243➗ _ =81
Multiplying and dividing integers

The vector u2 is (0, √3/3, 2/3). It is a unit vector that is orthogonal to both 8,-8,8 and 0,5,5.

Given two vectors 8,-8,8 and 0,5,5, we need to find another unit vector that is orthogonal to both the given vectors. Let's call this vector u1.The vector u1 can be obtained by taking the cross product of the two given vectors:u1 = (8,-8,8) × (0,5,5)u1 = (-40,-40,40)

To get a unit vector, we need to normalize u1 by dividing it by its magnitude:|u1| = √((-40)² + (-40)² + 40²) = 60u1 = (-40/60, -40/60, 40/60) = (-2/3, -2/3, 1/3)Now we need to find another unit vector that is orthogonal to u1.

One way to do this is to take the cross product of u1 with another vector, and then normalize the result. We can choose any vector that is not parallel to u1. For example, we can choose the vector (1,0,0).u2 = u1 × (1,0,0)u2 = (-2/3, -2/3, 1/3) × (1,0,0)u2 = (0,1/3,2/3)

To get a unit vector, we need to normalize u2 by dividing it by its magnitude:|u2| = √(0² + (1/3)² + (2/3)²) = 1/√3u2 = (0, √3/3, 2/3)

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Circumference= diameter × 3.14

C= 34 feet× 3.14= 106.76 feet

Answer:

I hope this helps please rate my answer

Step-by-step explanation:

2/5×60

2×12=24

To solve the question asked, you can say:  So the other side of the triangle will be as [tex]A = \sqrt73[/tex].

A triangle is a closed two-dimensional geometric object consisting of three line segments, called edges, that intersect at three places called vertices. Triangles are distinguished by their sides and angles. A triangle can be equilateral (all sides equal), isosceles, or odd, depending on the sides. Triangles are classified as acute (any angle less than 90 degrees), right (angles equal to 90 degrees), or obtuse (any angle greater than 90 degrees). The area of ​​a triangle can be calculated using the formula A =​​ (1/2)bh. where A is the area, b is the base of the triangle, and h is the height of the triangle.  

here in the triangle we have sides that are 3 and 8

we can use

[tex]A^2 = B^2 + C^2\\A^2 = 3^2 + 8^2\\A^2 = 9+64\\A^2 = 73\\A = \sqrt73[/tex]

So the other side of the triangle will be as [tex]A = \sqrt73[/tex].

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Answer: 24

Step-by-step explanation:

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. A low standard deviation means data are clustered around the mean, and a high standard deviation indicates data are more spread out.

A) A t-interval with 6 degrees of freedom: Mean +/- 0.76 * Standard Deviation

B) A t-interval with 2 degrees of freedom: Mean +/- 1.82 * Standard Deviation

C) A z-interval: Mean +/- 1.645 * Standard Deviation

Therefore, the intervals in order from narrowest to widest are:

A) A t-interval with 6 degrees of freedom,

C) A z-interval, and

B) A t-interval with 2 degrees of freedom.

The order from narrowest to widest is:

C) z-interval

A) t-interval with 6 degrees of freedom

B) t-interval with 2 degrees of freedom

Also,

The z-interval will be the narrowest because the z-distribution has a smaller variance than the t-distribution. The t-interval with 6 degrees of freedom will be wider than the z-interval because the t-distribution has a larger variance than the z-distribution.

Finally, the t-interval with 2 degrees of freedom will be the widest because the t-distribution has the largest variance when degrees of freedom is low.

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Answer: 32,760

Step-by-step explanation

12x+376

15x+280

when you put it in demos both of the line cross and you can see you answer when you click were the lines cross.if you use the giving value it would be 750

The time it will take both the boat and whale to meet is 18 minutes(nearest minutes).

Displacement is defined as the change in position of an object in a specified direction. It is measured in meters and it's a vector quantity.

[tex]\text{Since velocity} = \bold{displacement/time}[/tex]

[tex]\bold{displacement} = \text{velocity} \times \bold{time}[/tex]

The total space between the boat and the whale is 5 miles.

Using addition of vectors

[tex]5= v2t - v1t[/tex]

[tex]5= 46t - 30t[/tex]

[tex]5 = 16t[/tex]

[tex]t= 5\div16 = 0.3 \ hrs[/tex]

To minutes, = 0.3 × 60 = 18minutes(nearest minutes)

Therefore it will take the boat and the whale 18minutes to meet.

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Answer:

3 pounds of coffee.

