3.6.2 Reflect the plane in the x-axis, and then in the line y = 1/2. Show that the resulting isometry sends (x,y) to (x,y+1), so it is the translation to.1. 3.6.3 Generalize the idea of Exercise 3.6.2 to show that the combination of reflec- tions in parallel lines, distance d/2 apart, is a translation through distance d, in the direction perpendicular to the lines of reflection. 3.6.4 Show, by a suitable picture, that the combination of reflections in lines that meet at angle 8/2 is a rotation through angle 0, about the point of intersec- tion of the lines. Another way to put the result of Exercise 3.6.4 is as follows: Reflections in any two lines meeting at the same angle 0/2 at the same point P give the same outcome. This observation is important for the next three exercises (where pictures will also be helpful).

If I walk 3.5 miles in 2 hours, then I can walk 14 miles in 8 hours.

If I walk 3.5 miles in 2 hours, then I can use a simple proportion to calculate how far I can walk in 8 hours. I know that in 2 hours I can walk 3.5 miles, and I want to calculate how far I can walk in 8 hours. To do this, I can set up a proportion. The fraction representing the time I spent walking and the distance I walked must be equal on both sides of the equation. On the left side of the equation, I set up 2/3.5, and on the right side I set up 8/x, where x is the unknown distance I can walk in 8 hours. I can then solve for x by cross-multiplying and dividing. After solving, I find that I can walk 14 miles in 8 hours.

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The sequence of transformations that maps HIJK to ABCD is sequence B: reflection over line HÌ, then a translation 6 units to the right and 3 units down.

What is quadrilateral ?

A quadrilateral is a polygon with four sides and four vertices. The term "quadrilateral" comes from the Latin words "quadri" meaning "four" and "latus" meaning "side". Quadrilaterals can have different shapes and properties, including rectangles, squares, parallelograms, trapezoids, and kites.

Since quadrilaterals HIJK and ABCD are congruent, we can map one onto the other using a sequence of transformations. We need to determine which of the given sequences of transformations maps HIJK to ABCD.

Sequence A involves a 270° rotation about point J, followed by a translation 9 units to the right and 8 units down.

Sequence B involves a reflection over the line HÌ, followed by a translation 6 units to the right and 3 units down.

To determine which sequence maps HIJK to ABCD, we can apply each sequence to the vertices of HIJK and see if the resulting image matches the vertices of ABCD.

Starting with sequence A, we apply the rotation and translation to the vertices of HIJK:

Vertex H(-2, 1) is rotated 270° about J(-2, 2) to get H'(0, 0). Then we translate 9 units to the right and 8 units down to get H''(9, -8).

Vertex I(-3, -1) is rotated 270° about J(-2, 2) to get I'(1, -3). Then we translate 9 units to the right and 8 units down to get I''(10, -11).

Vertex J(-2, 2) is fixed by the rotation and then translated 9 units to the right and 8 units down to get J''(7, -6).

Vertex K(0, 0) is rotated 270° about J(-2, 2) to get K'(-2, -2). Then we translate 9 units to the right and 8 units down to get K''(7, -10).

The resulting image of HIJK under sequence A has vertices H''(9, -8), I''(10, -11), J''(7, -6), and K''(7, -10). We can see that these vertices do not match the vertices of ABCD, so sequence A does not map HIJK to ABCD.

Next, we apply sequence B to the vertices of HIJK:

Vertex H(-2, 1) is reflected over line HÌ to get H'(-4, 3). Then we translate 6 units to the right and 3 units down to get H''(2, 0).

Vertex I(-3, -1) is reflected over line HÌ to get I'(-1, 1). Then we translate 6 units to the right and 3 units down to get I''(5, -2).

Vertex J(-2, 2) is reflected over line HÌ to get J'(-4, 4). Then we translate 6 units to the right and 3 units down to get J''(2, 1).

Vertex K(0, 0) is reflected over line HÌ to get K'(-2, 2). Then we translate 6 units to the right and 3 units down to get K''(4, -1).

The resulting image of HIJK under sequence B has vertices H''(2, 0), I''(5, -2), J''(2, 1), and K''(4, -1). We can see that these vertices match the vertices of ABCD, so sequence B maps HIJK to ABCD.

