What is the value of m in the equation

Triangle XYZ will be translated to X'Y'Z' and the coordinates of Z' are (6,7).

A transformation known as a translation involves shifting each point in an image uniformly in one direction. It is also a type of transformation where every point in a figure is moved by the same amount in the same direction, producing a new figure that is identical to the original.

From the graph,

The coordinates of X are (7, 11)

The coordinates of Y are (10, 14)

The coordinates of Z are (8, 7)

When triangle XYZ is translated to X'Y'Z', the X-coordinate is given as (5, 11), which means the X-coordinate shifts left 2 points, so we need to subtract 2 from X-coordinate and keep Y-coordinate as it is.

Therefore the coordinate of the triangle X'Y'Z' are as follows,

The coordinates of X' are (7-2, 11) = (5,11)

The coordinates of Y' are (10-2, 14) = (8, 14)

The coordinates of Z' are (8-2, 7) = (6, 7)

Therefore the coordinates of Z' are (6,7)

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Answer:

We cannot determine the exact number of votes for Tim or Selena without additional information. However, we can determine the fraction of the whole class that voted for each candidate based on the given information.

If only one third of the students cast votes, that means that two thirds did not vote. Therefore, the fraction of the whole class that voted for Tim and Selena is each equal to one third of the total number of students.

To calculate these fractions, we can use the following formula:

Fraction of class = Number of students who voted / Total number of students

Let's assume that there are N students in the class. Then, the number of students who voted for Tim is (1/3)N, and the number of students who voted for Selena is also (1/3)N.

So, the fraction of the whole class that voted for Tim is:

(1/3)N / N = 1/3

Similarly, the fraction of the whole class that voted for Selena is also 1/3.

Since we don't know the exact number of votes for each candidate, we cannot determine who received more votes.

The circulatory system's primary functions are listed above. Service for the body's cells is provided by the heart, blood, and blood vessels.

Through the system of veins, arteries, and capillaries, blood transports carbon dioxide towards the lungs (for expiration) and takes up oxygen. Both liquid and solid components make up your blood. Water, salts, and protein make up the liquid component, known as plasma.

Plasma makes up most of your blood. Red blood cells, white blood cells, and platelets make up the solid portion of your blood. The oxygen from your lungs is carried to human tissues and organs by red blood cells (RBC).

The study on quality, organization, location, and change is what arithmetic is all about. Mathematicians look for patterns and come up with new theories.

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Therefore, the tree is 78.14 feet tall. Rounded to the nearest hundredth of a foot, the answer is 78.14 feet.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is a fundamental part of geometry and is used in many areas of science, engineering, and technology.

by the question.

A represents the top of the tree, and the line segment AB represents the height of the tree, which we want to find. The angle of elevation, which is the angle between the ground and the line of sight to the top of the tree, is 54°. The distance from the point on the ground to the tree is 52 feet, which we'll call d. Finally, h represents the distance from the ground to the point where the line of sight intersects the tree.

Using trigonometry, we know that:

tan (54°) = h/d

We can rearrange this equation to solve for h:

[tex]h = d * tan (54)[/tex]

Plugging in the values we know, we get:

[tex]h = 52 * tan (54) = 78.14[/tex]

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If Allie spins the spinner 2 times. the probability that Allie spins A on the first spin and & on the second spin is: B. 1/16.

Based on the information provided, the spinner has four possible outcomes: K, S, A, and %, each with equal probability of 1/4.

To find the probability that Allie spins A on the first spin and & on the second spin, we need to multiply the probability of spinning A on the first spin (1/4) by the probability of spinning & on the second spin (1/4), because the two events are independent.

Therefore, the probability is:

P(A on first spin and & on second spin) = P(A) × P(&) = (1/4) × (1/4) = 1/16

So the probability that Allie spins A on the first spin and & on the second spin is 1/16.

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The 16-inch pizza is a better deal as it costs about $0.10 per square inch while the 10-inch pizza costs about $0.13 per square inch.