Step-by-step explanation:

Equation

y = -7.37x + 80  

substitute 57.89 for y

57.89 = -7.37 + 80   Subtract 80 from both sides

57.89 - 80 = -7.37 + 80 - 80

-22.11 = -7.37x  Divide both sides by -7.37

3 = x

3 pound of coffee

Helping in the name of Jesus.

Answer:

rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?​

Step-by-step explanation:

Let's first find out how much money Rita spent on coffee:

$80 (initial balance) - $57.89 (remaining balance) = $22.11 spent on coffee

Now, let x be the number of pounds of coffee that Rita bought. Since the coffee costs $7.37 per pound, we can set up the equation:

$7.37x = $22.11

Solving for x, we can divide both sides by $7.37:

x = 3

Therefore, Rita bought 3 pounds of coffee.

The value of variable x for the given equation, 5x - 16xy +16y² +7x + 17y² is −33 y²/ 4(3 − 4y).

An algebraic expression is the idea of ​​using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here. An algebraic expression said to be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor. An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.).

5x - 16xy +16y² +7x + 17y²

= 12x - 16xy + 33y²

Using the Quadratic Formula, we have:

x = −33 y²/ 4(3 − 4y)

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Answer:

[tex](x+2)^{2} +(y+2)^{2} =9[/tex]

Step-by-step explanation:

the equation of circle:

center:(-2,-2)

The distance between the center and the side:3

So, the radius is 3

(x-h)^2+(y-k)^2=r^2

[tex](x - - 2)^{2} +(y- - 2)^{2} =3^{2}[/tex]

[tex](X+2)^{2} +(y+2)^{2} =9[/tex]

A vertical bar chart that shows frequency on the y-axis is called a histogram. It is a graph showing the distribution of continuous data.

Histograms are used to give an estimate of the probability distribution of a continuous variable sample. Additionally, a subset or part of a population is called a sample. A population is divided into groups, and some groups are selected, and all observations from each selected group are included in the sample. This is called stratified random sampling.

A collection of all data that is of interest is known as the universe.

A collection of attributes, labels, or nonnumerical entries is known as categorical data. This type of data is descriptive in nature, as it allows us to identify what features the data has or belongs to. For instance, age group, gender, and occupation are examples of categorical data. A sample where the population is divided into groups and several are randomly sampled from each group is called a cluster sample. Cluster sampling is an excellent method for conducting a survey when the population is widespread and heterogeneous.

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The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.

Here,

Since line B is perpendicular to line A, the product of their gradients is -1. Therefore, the gradient of line B is 1/5.

a) To find the y-intercept of line B, we need to know a point on the line. Since we don't have one, we can use the fact that the y-intercept is the point where the line intersects the y-axis. To find this point, we can set x = 0 in the equation of line B:

y = (1/5)x + c

0 = (1/5)(0) + c

c = 0

Therefore, the y-intercept of line B is (0,0).

b) The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

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In contrast to the CDC's reported success rate, the success rate for art at this clinic is substantially greater.

A claim or assumption that there is no statistically significant difference between two populations or sets of data is known as the null hypothesis. It serves as the beginning point for statistical hypothesis testing and is typically indicated as H0. According to the null hypothesis, any observed difference between the populations or data sets is the result of sampling error or random chance rather than a genuine difference.

given

The success rate for art at this clinic is not statistically different from the CDC's claimed success rate.

In contrast to the CDC's reported success rate, the success rate for art at this clinic is substantially greater.

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It would cost €27 to buy a sheet of area 4 meters by 75 centimeters.

We solve this problem easily by employing the unitary method. To answer this question, we need to first calculate the area of the metal sheet being sold and the area of the metal sheet being purchased.

The area of the metal sheet being sold is:

5 meters × 2 meters = 10 square meters

The area of the metal sheet being purchased is:

4 meters × 0.75 meters = 3 square meters

Now we can calculate the price per square meter of the metal sheet being sold:

€90 ÷ 10 square meters = €9 per square meter

Finally, we can calculate the cost of the metal sheet being purchased:

3 square meters × €9 per square meter = €27. Therefore, the cost to buy a sheet of area 4 meters by 75 centimeters which costs €90 to a metal of area 5 meters by 2 meters would be €27.

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The equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex]  tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

Trigοnοmetric equatiοns are equatiοns that invοlve trigοnοmetric functiοns such as sine, cοsine, tangent, etc. These equatiοns usually invοlve finding values οf the unknοwn angle(s) that satisfy the given equatiοn. They can be sοlved using algebraic techniques οr by using the prοperties οf trigοnοmetric functiοns.