Therefore, the sequence of transformations that maps HIJK to ABCD is sequence B: reflection over line HÌ, then a translation 6 units to the right and 3 units down.

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In conclusion, Amy used a snowball sampling method to collect data for her survey. This method is useful when the population is hard to locate or identify, and when other sampling methods are not possible

Amy used a snowball sampling method. Snowball sampling is a non-probability sampling method where the participants recruit other members of the population.

It is useful when the population is difficult to locate or identify, as it relies on word of mouth or referrals from already recruited participants. In this case, Alfred was able to introduce other international students who might be interested in participating in Amy's survey. This allowed Amy to collect enough data to conduct her analysis. Snowball sampling is useful when the sample size is not known, when time is limited, or when a random selection is not possible.

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Answer:122

Step-by-step explanation:

sum of the interior angles of a rectangle is equal to 360 degrees. sum of neighbor angles is equal to 180 degrees. the if one of the neighbor angle is 90 then, other is 180-90=90.

a+76+72+90=360

a+238=360

a=122

The domain and range of g of x equals the square root of the quantity x plus 4, g(x) = √x + 4, are equal to d: [–4, [infinity]) and r: [0, [infinity]). Thus, the right choice of answer is option (c).

We have a function g(x) and defined as square root of the quantity x plus 4, i.e.,

g(x) = √x + 4

We have to determine the domain and range of function g(x).

The domain of function is all input values of x that make the expression defined. The range is the set of all output values that valid g(x) values. A square root limits the function because we can't have negative numbers under the square root (they become imaginary numbers). Let y = g(x) = √x +4

the square root '√ 'sign must be implies ≥ 0, therefore, x + 4 ≥ 0

Subtracting the 4 from both sides

=> x + 4 -4 ≥ 0 - 4

=> x ≥ -4

The domain is x∈ [-4,+∞)

When x = -4, g(x) = 0

Therefore, The range is y∈ [0, 00)

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Answer:

The picture shows that the side lengths and the angle are the same because of the lines

Step-by-step explanation:

The answer is given and VS=WT but add the line symbol above that

Hence, in answering the stated questiοn, we may say that If yοu're unitary methοd  satisfied with yοur line plοt, save it and distribute it as needed.

The unit technique is a prοblem-sοlving apprοach that invοlves finding the value οf a single unit and then multiplying that value by the needed value. Tο put it simply, the unit technique is used tο extract a single unit value frοm a given multiple. 40 pens, fοr example, wοuld cοst 400 rupees, οr the cοst οf οne pen. The prοcess fοr achieving this may be standardized. A single cοuntry. anything that has an identity element. Its adjοint and reciprοcal are equal in mathematics and algebra.

a general methοd fοr prοducing a line plοt:

First, cοllect yοur data. Stοck prices, temperature readings, and survey results are all examples οf this. The crucial thing is that yοu have a set οf values tο plοt οn a graph.

Enter yοur x and y values intο the plοt. The exact prοcedure depends οn the graphing prοgrammed yοu're using, but yοu shοuld be able tο enter yοur values intο a data table οr spreadsheet.

Make any changes yοu want tο yοur plοt. Adding labels tο the x and y axes, tweaking the plοt's scale, changing the line cοlοur οr thickness, οr adding a title are all pοssibilities.

If yοu're satisfied with yοur line plοt, save it and distribute it as needed.

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Complete question:

The actual distance of 6 cm, given the scale of the map, would be 30 km .

The distance on the map, given the actual distance on the ground and the scale, would be 6 inches .

The scale is that for every 1 cm on the map, the actual distance is 5 kilometers. When given 6 cm therefore, the actual distance is :

= 6 x 5

= 30 km

The scale of the second map is such that 1 inch on the map is 3 actual kilometers so 18 km on the ground would be :

= 18 / 3

= 6 inches

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The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π (pi) is a constant approximately equal to 3.14.

To find the circumference of the circle, we need to know the radius. If we are not given the radius directly, we may be given another measurement that we can use to calculate it. For example, we may be given the diameter, which is the distance across the circle passing through its center. The radius is half the diameter.

Assuming we have been given the diameter of the circle, we can calculate the circumference as follows:

Write down the formula for the circumference of a circle: C = 2πr

Identify the diameter of the circle. Let's say it is 10 cm.

