Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by where the measurements are in meters. What is the width of the cooling tower at the base of the structure

Answers

Answer 1

The width of the cooling tower is 36 meters.

What is a cooling tower?

A cooling tower is a vent that is built for the purpose of releasing waste heat back to the atmosphere.

Now we can model the system using;  x²/324 - (y² - 90)²/1600. Thus, the width can be obtained from;

2 × ✓324

= 2 × 18

= 36 meters

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Missing parts;

Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.

36 meters

48 meters

80 meters

89 meters


Related Questions

Which statements and reasons are true and can be used in a proof that m∠8 Select all that apply.

Answers

The statements and reasons that are true and can be used in a proof that m∠8  <  m∠6 are:

A) m∠6+m∠2+ m∠3 = 180° because the sum of the measures of the interior angles of a triangle is 180°.

C) m∠8+m∠1+m∠2+m∠3+m∠4 = 180° because the sum of the measures of the interior angles of a triangle is 180°.

What is interior angles?

Interior angles can be created in geometry in two different ways. In one, parallel lines are cut by a transversal, and in the other, they are inside a polygon. Depending on how large they are, angles are divided into various types. Other angles fall into the category of pair angles because they need to be present in pairs in order to display a particular characteristic. One type of these is interior angles.

Interior angles can be outlined in two different ways:

Angles inside a polygon are referred to as interior angles because they are found inside a polygon, typically. The angles a, b, and c are interior angles in the following figure (a).Interior Angles of Parallel Lines: The angles that are located in the space bounded by two parallel lines intersected by a transversal are also called interior angles

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please help me!! i need it asap

Answers

b and c both equal 16

ava read 99 books in 11 months how many books per a month did she read

Answers

She has read 9 books per month divide 99 by 11 and you will get 9

Question 1 of 25
Which is an equation of the line through (0, 0) and (-3,-7)?
OA. y=-7x
O B. y = x
OC. y=-3x
OD. y = x
SUBMIT

Answers

The equation of the line with points (0.0) and (-3,-7) is y = 7/3 * x

What is Coordinate Geometry ?

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.

The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.

The points are (0,0) and (-3, - 7)

The equation of the line will be

y - 0 = (-7 - 0)/(-3-0) * (x - 0)

⇒y = 7/3 * x

The equation of the line with points (0.0) and (-3,-7) is y = 7/3 * x

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Someone please help!

Answers

Answer:

v/202

Step-by-step explanation:

formula: leg² + leg² = hyp²

11² + 9² = hyp²

121 + 81 = hyp²

202 = hyp²

v/202 = v/hyp²

hope this makes sense

need help finding the m

Answers

Answer:

79 degree

Step-by-step explanation:

A triangle is 180 degrees

We know that angle D and F is equal to each other

180 - 22 = 158 degree

158 / 2 = 79 degree

So, m<F = 79 degree

mr smith gives her class clues about 5 digit mystery numbers the 4 is in a place that is 10 times greater than the 9.

Answers

Answer:

Step-by-step explanation:

40

Suppose a function f(x) has a domain of (−[infinity],[infinity]) and range [-11,3]. If we define a new function g(x) by g(x) = f(6x) +1, then what is the range of g(x)? Express your answer in interval notation.

Answers

We can define a function f(x) with a domain of all real numbers (−[infinity],[infinity]) and a range of [-11,3].

Let's start by defining our function f(x):

f(x) = [-11,3]

Now, let's define our new function g(x):

g(x) = f(6x) + 1

This means that the range of g(x) is the range of f(x) plus 1, so the range of g(x) is [-67, 19]. In interval notation, this can be expressed as [-67, 19].

We can define a function f(x) with a domain of all real numbers (−[infinity],[infinity]) and a range of [-11,3]. To generate a new function, g(x), we can define it by g(x) = f(6x) +1. This means that the range of g(x) is the range of f(x) plus 1, so the range of g(x) is [-67, 19]. To express this in interval notation, we can write [-67, 19]. This means that the output of g(x) lies between the values -67 and 19. This new range can be found by multiplying each value in the range of f(x) by 6 and then adding 1 to each value. Therefore, the range of g(x) is [-67, 19] in interval notation.