Donnie's Pizza Palace Diameter (in.) Cost ($) Cost per Square Inch ($/in²)

10-inch 10 10 0.13

16-inch 16 20 0.1

To determine which pizza is the better deal, we need to compare the cost per square inch of each pizza.

For the 10-inch pizza:

Cost per square inch = Cost / (π x [tex](diameter/2)^2)[/tex]

Cost per square inch = 10 / [tex](3.14 x (10/2)^2)[/tex] ≈ $0.13

For the 16-inch pizza: Cost / (πx x [tex](diameter/2)^2)[/tex]

Cost per square inch =[tex]20 / (3.14 x (16/2)^2) ≈ $0.10[/tex]

Therefore, the 16-inch pizza is a better deal as it costs about $0.10 per square inch while the 10-inch pizza costs about $0.13 per square inch.

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Answer:

110.5 inches

Step-by-step explanation:

A=( a + b) / 2 h

A = (8 + 9) / 2 x 13

A = 17 / 2 x 13

A = 110.5 inches

The value of T(v), express v as linear combination in the basis B and the matrix representation of T obtain is T(v) = [4, -4].

To find T(v), we need to express v as a linear combination of the basis vectors of R^3 with respect to B:

v = (-1)[0] + (-1)[0] + (1)[1]

This means that the coordinate vector of v with respect to B is [-1, -1, 1].

To find the matrix representation of T with respect to the standard bases of R^3 and R^2, we can apply T to each of the basis vectors:

T([1, 0, 0]) = [1, 3]

T([0, 1, 0]) = [-1, 1]

T([0, 0, 1]) = [2, -2]

We can arrange the results in a matrix:

[1 -1 2]

[3 1 -2]

The matrix [1 -1 2; 3 1 -2] represents T with respect to the standard bases of R^3 and R^2.

To find T(v), we can multiply the matrix representation of T with the coordinate vector of v with respect to B:

T(v) = [1 -1 2; 3 1 -2] * [-1; -1; 1] = [4; -4]

Therefore, T(v) = [4, -4].

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the reference points for the transformation given by g(x) = 2*f(x) + 2 are (0, 4) and (1, 6).

The given function f has reference points (0, 1) and (1, 2). To find the reference points for the transformation given by g(x) = 2*f(x) + 2, we need to apply the transformation to each of the original reference points.

For the first reference point (0, 1), we have:

g(0) = 2f(0) + 2 = 21 + 2 = 4

So the transformed point is (0, 4).

For the second reference point (1, 2), we have:

g(1) = 2f(1) + 2 = 22 + 2 = 6

So the transformed point is (1, 6).

Therefore, the reference points for the transformation given by g(x) = 2*f(x) + 2 are (0, 4) and (1, 6).

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The average rate of change from year 1 to year 10 is: (150 - 69)/9 = 9 based on the given function.

The amount of maize the farmer's land is yielding in pounds per acre over x years is represented by the function f(x)=[tex]-x^2+20x+50[/tex].

We must compute the change in f(x) for the range [1,10] and divide by the interval's length to determine the average rate of change from year 1 to year 10.

f(1) = [tex]-(1)^2[/tex] + 20(1) + 50 = 69

f(10) = [tex]-(10)^2[/tex] + 20(10) + 50 = 150

Hence, the change in f(x) throughout the range [1,10] is as follows:

f(10) - f(1) = 150 - 69 = 81

And the interval [1,10] has the following length:

10 - 1 = 9

Thus, from year one to year ten, the average rate of change is:

(150 - 69)/9 = 9

By interpreting the average rate of change, we can conclude that from year 1 to year 10, the farmer's land's yield of maize per acre is growing at a pace of 9 pounds each year. This indicates that, on average, throughout the course of these ten years, the farmer can anticipate harvesting 9 extra pounds of maize per acre.

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The rate at which the height of the water is increasing when water is being pumped in at a rate of 2/3 m/s and the water is 9m deep is 0.667 m/s.

We can start by using the formula for the volume of a square pyramid to find the volume of water in the tank. Let V be the volume of water in the tank and h be the height of the water.