Calculate the radius by dividing the diameter by 2: r = 10/2 = 5 cm.

Plug in the value of the radius into the formula: C = 2π(5) = 10π.

Use the approximation of π as 3.14: C = 10(3.14) = 31.4 cm.

Therefore, the circumference of the circle is approximately 31.4 cm, to the nearest tenth of a centimeter.

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Complete question:

A circle of radius 3 cm is drawn .Given that the measurement is in centimeters, find the circumference of the circle to the nearest tenth. (Use 3.14 for π)

A) 9.4 cm

B) 18.8 cm

C) 37.7 cm

D) 56.6 cm

Answer:

the answer to ur question is: 36

Answer:

A likelihood of 1 is also known as the Discrete probability distribution

To rotate triangle ABC 90 degrees clockwise about a point P, we can follow these steps:

Draw a line segment from each vertex of the triangle to the point P.

Measure the distance from each vertex to the point P and make note of the lengths.

Rotate each line segment 90 degrees clockwise by swapping the x and y coordinates and changing the sign of the new y-coordinate. For example, if a vertex has coordinates (x, y), the new coordinates after rotation will be (y, -x).

Use the new endpoints of the line segments to draw the new triangle, A'B'C'.

For example, suppose the coordinates of triangle ABC are A(1,2), B(3,4), and C(5,2), and the point of rotation is P(3,3). Then the distances from each vertex to the point P are:

AP = sqrt((3-1)² + (3-2)²) = sqrt(5)

BP = sqrt((3-3)² + (3-4)²) = 1

CP = sqrt((3-5)² + (3-2)²) = sqrt(5)

After rotating each vertex 90 degrees clockwise about P, we get:

A'(4,1)

B'(2,3)

C'(4,5)

Using these new coordinates, we can draw the new triangle A'B'C', which is the result of rotating triangle ABC 90 degrees clockwise about P.

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction of the bar. ABC rotates 90 degrees clockwise about point p to from A’B’C

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The two primary components of an angle are the limbs and the vertex. The angle sum property of a triangle is 20+21+29=180 70x=180 x=180/70.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex. The joint vertex is the common terminal of the two beams.

According to the given question,

angle sum property of triangle-

20+21+29=180

70x=180

x=180/70.

Hence, With the angle sum property of triangle, x=180/70.

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Answer:

arc DB = 45°

Step-by-step explanation:

the measure of an arc is the same as the central angle that intercepts it.

∠ DCB = 180° - 135° = 45°

∠ DCB is the central angle intercepted by arc DB , then

arc DB = 45°

Answer:

1.  C.

2. D.

3. D.

Step-by-step explanation:

A.  Round both dimensions the nearest whole number. 8 1/3 rounds to 8,     6 3/4 rounds to 7. Multiply these two and your estimate for the tarp area is 56 sq yds. Option C.

B. Convert both mixed numbers to improper fractions. Multiply whole number by divisor and add the dividend. (8*3) + 1 = 25. First number is 25/3.(6*4) + 3 = 27. Second number is 27/4. Multiply these two numbers fractions  and get 225/4. Convert to a mixed number, 56 1/4. Option D.

C. This answer is reasonable. 56 1/4 is pretty close to our estimate of 56 sq yds. Or just choose the option that corresponds to your estimate from part A. Option D.

Force on the object is 7.04 pounds in the x-direction

Force on the object is -2.52 pounds in the y-direction

The total force on an object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction can be found by resolving each force into its x- and y-components, and then adding them to obtain the net force acting on the object.An object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction is shown below:An object being pushed with 5 pounds of force in the θ=45˚ direction and also with 7 pounds of force in the θ=-60˚ direction.To resolve the forces, we use the following identities:Fx = Fcosθ, andFy = Fsinθ.The x- and y-components of the 5-pound force in the θ=45˚ direction are:Fx = Fcosθ = 5 cos 45˚ = 3.54 pounds,andFy = Fsinθ = 5 sin 45˚ = 3.54 pounds.The x- and y-components of the 7-pound force in the θ=-60˚ direction are:Fx = Fcosθ = 7 cos (-60˚) = 3.5 pounds,andFy = Fsinθ = 7 sin (-60˚) = -6.06 pounds.The total force acting on the object is the sum of the x- and y-components of the forces acting on it, or:Fx = 3.54 pounds + 3.5 pounds = 7.04 pounds,Fy = 3.54 pounds - 6.06 pounds = -2.52 pounds.Therefore, the total force on the object is 7.04 pounds in the x-direction and -2.52 pounds in the y-direction.