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In ΔOPQ, o = 10 cm, p = 67 cm and ∠Q=24°. Find ∠P, to the nearest degree.

Answers

In ΔOPQ, o = 10 cm, p = 67 cm, ∠Q=24,∠P=152.

What are triangle?

A triangle in geometry is a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.

This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.

In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.

The vertex is the intersection of two straight lines. The triangle therefore has three vertices.

Hence, In ΔOPQ, o = 10 cm, p = 67 cm, ∠Q=24,∠P=152.

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Latoya' Coffee Shop make a blend that i a mixture of coffee type A and B. In one bag of the blend, there are 6 kilogram of type A. Four bag of the blend are a total of 36 kilogram. How many kilogram of type B are there in one bag?

Answers

The Kilograms of type B that are in one bag of the Latoya's Coffee shop blend would be = 3kg

What is a mixture?

A mixture is defined as the combination of two or more components which can or cannot be separated by ordinary methods.

The coffee blend of LaToya shop = Type A and B

A bag of the coffee blend = 6kg of Type A.

4 bags of coffee blend = 36kg

Therefore 4 bags of coffee blend contains = 6 see×4 = 24 kg of Type A

Type B in each bag = 36 - 24 = 12/4 = 3kg.

We are tasked with finding the amount in kilograms of type B coffee present in a bag of coffee.

We already know that in a bag , there are 4kg of type A coffee. Hence, in 6 bags, what we will be having would be 6 * 4kg = 24kg of type A coffee

The total kilograms of coffee in 6 bags of coffee is 48kg. Now we know we have 24kg of type A, the amount of type B coffee present is thus 48kg -24kg = 24kg

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Mark loads a crate that weighs 22.5 pounds and 12 boxes that each weigh 11.25 pounds onto a truck . what is the total weight of the crate and the boxes

Answers

Answer:

157.5 pounds

Step-by-step explanation:

11.25×12=135 then add 135 to 22.5

Solve the following system of equations: x = 60 + 4y 7x + 12y = 500 a (68, 2) b (50, 12.5) c (12.5, 50) d (2, 68)

Answers

The value of x and y in the equation is (x,y) = (68,2) (optionA)

What is Simultaneous equation?

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

x= 60+4y equation 1

7x + 12y = 500 equation 2

rearranging the equation

x- 4y = 60

7x+12y = 500

using elimination method

7x-28y = 420 equation 3

7x+12y = 500 equation 4

subtract equation 4 from 3

-40y = -80

divide both sides by -40

y = -80/-40

y= 2

substitute 3 for y in equation 1

x = 60+4(2)

x= 60+8

x= 68

Therefore the value of x and y is 68 and 2 respectively.

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How do you find the center of a transformation?

Answers

The center of a transformation refers to the fixed point through which the transformation takes place.

The center of a transformation can be found by the following methods:

Translation: The center of a translation is the point that remains fixed during the transformation.

Rotation: The center of rotation is the point around which the object rotates.

Reflection: The center of reflection is the line of reflection or the point of symmetry.

Dilation: The center of dilation is the point that remains fixed during the transformation and all the distances from it are multiplied by a scale factor.

Combination of Translations, Rotation, Reflection, and Dilation: The center of transformation will be the point of intersection of all the fixed points of above mentioned four transformations.

It is important to note that not all transformations have a center, and some may have multiple centers.

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What is the slope-intercept form the linear equation 2x y 10?

Answers

The slope-intercept form of the given linear equation 2x + y = 10 is y = -2x + 10.

If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, c, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Now, change the given equation to slope-intercept form, y = mx + c, where m is the slope and c is the y-intercept.