Accοrding tο the given infοrmatiοn:

The given functiοn is [tex]f(t) = -5t^2 + 20t[/tex], which mοdels the height οf an οbject in feet as a functiοn οf time in secοnds.

Tο find the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch, we need tο sοlve the equatiοn [tex]-5t^2 + 20t = 18[/tex].

Tο sοlve this quadratic equatiοn using the quadratic fοrmula, we first identify the values οf a, b, and c frοm the general fοrm οf a quadratic equatiοn, [tex]ax^2 + bx + c = 0[/tex].

In this case, a = -5, b = 20, and c = -18. Substituting these values intο the quadratic fοrmula, we get:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

Plugging in the values οf a, b, and c, we get:

[tex]t = (-20 \± \sqrt{+(20^2 - 4(-5)(-18)})) / 2(-5)[/tex]

Simplifying this expressiοn, we get:

[tex]t = (-20 \± \sqrt{(400 - 360))} / (-10)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

[tex]t = 2 \± 0.632[/tex]

Therefοre, the twο pοssible values οf t are:

t = 2 + 0.632 = 2.632 secοnds

t = 2 - 0.632 = 1.368 secοnds

Therefοre, the equatiοn that cοrrectly shοws the quadratic fοrmula being used tο determine the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch is:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

[tex]t = (-20 \± \sqrt{(20^2 - 4(-5)(-18))}) / 2(-5)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

t = 2 ± 0.632

Therefοre, the equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

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The correct answer is p=62

The five-number summary for the given data is Min = 107, Q1 = 138, M = 175, Q3 = 190, and Max = 195.

In statistics, the five-number summary is a set of descriptive statistics that provide a summary of the distribution of a dataset. The five-number summary consists of the minimum value, the first quartile (Q1), the median (M), the third quartile (Q3), and the maximum value.

To find the five-number summary for the given data on the number of calories in a hot dog for each of 17 brands of meat hot dogs, we need to order the data from smallest to largest.

107 135 136 138 139 146 147 153 172 173 175 179 182 190 191 195

The minimum value is the smallest value in the dataset, which is 107.

The first quartile (Q1) is the value that is greater than or equal to 25% of the data and less than or equal to 75% of the data. To find Q1, we take the median of the lower half of the data:

Q1 = median(107, 135, 136, 138, 139, 146, 147, 153) = 138

The median (M) is the value that is in the middle of the dataset when the data is ordered from smallest to largest. For the given data, there are 17 values, so the median is the 9th value:

M = median(107, 135, 136, 138, 139, 146, 147, 153, 172, 173, 175, 179, 182, 190, 191, 195) = 175

The third quartile (Q3) is the value that is greater than or equal to 75% of the data and less than or equal to 25% of the data. To find Q3, we take the median of the upper half of the data:

Q3 = median(172, 173, 175, 179, 182, 190, 191, 195) = 190

The maximum value is the largest value in the dataset, which is 195.

Therefore, the five-number summary for the given data is Min = 107, Q1 = 138, M = 175, Q3 = 190, and Max = 195.

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The expected value of the area of t is 1/12.

The length of the hands of the clock is 1. If a time of day is chosen uniformly at random, what is the expected value of the area of t?

The area of the triangle is given by the formula

A=1/2 ab sinC.

Here, we use Law of cosines to determine the angle C, which is enclosed by the hour and minute hands.

[tex](\cos C)_{h,m}=\frac{h^2+m^2-1}{2hm}[/tex]

So, we can write the expected value of the area of t as

[tex]\begin{aligned}E[A]&=\int_{0}^{2\pi}\frac{1}{2}(1)(1)sinC\left(\frac{1}{12}+\frac{1}{720}((Cos C)_{h,m})^2\right)dC \\ &=\frac{1}{24\pi}\int_{0}^{2\pi}(sinC+sin(11C))dC \\ &=\frac{1}{12}\end{aligned}[/tex]

Hence, the expected value of the area of t is 1/12.

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Answer:

29.12 square cm

Step-by-step explanation:

     Side = a = 8.2 cm

    [tex]\boxed{\bf Area \ of \ equilateral \ triangle = \dfrac{\sqrt{3}}{4}a^2}[/tex]

                                                       [tex]\sf = \dfrac{\sqrt{3}}{4}*8.2*8.2\\\\= \sqrt{3}*4.1 * 4.1\\\\= 1.732 * 4.1 *4.1\\\\= 29.12 \ cm^2[/tex]

We can simplify the expressiοn tο  [tex]52x^3y,[/tex] nοt [tex]52x^2y[/tex].