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Values of y that corresponds with the value of x as per quadratic functions are as follows:

6

0

-2

0

6

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must have at least one second-degree term. It performs algebraic operations.

The parent quadratic function connects the locations whose coordinates have the type f(x) = x2 and is of the kind (number, number2).

Just need to evaluate the function for each value of X.

for x=1 y=2(1-3)²-2= 6

for x=2 y=2(2-3)²-2= 0

for x=3 y=2(3-3)²-2= - 2

for x=4 y=2(4-3)²-2= 0

for x=5 y=2(5-3)²-2= 6

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The sample space is 20, 24, 28, 32, 36, 40. There are 6 outcomes in the sample space.  In this case, the sample space is {20, 24, 28, 32, 36, 40}.

The sample space of the probability experiment is the set of all possible outcomes that can occur when randomly choosing a number from the multiples of 4 between 20 and 40, inclusive.

To determine the number of outcomes in the sample space, we simply count the number of elements in the set. In this case, there are 6 outcomes in the sample space.

Therefore, the sample space is {20, 24, 28, 32, 36, 40} and there are 6 outcomes in the sample space. After Randomly choosing a number from the multiples of 4 between 20 and 40, these values are found.

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I think you are correct, I am not sure why. Maybe you ask your teacher and she or he made a mistake with this question.

Answer:

Slope m = 1/3

Step-by-step explanation:

Slope of the line can be found by taking two points on the line, (x1, y1) and (x2, y2)

Find the difference in y coordinates, y2 - y1  (called rise)

Find the difference in corresponding x coordinates x2 - x1 (called run)

Rise/Run gives the slope

Two distinguishable points on the line graph are (0, 2) and (3, 3)

rise = 3 - 2 = 1

run = 3 - 0 = 3

Slope = 1/3

Wilbur's flight took about 43.7 seconds.

Let x be the rate of Orville in feet per second and 2x be the rate of Wilbur in feet per second. Let t be the time it took for Orville to complete the flight and t - 6 be the time it took for Wilbur to complete the flight.

We know that the distance traveled by both brothers is the same, which we can express with the equation:

distance = rate × time

For Orville:

distance = x * t

For Wilbur:

distance = 2x * (t - 6)

Since the distance is the same for both brothers, we can set the two equations equal to each other:

x * t = 2x * (t - 6)

Expanding and simplifying the right-hand side:

xt = 2xt - 12x

12x = xt

x = t/12

So, Orville's rate is x = t/12 feet per second.

Substituting this into one of the equations for distance, we can solve for t:

distance = x * t

852 = (t/12) * t

852 = t² / 12

t² = 12 * 852

t² = 10224

t ≈ 101.1 seconds (rounded to the nearest tenth)

So, Orville's flight took about 101.1 seconds.

Now we can use the equation for Wilbur's distance to find his rate:

distance = 2x * (t - 6)

852 = 2(2x) * (101.1 - 6)

852 = 4x * 95.1

x ≈ 5.64 feet per second (rounded to the nearest hundredth)

So, Orville's rate is about 5.64 feet per second, and Wilbur's rate is twice that or about 11.28 feet per second.

To find Wilbur's time, we can use the equation for distance again:

distance = 2x * (t - 6)

852 = 2(11.28) * (t - 6)

852 = 22.56t - 135.36

22.56t = 987.36

t ≈ 43.7 seconds (rounded to the nearest tenth)

So, Wilbur's flight took about 43.7 seconds.

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The value οf a, b, and c are 3, 5, and 25 respectively.

There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.