2x + y = 10

Subtract 2x from both sides of the above equation, we get

y = -2x + 10

This is the required slope-intercept form of the given linear equation.

-- The given question is incorrect, the correct form of equation is

"What is the slope-intercept form the linear equation  2x + y = 10?" --

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What is the simplified form of the following expression? rootindex 3 startroot startfraction 4 x over 5 endfraction endroot.

Answers

The simplified expression of the ∛4x / 5 is ∛4x / ∛5

Index laws are the rules for simplifying expressions involving powers of the same base number, these laws are also called Laws of indices.

Laws of indices provide us with rules for simplifying calculations or expressions involving powers of the same base. The indices are also known as powers or exponents.

It is represented in the form:

am = a × a × a ×……× a (m times)

we have the  law of indices formula:

[tex]\sqrt[a]{b}=b^\frac{1}{a}[/tex]

∛4x / 5 = (4x/5)^1/3

Therefore,

∛4x / 5 = ∛4x / ∛5

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Tell whether the ratios form a proportion.

4 : 12 and 5 : 15

The ratios _____ (do or do not) form a proportion. The cross products are _____ (state the cross product or state "not equal")

Response:
--------------------------------------
--------------------------------------

Answers

Talking about the 4:12 and 5:15 can be written in the form of 1:3

What do you mean by ratios?

Mathematical ratios show how many times one number appears in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a fruit plate. The ratio of lemons to oranges is 6:8, while the ratio of oranges to the total amount of fruit is 8:14.

How to address a ratio issue

The total number of shares can be calculated by adding the ratio's component parts.By the total number of shares, divide the entire sum.Add the necessary amount of shares together

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Solve 6 sin² (x) - 5 cos(x) — 7 = 0 for all solutions 0 < x < 2π
x =

Answers

6 sin² (x) - 5 cos(x) — 7 = 0 for all solutions 0 < x < 2π :  x = π

What is meant by integer?Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of the equivalent positive numbers, which are additive, are the negative numbers. The blackboard bold mathbb Z or boldface Z is a common way to represent the set of integers in mathematical terminology. Only positive and negative whole numbers as well as natural numbers are included in the category of integers, a form of real number. Integers cannot include fractions, but real numbers can because of rational and irrational numbers.

[tex]& \sin ^2 x-5 \cos x=5 \\[/tex]

[tex]& 1-\cos ^2 x-5 \cos x=5 \\[/tex]

[tex]& \cos ^2 x+5 \cos x+4=0 \\[/tex]

[tex]& \cos ^2 x+\cos x+4 \cos x+4=0 \\[/tex]

[tex]& \cos x(\cos x+1)+4(\cos x+1)=0 \\[/tex]

[tex]& (\cos x+1)(\cos x+4)=0 \\[/tex]

[tex]& \cos x+1=0 \quad(\because \cos x \neq-4) \\[/tex]

[tex]& \cos x=-1 \\[/tex]

[tex]& \cos x=\cos \pi \\[/tex]

[tex]& x=(2 k+1) \pi[/tex]

Where, k is any integer i.e  k = 0 ± 1, ± 2, ± 3,....

But x ∈[0,2π)  hence setting k = 0 we get the solution

x = π

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evaluate the integral ( 4 to 1) 6 + x2 / x^2 dx

Answers

So the value of integral [tex]\int\limits^4_1 {\frac{x}{x^2+13} } \, dx[/tex] is 0.51

Define integral:

An integral is a mathematical concept used to calculate area or change over an interval, represented by ∫. It is opposite of derivative, with two types: definite and indefinite. Used in many areas of mathematics and physics.

The integral of x/(x^2+13) from x=1 to x=4 can be evaluated using the method of substitution.