Yοu must substitute a number fοr each variable and perfοrm arithmetic οperatiοns tο evaluate an algebraic expressiοn. Because 6 + 6 = 12, the variable x in the preceding example is equal tο 6. We can evaluate the expressiοn after replacing the variables with their values if we knοw their values.

We can use expοnent prοperties tο simplify the expressiοn [tex]13x[/tex]• [tex]4x^2y[/tex]:

[tex]13x[/tex]•[tex]4x^2y = 13[/tex] • [tex]x^1[/tex]• 4 • [tex]x^2[/tex]•[tex]y^1[/tex]

[tex]= 52[/tex]• [tex]x^3[/tex]•[tex]y^1[/tex]

As a result, we can simplify the expressiοn tο [tex]52x^3y[/tex] rather than[tex]52x^2y.[/tex]

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The circumference of the circle with a radius of 16 is 32π using formula for the circumference of a circle is C = 2πr.

The circumference of a circle is the distance around the perimeter of the circle. The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is the constant pi, and r is the radius of the circle.

In this case, the radius of the circle is 16, so we can substitute this value into the formula and simplify:

C = 2πr

C = 2π(16)

C = 32π

This means that if we were to measure the distance around the perimeter of the circle, we would get a value of 32π units, where π is the irrational number approximately equal to 3.14159.

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Answer:

20.864

Step-by-step explanation:

8.15 x 4 is 32.6. I used a calculator but what I would do if I were solving on paper would be to double it, and then double it again.

Then, we divide 32.6 by five to get 6.52. I did this with a calculator, but if I were solving on paper, I would divide by 10 (move decimal point), and then double it.

Finally, we muliply 6.52 by 3.2. I did this with a calculator and got 20.864, but if I was doing this on paper, I would just solve using standard form!

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Based on the exponential decay equation, the number of employees for the company that has been decreasing yearly by 5%, will in 10 years be approximately 515.

The exponential decay equation or function gives the value in t years that has a constant ratio of decrease.

Exponential decay equation is one of the two exponential functions.  The other is the exponential growth equation.

The annual decrease in the number of employees = 5%

The current number of employees in the company = 860

The expected time = 10 years.

The exponential decay equation is as follows, y = 860 x 0.95^10.

y = 860 x 0.95^10 = 515

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the length of the steel beam is approximately 31.4 meters to the nearest meter.

The length of the steel beam is equal to the circumference of the semi-circle formed by bending the beam into the shape of an arch.

The formula for the circumference of a circle is:

C = πd

Where C is the circumference, π is the value of pi, and d is the diameter of the circle.

Since the arch is a semi-circle, the diameter is equal to the span of the arch, which is 20m. So we can calculate the circumference of the arch as follows:

C = πd/2

= 3.14 x 20m / 2

= 31.4m

Therefore, The steel beam measures, to the nearest meter, 31.4 meters in length.

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Complete Question

An arch of a bridge is made by bending a steel beam into the shape of a semi circle, if the span (diameter) of the arch in 20m, use the value 3.14 for pi to find the length of the steel beam to the nearest meter.

Answer:

45 yo

Step-by-step explanation:

Let's start by defining some variables to represent the ages of Ted and Rosie:

- Let's call Ted's current age "T"

- Let's call Rosie's current age "R"

From the problem statement, we know that:

- Ted is five times as old as Rosie was when Ted was Rosie's age. Written as an equation, this becomes:

T = 5(R - (T - R))

Simplifying this equation, we get:

T = 5(R - T + R)

T = 10R - 5T

- When Rosie reaches Ted's current age, the sum of their ages will be 72. Written as an equation, this becomes:

R + T = 72 - T

We now have two equations with two variables. We can use substitution to solve for T.

Substitute the second equation into the first equation to eliminate R:

T = 10R - 5T

T = 10(72 - T) - 5T

T = 720 - 15T

16T = 720

T = 45

Therefore, Ted's current age is 45.

Option (c) 1/3 is the correct answer.Let us first understand the given problem,It is given that the fair 6-sided die is rolled and let X indicates the event that an odd number is rolled and Y indicates the event that 3,4, or 5 is rolled.