V = (s² [h])/3

We know that the base of the pyramid is 3m by 3m, so s = 3. Also, the height of the pyramid is 16m, so we have:

V = (3² [h])/3

V = 3h

Now, we can find the rate of change of the volume with respect to time:

dV/dt = 3 [dh/dt]

We know that water is being pumped in at a rate of 2/3 m/s, so dh/dt = 2/3. We want to find how fast the height increases when the water is 9m deep, so h = 9. Substituting these values, we get:

dV/dt = 3 [dh/dt]

dV/dt = 3 [2/3]

dV/dt = 2

Therefore, the rate at which the volume of water is increasing is 2 cubic meters per second. To find the rate at which the height of the water is increasing, we need to solve for dh/dt:

dV/dt = 3 [dh/dt]

2 = 3 * dh/dt

dh/dt = 2/3

So the height of the water is increasing at a rate of 2/3 m/s when the water is 9m deep. Rounded to 3 decimal places, the answer is 0.667 m/s.

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Therefore, the man finished his trip at 8:40 pm with total travelling time of 10 2/3 hours.

In mathematics, a fraction is a representation of a part of a whole or a ratio between two quantities. It consists of two numbers, a numerator and a denominator, separated by a horizontal line, also called a fraction bar or a vinculum. The numerator represents the number of equal parts being considered, while the denominator represents the total number of parts that make up the whole.

Here,

We can solve this problem using the formula:

distance = rate x time

Let's start by finding the time it took for the man to travel 450 kilometers at an average speed of 50 kilometers per hour:

time = distance / rate

time = 450 km / 50 km/h

time = 9 hours

So the man spent 9 hours travelling. However, he also took two breaks: a 40-minute rest and a 1-hour lunch break. We need to convert these times to hours to include them in our calculation.

40 minutes is equal to 40/60 = 2/3 hours, and 1 hour is simply 1 hour. So the total time the man spent travelling, including the breaks, is:

total time = 9 hours + 2/3 hours + 1 hour

total time = 10 2/3 hours

To find the finishing time, we add the total time to the starting time of 10 am:

finishing time = 10 am + 10 2/3 hours

finishing time = 8:40 pm (rounded to the nearest minute)

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Part a: ∠ABE and ∠DBE share a ray EBC as EBC is a straight line.

Part b: ∠ABE and ∠DBE are opposite to each other. Thus, the are termed as the  vertical angles.

Angles that are opposing each other whenever two lines connect are known as vertical angles. According to the vertical angles theorem, vertical angles are consistently congruent.

When two lines in geometry connect, four angles are created. Vertical angles are those that are not next to one another or that are opposing one another. Since they always utilize the same measure, vertical angles are unique.

Postulate for Angle Addition: When two neighbouring angles combine to make a straight line, its result is 180°.

The given angles:

∠ABE = ∠DBE (vertical angles)

Part a: ∠ABE and ∠DBE share a ray EBC .

Part b: ∠ABE and ∠DBE are opposite to each other. Thus, the are termed as the vertical angles.

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The surface area of the triangular prism is 891 square inches, calculated by finding the area of each face (two triangular and three rectangular) and adding them up.

To find the surface area of the triangular prism, we need to find the area of each face and add them up.

The triangular prism has two identical triangular faces and three rectangular faces. The triangular faces have base 9 inches, height 12 inches, and hypotenuse 15 inches. The area of each triangular face can be found using the formula for the area of a triangle:

Formula for area of each triangular face = (1/2) x base x height

= (1/2) x 9 x 12

= 54 square inches

The prism also has three rectangular faces, each with length equal to the base of the triangle (9 inches) and width equal to the height of the prism (29 inches). The area of each rectangular face can be found using the formula for the area of a rectangle:

Area of each rectangular face = length x width

= 9 x 29

= 261 square inches

Hence, the triangular prism's total surface area is:

Total surface area = 2(Area of each triangular face) + 3(Area of each rectangular face)

= 2(54) + 3(261)

= 108 + 783

= 891 square inches

Therefore, the surface area of the triangular prism is 891 square inches.