Let u = x^2+13, then du/dx = 2x dx

so x dx = du/2

now the integral becomes 1/2 * integral (1/u) du

so intergral is 1/2* [tex]\int\limits {\frac{1}{u} } \, du[/tex]

=> 1/2 [tex]\left \{ {{x=4} \atop {x=1}} \right.[/tex] ln([tex]x^2[/tex]+13)

=> 0.5 ( ln(39)-ln(14))

=>0.51

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Complete question:

evalute integral [tex]\int\limits^4_1 {\frac{x}{x^2+13} } \, dx[/tex]

A 2 column table with 5 rows. The first column, yards of red fabric, x, has the entries 1, 2, 3, 4. The second column, yards of blue fabric, y, has the entries 27, 26, 25, 24.
Sophie is buying fabric to make items for a craft fair. The table shows some combinations of how much of each color fabric she might buy. Which equations model the total yards of fabric Sophie will buy? Check all that apply.

Answers

The answer choices which correctly represent equations which model the total yards of fabric Sophie will buy is; x + y = 28, 28 - x = y and 28 - y = x.

Which equations correctly model the total yards of fabric Sophie will buy?

It follows from the attached table, where x represents the yards of red fabric she buys and y represents the yards of blue fabric she buys.

It follows that the following x and y pairs are possible; (1, 27), (2, 26), (3, 25) and (4, 24).

On this note, it can be inferred that in each of the red and blue fabric pairs; x + y = 28.

Ultimately, the equations which model the total yards of of fabric Sophie will buy as required are; x + y = 28, 28 - x = y and 28 - y = x.

Complete question; The given answer choices are; x+y=28, 28+x=y, x-y=28, 28-x=y and 28-y=x.

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Use elimination to find the solution to the system of equations.

4x+y=8
3x-2y=6

A. x=6, y=6
B. x=2, y=0
C. x=-3, y=20
D. x=6, y=-16

Answers

Answer: To use the elimination method to solve the system of equations, we'll try to eliminate one of the variables by adding or subtracting the equations.

We have:

4x+y=8

3x-2y=6

multiplying the first equation by -2:

-8x-2y=-16

and adding it to the second equation:

3x-2y+(-8x-2y)=6+(-16)

-5x = -10

x = 2

substituting x=2 in the first equation:

4(2)+y = 8

8+y = 8

y = 0

So the solution is x=2 and y=0, that corresponds to the option B.

Why might squaring a number and taking the square root of a number be thought of as opposite operations give an example to justify your answer?

Answers

Finding a number's square root is the equivalent as squaring it, or the opposite process. When you multiply the square root of a given integer by itself, you get the original number. Since 8 x 8 equals 64, as fact, 8 is the square root of 64.

What is square roots?

It is possible to multiply an integer by its square root in order to obtain the original value. Square root of, end square root is the symbol for this mathematical concept. Contrary to squaring, finding a number's square root is the reverse.

For instance, 3 is squared at 9, 32, and its square root at 9, which is 9, is equal to 3. It is simple to multiply by 9 since it is a perfect square.

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Plot the points A(3,-2), B(-3, 8), C(-5, -1) on the coordinate axes below. State
the coordinates of point D such that A, B, C, and D would form a
parallelogram.
(Plotting point D is optional.)

Answers

The points A(3,-2), B(-3, 8), C(-5, -1) and D(2,16) would form a parallelogram.

How to plot points on graph?

In mathematics, points on a graph are typically plotted on a coordinate plane. The x-coordinate and y-coordinate of each point determine its location on the plane. To plot a point, you will need to know its coordinates (x, y).

To plot the points A(3,-2), B(-3, 8), C(-5, -1) on the coordinate axes, we can start by drawing the x-axis and y-axis, where the x-axis is the horizontal line and y-axis is the vertical line.

We can then locate point A by starting at the origin (0,0) and moving 3 units to the right on the x-axis and 2 units down on the y-axis. Point B can be located by starting at the origin and moving 3 units to the left on the x-axis and 8 units up on the y-axis. Point C can be located by starting at the origin and moving 5 units to the left on the x-axis and 1 unit down on the y-axis.