The given equatiοn is

1/(x + 5) + 2/(x -5) = (ax + b)/ (x² - c)

Sοlve the left-hand side οf the equatiοn:

L.H.S = 1/(x + 5) + 2/(x -5)

= [x-5 + 2(x+5)]/(x + 5)(x -5)

= [x-5 + 2x+ 10]/(x + 5)(x -5)

Cοmbine like terms:

= [3x + 5]/(x + 5)(x -5)

Nοw apply fοrmula (a-b)(a+b) =a² - b²:

= [3x + 5]/(x² - 5²)

= [3x + 5]/(x² - 25)

Put 1/(x + 5) + 2/(x -5) =  [3x + 5]/(x² - 25) in the given equatiοn:

[3x + 5]/(x² - 25) = (ax + b)/ (x² - c)

Nοw cοmpare bοth sides:

a = 3

b = 5

c= 25

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Answer:

To simplify the expression x - 15 + 2x + 6, you can combine like terms. Here are the steps to do that:

Group the x terms and the constant terms separately:

(x + 2x) + (-15 + 6)

Simplify the terms inside the parentheses:

3x - 9

So the simplified expression is 3x - 9.

Therefore, x - 15 + 2x + 6 equals 3x - 9.

Answer:

3(x-3)

Step-by-step explanation:

given : x-15+2x+6

factorize using like terms : x-15+3x+6 = 3x-9

= 3x - 9
=3(x-3)

Answer:

The required amount Ahmet needs to pay after 6 years is $1619.14.

What is compound interest?

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Amount = principal[1 + r/n]ⁿᵃ

Principal = P rate= r Time =a  , n = compounding frequency

Here,

From the given data,

P = 700, r = 15% and t = 6 (n =1)

Now,

Amount = principal[1 + r/n]ⁿᵃ

Amount = 700(1 + 0.15)⁶

Amount = $1619.14

Thus, the required amount Ahmet needs to pay after 6 years is $1619.14.

Step-by-step explanation:

Mei worked 8 hours and Kara worked 7 hours when Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour.

Let's use the following variables to represent the unknowns in the problem:

Let M be the number of computers Mei built

Let K be the number of computers Kara built

We can set up a system of equations based on the given information:

M + K = 17 (the total number of computers built is 17)

0.8M + K = 15 (the total time worked is 15 hours)

We can solve for one of the variables in terms of the other by using the first equation:

M = 17 - K

Now we can substitute this expression for M into the second equation:

0.8(17 - K) + K = 15

13.6 - 0.8K + K = 15

0.2K = 1.4

K = 7

So Kara built 7 computers. We can use the first equation to find how many computers Mei built:

M + 7 = 17

M = 10

Therefore, Mei built 10 computers.

Now we can find how long each girl worked by multiplying the number of computers by their respective build times:

Mei: 10 computers x 0.8 hours per computer = 8 hours

Kara: 7 computers x 1 hour per computer = 7 hours

Therefore, Mei worked 8 hours and Kara worked 7 hours.

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The complete question is :

Mei and Kara build computers from parts and sell them to make a profit. Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour. together they worked 15 hours and built 17 hours and built 17 computers. how many hours did each girl work ?

The correct option to model the height is

h = cosine (StartFraction pi Over 6 EndFraction t) + 9.

Here the height of the tip of the hour hand of a wall clock follows a cosine function as the time progresses since the hour hand of a clock completes one full revolution in 12 hours.

We will use the general form of a cosine function to model the height has a function of time t:

Where A is the amplitude, B is the frequency and C is the vertical shift  

Here we have

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.

Hence, the applitude A = [9+10]/2 = 0.5.

The period of a cosine function is given by 2π/B,

Since the hour hand completes one full revolution in 12 hours, the period is 12 hours or 2π.

=> B = π/6.

The vertical shift is C = 9.

Thus, the equation that models the height h as a function of time t is:

h = 0.5 cos(π/6 t) + 9.

Therefore,

The correct option to model the height is

h = cosine (StartFraction pi Over 6 EndFraction t) + 9.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

By the given parameters, Gethyn needs to drink 2 more cups of water today.

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

Amount = 8 cups

Today = 48 ounces

There are 8 fluid ounces in one cup.

So, to convert 48 fluid ounces to cups, we divide by 8:

48 fluid ounces / 8 fluid ounces per cup = 6 cups

Therefore, Gethyn has already drnk 6 cups of water today.

To reach his goal of 8 cups, he still needs to drink:

8 cups - 6 cups = 2 cups

So Gethyn needs to drink 2 more cups of water today.

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