P(X=0,Y=1)Solution:When an odd number is not rolled, then an even number is rolled. So, the possible even numbers that can be rolled on a die are 2,4 and 6. Therefore,X = 0, when an even number is rolledY = 1, when 3, 4 or 5 is rolledLet's find P(X=0,Y=1).P(X = 0, Y = 1) = P(rolling 4) = 1/6The sample space for a fair die will be {1,2,3,4,5,6}.

The odd numbers are {1,3,5}. Therefore,P(X = 1) = probability of getting an odd number= 3/6 = 1/2 (3 possible odd numbers out of 6)P(X = 0) = probability of getting an even number= 3/6 = 1/2 (3 possible even numbers out of 6)P(Y = 1) = probability of getting 3, 4, or 5= 3/6 = 1/2 (3 possible numbers out of 6)P(Y = 0) = probability of getting 1, 2, or 6= 3/6 = 1/2 (3 possible numbers out of 6)P(X = 0, Y = 1) = P(rolling 4) = 1/6. Therefore, P(X=0, Y=1) = 1/6Therefore, option (c) is correct.

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The principal sum is Rs. 1640 if the difference in simple interest between 3 years and 4 years is Rs. 82 at a rate of 5% per annum.

Let x be the principal sum. According to the problem, the difference in simple interest between 3 years and 4 years is Rs. 82. This means that the interest earned in the fourth year is Rs. 82 more than the interest earned in the third year.

Using the formula for simple interest, we can calculate the interest earned in each year:

Simple interest for 3 years = (x * 5% * 3) = 0.15x

Simple interest for 4 years = (x * 5% * 4) = 0.2x

The difference between the two is:

0.2x - 0.15x = 0.05x

We are given that this difference is equal to Rs. 82, so:

0.05x = 82

Solving for x, we get:

x = 82 / 0.05 = 1640

Therefore, the principal sum is Rs. 1640.

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a)  When x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.

Using implicit differentiation, we have:

2x(dx/dt) + 2y(dy/dt) = 0

Solving for dy/dt, we get:

dy/dt = -(x/y)(dx/dt)

Substituting x = 6, y = 8, and dx/dt = 4, we get:

dy/dt = -(6/8)(4) = -3

Therefore, when x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.

b) Using implicit differentiation again, we have:

2x(dx/dt) + 2y(dy/dt) = 0

Solving for dx/dt, we get:

dx/dt = -(y/x)(dy/dt)

Substituting x = 8, y = 6, and dy/dt = -2, we get:

dx/dt = -(6/8)(-2) = 1.5

Therefore, when x = 8 and y = 6, and dy/dt = -2, the value of dx/dt is 1.5.

To find the values of dy/dt and dx/dt, we used implicit differentiation, which is a technique used to find the derivative of an equation that is not expressed in the form y = f(x).

In this case, we had the equation x^2 + y^2 = 100, and we differentiated both sides of the equation with respect to t. Then, we solved for the required derivative using the given values of x, y, and the other derivative.

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If Maria state that (-4,2) (2,4),(2,-2),(-4,-1) are the coordinate pairs of the vertices of her figure, then the area of her quadrilateral figure is equals to the 9 sq. units.

A quadrilateral is a four-sided and 2D geometrical figure whose sum of all the four internal angles is 360°. Also, it has 4 edges and four vertices (or corners). Let's consider the vertices of a quadrilateral ABCD be A( x₁,y₁), B(x₂,y₂), C(x₃,y₃), D(x₄,y₄). The area of quadrilateral ABCD is written as A = (1/2) |(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) – (x₂y₁ + x₃y₂ + x₄y₃ + x₁y₄)|

Now, Maria defines a quadrilateral with the following vertices (-4,2),(2,4),(2,-2),(-4,-1). After comparing these vertices with (x₁,y₁),(x₂,y₂), (x₃,y₃), (x₄,y₄), we see, x₁ = -4 ,y₁ = 2, x₂ = 2, y₂ = -2, x₃ = 2, y₃ = -2, x₄ = -4, y₄ = -1. Substitute all known values into above formula, Area of her quadrilateral figure, A = (1/2)|((-4)(-2) + 2(-2) + 2(-1) + (-4)2) – (2×2 + 2×(-2) + (-4)(-2) + (-4)(-1))|

= (1/2)|( 8 - 4 - 2 - 8) - (4 - 4 + 8 + 4)|

= (1/2)|-6 - 12| = 9 sq. units

Hence, required area of quadrilateral is 9 sq. units.

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Complete question:

Maria states that (-4,2) (2,4),(2,-2),(-4,-1) are the coordinate pairs of the vertices of her figure. Calculate the area of her figure.