhead costs.

1) If Derick plans to buy 6 tacos, let's calculate the total cost of each option:

General Admission:

Admission: $10

Tacos: 6 x $4 = $24

Total: $10 + $24 = $34

VIP:

Admission: $35

Tacos: 6 x $1.50 = $9

Total: $35 + $9 = $44

Therefore, if Derick plans to buy 6 tacos, he should choose the General Admission option as it is cheaper.

2) If Derick has $50 to spend and wants to eat as many tacos as he can, let's calculate the maximum number of tacos he can buy under each option:

General Admission:

Tacos: ($50 - $10 - $5) / $4 = 8.75 tacos (rounded down to 8 tacos)

Total cost: $10 + $4 x 8 + $5 = $43

VIP:

Tacos: ($50 - $35) / $1.5 = 10.67 tacos (rounded down to 10 tacos)

Total cost: $35 + $1.5 x 10 = $50

Therefore, if Derick has $50 to spend and wants to eat as many tacos as he can, he should choose the VIP option as he can buy more tacos for the same amount of money.

3) To find the number of tacos that Derick must buy for the VIP option to be cheaper than General Admission, we need to set up an equation to solve for the number of tacos:

General Admission: $10 + $4x = total cost

VIP: $35 + $1.5x = total cost

We want to find the value of x (number of tacos) where the cost of the VIP option is less than the cost of the General Admission option:

$35 + $1.5x < $10 + $4x

Simplifying the inequality, we get:

$25 < $2.5x

Dividing both sides by $2.5, we get:

x > 10

Therefore, Derick must buy more than 10 tacos for the VIP option to be cheaper than General Admission.

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The simplification of the given square root expression by using the rules of indices is obtained as: 9/8.

Any product of numbers is written relatively succinctly using a power or an index. Indexes is the plural of index. In this booklet, we will remind everyone of how to do this and list some laws or principles that can be applied to make indices-based expressions simpler.

The laws of indices are a set of guidelines used to regulate expressions involving indices.

The given expression is-

= [tex]\sqrt{(\frac{9}{8})^{2} }[/tex]

Convert the square root into the fractional power.

= [tex]((\frac{9}{8} )^{2}) ^{\frac{1}{2} }[/tex]

This, power 1/2 and 2 will get cancelled to give:

= 9/8

Thus, the simplification of the given square root expression by using the rules of indices is obtained as: 9/8.

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Answer: [tex]6\sqrt{2}[/tex]

Step-by-step explanation:

We know that one angle is 45 degrees and another is 90 degrees. That means the third angle is also 45 degrees, because all angles in a triangle add up to 180 degrees. This means that the triangle we are dealing with is an isosceles right triangle, meaning the the 2 equal legs form a right angle and are equal in length. If one leg is 6, the other leg must be 6, too.

Then, by the Pythagorean theorem, x=[tex]\sqrt{6^2+6^2}[/tex]=[tex]\sqrt{72}=6\sqrt{2}[/tex].

In response to the query, we can state that We can broaden the equation to test if it corresponds to the provided table:

[tex]0: p(0) = 0^2 - 11(0) + 19.25 = 17\s1: p(1) = 1^2 - 11(1[/tex]

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

[tex]ax^2 + bx^2 + c = p(x)[/tex]

We can determine a and b by using the coordinates of any two points on the parabola. Using points (1, 7) and (2, 1) as examples

[tex]a(1)^2 + b(1) + c = 7\\a(2)^2 + b(2) + c = 1[/tex]

When we simplify each equation, we obtain:

[tex]a + b + c = 7\\4a + 2b + c = 1\\h = -b / 2a = -(-11) / 2(1) = 5.5[/tex]

Hence, the vertex is (5.5, p(5.5)), and to finish the equation, we merely need to determine p(5.5).