To form a parallelogram, point D must be opposite of point B and have the same distance from point C and point A. Since a translation of a vector is a linear transformation, D is the translation of vector AB to point C.

The coordinates of point D would be (2,16), which is the translation of point B by the vector (2,8) to point C.

So the points A(3,-2), B(-3, 8), C(-5, -1) and D(2,16) would form a parallelogram.

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Alliosn walks 1/2 mile each 1/5 hour. She continues to walk at the same pace. If allsion walked 1 1/4 miles, hiw long did she walk take

Answers

27.5 hrs are  long did she walk take to cover distance .

In math, what is a distance?

The length of the segment of the line that connects the supplied two points determines the distance between them.

                    The shortest segment of a line connecting a point to a line will have a length equal to the distance between them.

Distance covered by Alliosn =  1/2 km

Time taken by Alliosn  = 1/5hr

Hence,

speed of peter = Distance/time

= (1/2)/(1/5) km/hr

= 1/10 km/hr

Distance travelled by Alliosn = 1  1/4 km

=  11/4km

Speed = distance/time

1/10 = (11/4) / time

i.e.

Time = 11 * 10/4

       = 27.5 hrs

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B. Exercises
Find the sums or differences.
21, 2,973+56 +37,468 +784
22. 37,205-19,804
23. 861,519-179,321
24. 1,733,642 +18,082+43,605
Perform the indicated operations. Do those inside the parentheses first.
29, (736-565)+189
30. 600-(718-453)
31. (3,264-1,628)+4,356
25. 19+73,048 +314+ 5,080
26. 8,496-6,338
27) 4,000,000-832,971
28. 46,525+273,199 +5,636,024
32. 894+ (1,036-478)
33. 2,457-(986+759)
34. (61,432-38,617)-15,674

Answers

Answer:

21. 41,281

22. 17,401

23. 682,198

24. 1,795,329

29. 360

30. 335

31. 5,992

25. 78,461

26. 2158

27. 3167029

28. 5955748

32. 1452

33. 612

34. 7141

Your welcome

Find the output, h, when the input,
is -18.
h = 17+ 6
h=?

Answers

When the input x is -18, the output h is 14. The answer is obtained using substitution method.

What is substitution method?

One of the algebraic techniques for solving simultaneous linear equations is the substitution approach. It entails changing any variable's value from one equation to the other by substituting it in. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.

Now, we are given h = 17+x/6

So, when the input x is -18, using substitution method,

h=17+(-18/6)

=17+(-3)

=17-3

=14

Hence, when the input x is -18, the output h is 14.

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What is the ratio of a circles area?

Answers

The ratio of the area of a circle to the area of a square with sides of length equal to the circle's diameter is π/4.

This can be expressed mathematically as A_circle/A_square = π/4, where A_circle is the area of the circle and A_square is the area of the square.

To calculate the area of the circle, use the formula A_circle = πr^2, where r is the radius of the circle. To calculate the area of the square, use the formula A_square = (d^2)/4, where d is the diameter of the circle. Therefore, the ratio of the area of the circle to the area of the square is A_circle/A_square = πr^2/(d^2/4) = 4πr^2/d^2.

For example, if the radius of the circle is 4 cm, then the diameter is 8 cm, and the ratio of the area of the circle to the area of the square is A_circle/A_square = 4π(4^2)/(8^2) = 16π/64 = π/4.

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Sandra drops a brick into a beaker filled with water. Volume increases by 2 liters. Then she uses the density to make a prediction about its weight in kilograms. If the density of the brick is approximately 2 grams per millimeters, what should the prediction be?

Answers

The weight of the brick that Sandra dropped is 40 N.

What is the density?

We must know that we can be able to define the density as the ratio of the mass to the volume of the object. We know that the density can be regarded as an intrinsic property of the substance.