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Answer: 8800

Step-by-step explanation:

Rounds down because 42 is less than 50

The probability of landing in the color green is P = 0.41, and out of 160 spuns, we can expect to get the color green 66 times.

We have a table and we want to use it to find the probability of the spinner landing on green.

It is equal to the quotient between the number of times that we got green and the total number of times that we spun the spinner.

We got green 325 times, and the total number is:

T = 116 + 325 + 359

T = 800

Then the probability is P = 325/800 = 0.41

b) If it is spun 160 times, then we will get 0.41 times 160 green landings, it is:

160*0.41 = 65.6

This can be rounded up to 66, we can expect to land in the green section 66 times.

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The space-mean speed of the four vehicles is approximately 64 mph.

The given information about the speeds of four vehicles measured at the midpoint of a roadway section are as follows:Vehicle Speed (mph)A 55B 50C 74D 78The space-mean speed of the four vehicles can be found out by the following formula:Space-mean speed = {Sum of the individual speeds of the vehicles}/{Number of vehicles}Space-mean speed = (55 + 50 + 74 + 78)/4Space-mean speed = 257/4Space-mean speed ≈ 64 mph (rounded to the nearest mph)

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The value of c is equal to 4.

The value of d is equal to 0.

In Geometry, a reflection across or over the x-axis is modeled and represented by the following transformation rule (x, y) → (x, -y). Therefore, a reflection across or over the x-axis would maintain the same x-value while the sign of the y-value would change from negative to positive or positive to negative as the case may be.

One of the vertices of triangle A is given by:

(x, y)                 →         (x, -y)

A (-1, -1)            →         A' (-1, -(-1) = (-1, 1)

When a translation is applied to triangle A', one of the corresponding or resulting vertices of triangle B is given by:

B (3, 1)

A' (-1 + c, 1 + d) → B (3, 1)

-1 + c = 3

c = 3 + 1

c = 4.

1 + d = 1

d = 0

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Therefore, the area of the shaded region is 72 square meters.

A triangle is a three-sided polygon that is formed by connecting three straight lines or line segments. It is a basic geometric shape that is commonly studied in mathematics, geometry, and trigonometry. Triangles have a wide range of properties and characteristics that are important in various fields of study, including their angles, sides, and area. Triangles can be classified based on their angles (as acute, right, or obtuse triangles) or based on their sides (as equilateral, isosceles, or scalene triangles). The study of triangles is fundamental in many areas of mathematics and physics and is also important in practical applications such as engineering, architecture, and surveying.

by the question.

To find the area of the shaded region, we first need to find the area of the entire rectangle. The area of a rectangle is given by the formula: length x width.

The length of the rectangle is 12 meters, and the width is 8 meters, so the area of the entire rectangle is:

12m x 8m = 96 square meters

Next, we need to find the area of the triangle that is not shaded. The base of the triangle is 6 meters, and the height is 8 meters. The area of a triangle is given by the formula: 1/2 x base x height.

1/2 x 6m x 8m = 24 square meters

Finally, we can find the area of the shaded region by subtracting the area of the triangle from the area of the entire rectangle:

96 square meters - 24 square meters = 72 square meters

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The correct option is A: the probability distribution for the winning ticket:

1          2        3       4      5      6       7       8       9      10

0.10  0.10  0.10  0.10  0.10  0.10  0.10  0.10  0.10  0.10

A frequency distribution that has been idealised is a probability distribution.

Total people = 10 (1 - 10)

One ticket is selected at random from each person.

As the selection is independent events of each other, each will have the same probability.

So,

probability = favourable outcome / total outcome.

probability = 1/10

probability = 0.10.

Thus, the correct option is A: the probability distribution for the winning ticket:

1          2        3       4      5      6       7       8       9      10

0.10  0.10  0.10  0.10  0.10  0.10  0.10  0.10  0.10  0.10

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1. Let us suppose the amount saved = s. 2. The inequality is 62 + s ≥ 100. 3. The value of s is: s ≥ 38. 4. Vin can save at least $38 from now until the end of the month to meet his goal of saving at least $100.