We can broaden the equation to test if it corresponds to the provided table:

[tex]p(x) = (x - 5.5) (x - 5.5)\\a^2 - 11\s= x^2 - 11x + 30.25 - 11\s= x^2 - 11x + 19.25\\-1: p(-1) = (-1) (-1)\\a^2 - 11(-1) + 19.25 = 31\\[/tex]

[tex]0: p(0) = 0^2 - 11(0) + 19.25 = 17\s1: p(1) = 1^2 - 11(1[/tex]

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Answer:

Z = 108º

Step-by-step explanation:

The interior angles of a quadrilateral (4-sided figure) sum to 360º (think about a rectangle). Therefore,

(x + 2x + 4x + 3x)º = 360º

↓ combining like terms

10xº = 360º

↓ dividing by 10º

x = 36

We can use this x-value to find the measure of angle Z.

Z = 3xº

Z = 3(36)º

Z = 108º

Answer: f(0) ≈ 4.37

Step-by-step explanation:

We can use the information given to find the base and the equation of the exponential function.

Let the exponential function be of the form f(x) = a*b^x, where a is the initial value of f(0) and b is the base of the exponential function.

From the given information, we have:

f(-3) = 27 = ab^(-3)

f(0.5) = 83 = ab^(0.5)

To eliminate the variable a, we can divide the second equation by the first equation:

f(0.5)/f(-3) = (ab^(0.5))/(ab^(-3))

83/27 = b^(0.5+3)

b^3 = (83/27)^2

b = (83/27)^(2/3)

Substituting this value of b in the first equation, we can solve for a:

27 = a*(83/27)^(-1)

a = 27*(83/27)

Therefore, the equation of the exponential function is f(x) = (83/27)^(2/3)*((83/27)^(-1))^x.

To find f(0), we substitute x = 0 in the above equation:

f(0) = (83/27)^(2/3)*((83/27)^(-1))^0

f(0) = (83/27)^(2/3)

f(0) ≈ 4.37

Solution set is {7, -6}

The given logarithmic equation is as follows:loga(x - 2) - loga(x + 9) = loga(x - 3) - loga(x + 4)To determine the equation to be solved after removing the logarithm, we need to apply the logarithmic identity:loga(b) - loga(c) = loga(b / c)Using this identity in the above equation, we get:loga[(x - 2) / (x + 9)] = loga[(x - 3) / (x + 4)]Now, we can equate the logarithmic expressions inside the function. Therefore,(x - 2) / (x + 9) = (x - 3) / (x + 4)Cross-multiplying the above equation, we get:(x - 2)(x + 4) = (x + 9)(x - 3)Simplifying the above equation, we get:x² - 5x - 42 = 0Factoring the above equation, we get:(x - 7)(x + 6) = 0Therefore, the solutions are x = 7 and x = -6. Hence, the solution set is {7, -6}.Thus, the correct choice is A. The solution set is {7, -6}.

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Step-by-step explanation:

See image:

A typical student in Mr. Hart’s class studies 1.56 hours per week and a typical student in Ms. Perry’s class studies 1.67 hours per week.

The mean is the average of a set of data, calculated by adding all the values in the set and dividing the sum by the number of values. The formula for calculating the mean is:

Mean = (Sum of all values) / (Number of values)

To calculate the mean of Mr. Hart’s class, we will first add up all the values from 0 to 8 in the dot plot:

0 + 0 + 2 + 2 + 1 + 4 + 2 + 1 + 2 = 14

We then divide this sum by the total number of values, which is 9:

Mean = 14 / 9 = 1.56

The mean of Mr. Hart’s class is 1.56 hours of studying per week.

Similarly, to calculate the mean of Ms. Perry’s class, we will add up all the values from 0 to 8 in the dot plot:

2 + 4 + 1 + 3 + 2 + 1 + 1 + 0 + 1 = 15

We then divide this sum by the total number of values, which is 9:

Mean = 15 / 9 = 1.67

The mean of Ms. Perry’s class is 1.67 hours of studying per week.

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The answer of the given question based on similarity is the missing length UT is approximately 66.67.

A triangle is  basic two-dimensional geometric shape that consists of the three straight sides and three angles. Triangles can be classified in different ways based on the sides and angles. Based on their sides, triangles can be classified as the equilateral, the isosceles or the scalene. the equilateral triangle has three equal sides, the  isosceles triangle has two equal sides, and the scalene triangle has no equal sides.