We can see that;

Density = mass/volume

mass = Density * volume

Volume = 2 L or 2000 mL

Density = 2 grams per millimeters

Mass = 2 * 2000

Mass = 4000 g or 4 Kg

Weight = mass * acceleration due to gravity

Weight = 4 Kg * 10 m/s^2

Weight = 40 N

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Jorge completed the obstacle course in 18.2 seconds. Kaitlyn finished 3.5 seconds in front of Jorge. Which equation shows Kaitlyn's time?​

Answers

The equation will be [tex]x-3.2=18.2[/tex] by simple calculation.

What are equations in one step?

An algebraic equation that only requires one step to solve is known as a one-step equation. Once you've figured it out, you'll know what the variable's value is that makes the equation true. In order to obtain the variable by itself when solving one-step equations, we perform the inverse (opposite) of the operation that is being applied to the variable.

How do two step equations work?

An equation that must be solved in two steps is referred to as a two-step equation. Any constant that is on the same side as the variable must be removed first. To solve, isolate the variable on its own using inverse operations. Keep in mind that anything you do to one side must also be done to the other.

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What is the LCM and HCF of 4 and 10?

Answers

The Least Common Multiple (LCM) of 4 and 10 is 20, and the Highest Common Factor (HCF) of 4 and 10 is 2.

HCF is the highest integer that can divide 4 and 10 is 2. HCF stands for Highest Common Factor.

Now, 4 and 10 can be expressed as:

4 = 2 × 2 

10 = 2 × 5 

The common prime factor is 2. 

Therefore HCF (4, 10) = 2

The Least Common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers.

Similarly, Calculating the LCM, 4 and 10 can be expressed as;

4 = 2 x 2

10 = 2 x 5

LCM (4, 10) = 2 x 2 x 5 = 20

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Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) is dilated using a scale factor of one fourth to create polygon A′B′C′D′. Determine the vertices of polygon A′B′C′D′.

A′(−0.8, 1.2), B′(−0.4, 0.4), C′(0.8, −0.4), D′(0.8, 0.8)
A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)
A′(−2, 3), B′(−1, 1), C′(2, −1), D′(2, 2)
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)

Answers

With a dilation factor of 1 / 4, Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) would be: A(-1, 1.5), B(-0.5 , 0.5), C(1, -0.5), D(1 , 1). Second option

How to dilate the vertices to scale

The solution to the problem would be the solution that is gotten when we divide these points by 1/4. This is the dilation factor

we would have:

A(−4, 6), B(−2, 2), C(4, −2), D(4, 4)

= (-4 * 1/4, 6 * 1/4) , B(-2 * 1/4, 2 * 1/4), C(4 * 1/4, -2 * 1/4), D(4 * 1/4, 4 * 1/4)

= A(-1, 1.5), B(-0.5 , 0.5), C(1, -0.5), D(1 , 1)

Hence the second option is correct.

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Answer:A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1).

Step-by-step explanation:

To dilate a point using a scale factor, you multiply both the x-coordinate and the y-coordinate of the original point by the scale factor.

Given the original vertices of the polygon ABCD and a scale factor of one fourth (1/4), we can find the coordinates of the dilated vertices A', B', C', and D':

Original vertex A(-4, 6):

x-coordinate of A': -4 * 1/4 = -1

y-coordinate of A': 6 * 1/4 = 1.5

So, vertex A' is (-1, 1.5).

Original vertex B(-2, 2):

x-coordinate of B': -2 * 1/4 = -0.5

y-coordinate of B': 2 * 1/4 = 0.5

So, vertex B' is (-0.5, 0.5).

Original vertex C(4, -2):

x-coordinate of C': 4 * 1/4 = 1

y-coordinate of C': -2 * 1/4 = -0.5

So, vertex C' is (1, -0.5).

Original vertex D(4, 4):

x-coordinate of D': 4 * 1/4 = 1

y-coordinate of D': 4 * 1/4 = 1

So, vertex D' is (1, 1).

Comparing the calculated coordinates with the options given:

A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)

Among the given options, the correct vertices of polygon A′B′C′D′ are A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1).

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