A mathematical statement illustrating the relationship between two amounts or expressions that are not always equal is known as an inequality. To represent the connection between the two values, an inequality may employ a number of symbols, including (less than), > (greater than), (less than or equal to), or (greater than or equal to). In algebra and other branches of mathematics, inequalities are frequently used to indicate restrictions, such as limitations on a variable, and to address issues with variables or unknown numbers. An inequality's solution, which may be a range of values rather than a single value, is the collection of all values that meet the inequality.

1. Let us suppose the amount saved = s.

2. The inequality is 62 + s ≥ 100

3. Solving for s we have:

62 + s ≥ 100

s ≥ 100 - 62

s ≥ 38

On the number line, all values greater than or equal to 38 would satisfy this inequality.

4. Vin can save at least $38 from now until the end of the month to meet his goal of saving at least $100.

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It will take 2.2 hours for the two trains to meet.

We can find the time taken by the two trains to meet by using the formula,

large Time=Distance/Speed

Let's consider the time taken by the two trains to meet be "t".The distance between two trains = 418 miles.

Now, the first train is traveling at a speed of 85 mph and the second train is traveling at a speed of 105 mph.

Let's calculate the distance covered by both the trains in time "t".The distance covered by the first train in time "t"=85t.

The distance covered by the second train in time "t"=105t.

So, the total distance covered by both the trains in time "t" is,

Distance covered = 85t+105t=190t.

But we know the distance between the two trains is 418 miles.

Therefore,190t = 418

Now, solve for "t"t = 418/190t = 2.2 hours

Therefore, the two trains will meet in 2.2 hours.

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The volume of the cake box is c. 648 cubic inches.

Volume refers to the amount of space occupied by an object or a three-dimensional figure. It is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³).The volume of an object can be determined by multiplying its length, width, and height if it has a regular shape such as a rectangular prism or cube.

A rectangular box's volume is equal to its length, width, and height.

Substituting the given values, we get:

Volume of a cake box = 12 inches x 9 inches x 6 inches

Volume = 648 cubic inches

Therefore, the volume of the cake box is 648 cubic inches.

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Answer:

192

Step-by-step explanation:

320/20=16

12x16=192

Answer:

[tex]x = \frac{3(6+y)}{4}[/tex]

Step-By-Step Explanation:

First Step:

[tex]4x=18+3y[/tex]

Second Step:

[tex]x = \frac{18+3y​}{4}[/tex]

Last Step:

[tex]x = \frac{3(6+y)}{4}[/tex]

Answer:

below

Step-by-step explanation:

A (0,8)

B (8,0)

C(0,-8)

D(-8,0)

AB ( 4, 4 )

8/2 , 8/2

(x1+x2/2, y1+y2/2)

BC ( 4,-4 )

8/2 , -8/2

CD ( -4,-4 )

-8/2 -8/2

AD ( -4,4 )

-8/2 8/2

The polygon formed is a square because they all have sides with same lengths

If it was repeated it will still be a square

Answer:

56.54 inches

Step-by-step explanation:

If the radius is 3 inches, to find the area of the circle your equation would be A = (pi) x r^2

Your equation would look like this:

A = (pi) x 3^2

A = 28.27

Now to get the volume of the pie, you would multiply 28.27 x 2 which gives you an answer of 56.54 inches.

Answer:

12y-8

Step-by-step explanation:

The parts that are called radius as shown from the diagram are: OC and OB (option A and B)

The radius of a circle is defined as the distance from the center of the circle to any point on the circumference. However, the radius is also obtained by dividing the diameter of a circle by 2

Now, we shall consider the diagram given to determine the distance from the center to the circumference (i.e radius). This is shown below:

Considering the options given from the question, we can conclude that the parts of the circle which is called the radius are: OC and OB (option A and B)

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Step-by-step explanation:

If it is parallel to the line y = -x + 6, they have the same gradient and the gradient is the coefficient of x which is -1.

We use the equation y=mx+c

Y is 2

M is -1

X is -4

2 = (-1×-4) + c

2 = 4 + c

C = 2 - 4 = -2

Y = -x -2