Based on their angles, triangles can be classified as acute, obtuse, or right-angled. A right-angled triangle has one angle that is a right angle (90 degrees), an acute triangle has all angles less than 90 degrees, and an obtuse triangle has one angle greater than 90 degrees.

Since the triangles UVT and MLK are similar, their corresponding sides are proportional. We can set the following proportion:

UT/UVT = LK/MLK

Substituting the given values, we get:

UT/60 = 130/117

Solving for UT, we get:

UT = (60 x 130)/117

UT ≈ 66.67

Therefore, the missing length UT is approximately 66.67.

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Answer: x=10

Step-by-step explanation:

sum of all the angles inside triangle is equal to 180degrees.

First angle: 9x-16

Second angle: 7x-5

Third angle: 3x+11

let's sum this angles:

9x-16+7x-5+3x+11=19x-10=180

19x=180+10=190

x=190/19=10

The number of cubes that are needed to fill the rectangular prism is given as follows:

648 cubes.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions of the prism are given as follows:

l = 6 cm, w = 3 cm, h = 4.5 cm.

Hence the volume of the prism is given as follows:

V = 6 x 3 x 4.5

V = 81 cm³.

The volume of the cube is given as follows:

V = (0.5)³

V = 0.125.

Hence the number of cubes needed to fill the prism is given as follows:

81/0.125 = 648 cubes.

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Answer:

all are irrational except 2 and 3

The probability that fewer than three calls will be received in the first 6 seconds is 0.9197 or approximately 0.92.

Given:

Let's convert the given time period of 6 seconds into minutes, as our arrival rate is in calls per minute.

6 seconds = 6/60 minutes = 0.1 minutes

We are given that the average rate of calls is 10 per minute, which means that the arrival rate per 0.1 minute is:

A = 10/minute * 0.1 minute = 1 call

We need to find the probability that fewer than three calls will be received in 0.1 minutes. We can use the Poisson distribution formula to calculate this probability:

Pr(X < 3) = Pr(X=0) + Pr(X=1) + Pr(X=2)Pr(X=k) = At^k/k! , so

Pr(X=0) = e^(-A)*(A^0/0!) = e^(-1) = 0.3679

Pr(X=1) = e^(-A)*(A^1/1!) = e^(-1)*1 = 0.3679

Pr(X=2) = e^(-A)*(A^2/2!) = e^(-1)11/2 = 0.1839

Therefore,

Pr(X < 3) = 0.3679 + 0.3679 + 0.1839 = 0.9197

Hence, the probability that fewer than three calls will be received in the first 6 seconds is 0.9197 or approximately 0.92.

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The reason why fixed effect models cannot estimate coefficients on variables that do not vary within a unit is because the de-meaned variables will not vary. The correct option is that the de-meaned variables will not vary within the unit.

A fixed-effect model is a statistical approach that is used to estimate the impact of time-invariant variables on an outcome variable. The model evaluates the fixed effects or constant differences between individual entities in a sample by controlling for the unobserved heterogeneity. In general, fixed effects models are commonly used in fields like economics, political science, public health, and social sciences.

In a fixed effect model, a "unit" refers to the subjects or observations that are being studied. A unit could be an individual, a company, a region, or anything else that the researcher is interested in studying. The fixed effect model is used to estimate the constant differences in the outcome variable between individual units by controlling for the unobserved heterogeneity.

What are the limitations of fixed effect models?

One of the limitations of fixed effect models is that they cannot estimate coefficients on variables that do not vary within a unit. This is because the de-meaned variables will not vary within the unit. Additionally, fixed effect models cannot be used to estimate the impact of time-invariant variables on the outcome variable. This is because these models rely on within-unit variation to identify the effects of the independent variables.

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Answer:

If E(x,y), then E’(x-5,y+3)

Step-by-step explanation:

Depending on E, E’ changes. The new coordinates for E’, however, is (x-5, y+3), if (x,y) is E, since you move left (-) 5 and up (+) 3.

Answer:2.5e-9

Step-by-step explanation:

Para resolver la multiplicación 34 x 4 usando sumas repetidas, podemos seguir los siguientes pasos:

Empezamos sumando 34 cuatro veces:

34 + 34 + 34 + 34 = 136

La suma resultante de la etapa anterior es la respuesta, por lo que podemos concluir que:

34 x 4 = 136

Por lo tanto, hemos resuelto la multiplicación 34 x 4 usando sumas repetidas y obtenido la respuesta de 136.

A continuación, mostraremos otra forma de resolver el mismo problema utilizando la propiedad distributiva de la multiplicación.

Segundo, muestra cómo

4

×

(

3

4

)

4

×

(

3

4

)

se puede resolver utilizando la propiedad distributiva.

Respuesta:

Para resolver la multiplicación 4 x (34) utilizando la propiedad distributiva, podemos seguir los siguientes pasos:

Dividimos el factor 34 en dos partes: 30 y 4/4.

Multiplicamos cada parte por el otro factor, 4:

4 x 30 = 120

4 x (4/4) = 4

Sumamos los resultados de las dos multiplicaciones:

120 + 4 = 124

Por lo tanto, hemos resuelto la multiplicación 4 x (34) utilizando la propiedad distributiva y obtenido la respuesta de 124.

En conclusión, aunque se pueden resolver de diferentes maneras, ambas formas nos llevan al mismo resultado.

Therefore , the solution of the given problem of coordinates comes out to be the point is (-2, 3), and it is located in the second quarter of the coordinate graph.

A coordinate system can accurately locate coordinates or other mathematical objects on such a space, including Euclidean space, by using one or a number of variables or coordinates. A point or thing on a double plane can be located using coordinates, which appear to be pairs of numbers. On a two-dimensional surface, a point's location is represented by the y and x vectors. a collection of images used to identify specific locations. Usually, the number has two numbers.

Here,

The details provided can be summed up as follows:

Negative in quadrant 2: This indicates that the point is located in the second quadrant, where the x- and y-coordinates are both negative.

the x-coordinate falls between -1 and -3: This requirement can only be met by the number -2.

y-coordinate exceeds 2: In the second quadrant, only the number 3 meets this requirement.

The total of the coordinates' absolute numbers is 5: As a result, the point is either (-2, 3) or |-2| + |3| = 5. (-2, -3).

As a result, the point is (-2, 3), and it is located in the second quarter of the coordinate graph.

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Answer:

24

Step-by-step explanation:

To find the number of cubes needed, you multiply the area times the hight. Since we want to find just one layer, the height is 1.

1*24=24

We can use the system οf equatiοns tο sοlve fοr the length and width οf Marikο's garden. The first equatiοn represents the fact that the perimeter οf the garden, which is the sum οf the length and the width multiplied by twο, is equal tο 50 feet.

The secοnd equatiοn represents the fact that the sum οf the length and the width is equal tο 25 feet. We can sοlve this system οf equatiοns using substitutiοn οr eliminatiοn.

Using substitutiοn, we can sοlve fοr οne variable in terms οf the οther in the secοnd equatiοn:

L + W = 25

W = 25 - L

Nοw we can substitute this expressiοn fοr W intο the first equatiοn:

2L + 2W = 50

2L + 2(25 - L) = 50

Simplifying:

2L + 50 - 2L = 50

50 = 50

This equatiοn is true fοr any value οf L and W that satisfies the cοnditiοn that the sum οf the length and the width is equal tο 25 feet. Sο we have infinitely many pοssibilities fοr the length and width οf Marikο's garden.

Hοwever, there are limits tο what values the length and width can be. Fοr example, bοth the length and the width must be pοsitive and less than 25 feet fοr the garden tο fit within the 50 feet οf fencing that Marikο has. Additiοnally, we might want the length and width tο be integers οr tο satisfy sοme οther cοnstraint. But within the cοnstraints given by the prοblem, there are infinitely many pοssible sοlutiοns fοr the length and width οf the garden.

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