Elena wants to prove that the measures of the 3 angles in a triangle always
sum to 180 degrees. She starts by using rigid motions to rotate triangle ABC
180° around 2 midpoints. Explain how Elena labeled her diagram and finish
her proof.
E
D
o
6
С
В
B

Answer:The answer is under the question

Step-by-step explanation:The answer is under the question

The volume of an ice cube produced by this machine is of:

Volume ice cube = 1 inch³

  A volume is the physical space that an object occupies in space, although it is also defined as the capacity of space that a hollow object may have.

If this machine produces ice that has a cube shape with a side of 1 inch, then to know the value of the volume of these cubes we will use the following equation:

Volume cube = side x side x side

Volume cube = side³

side = 1 inch

Volume ice cube = 1 inch³

As the side is 1 the volume and area will be 1 but with corresponding unit

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The simple interest rate charged on the purchase per monthly payment is approximately 0.5735%.

To determine the simple interest rate charged per monthly payment on the flat screen television, please follow these steps:

1. Calculate the total amount paid in monthly payments: 24 payments * $80 = $1920.
2. Subtract the down payment: $1920 - $100 = $1820.
3. Subtract the original cost from the total amount paid: $1820 - $1600 = $220. This is the total interest paid.
4. Divide the total interest by the number of monthly payments: $220 / 24 = $9.1667 interest per month.
5. Calculate the interest rate per monthly payment: ($9.1667 / $1600) * 100 = 0.5735% per month.

The simple interest rate charged on the purchase per monthly payment is approximately 0.5735%.

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A.  This expression gives: AC = -38 + 150/Q

B.  The manufacturer receives a maximum weekly profit of £594.50 when it produces 12.25 units per week.

C. The profit function is maximized at this point, since it is increasing for smaller values of Q and decreasing for larger values of Q.

a) The total cost (TC) function is given by the sum of fixed costs and variable costs:

TC = FC + VC

where FC is the weekly fixed cost of £150 and VC is the weekly variable cost per unit, which is given by VC = 2Q - 40. Substituting this expression into the TC function gives:

TC = 150 + 2Q - 40Q

Simplifying this expression gives:

TC = -38Q + 150

The average cost (AC) function is given by the total cost divided by the quantity:

AC = TC/Q

Substituting the expression for TC gives:

AC = (-38Q + 150)/Q

Simplifying this expression gives:

AC = -38 + 150/Q

b) The profit function (π) is given by the difference between revenue and cost:

π = TR - TC

where TR is the total revenue, which is equal to price times quantity, or PQ. Substituting the demand function P = 60 - 4Q gives:

TR = PQ = (60 - 4Q)Q = 60Q - 4Q^2

Substituting the expression for TC gives:

π = TR - TC = (60Q - 4Q^2) - (-38Q + 150)

Simplifying this expression gives:

π = -4Q^2 + 98Q - 150

To find the profit-maximizing level of output, we take the derivative of the profit function with respect to Q and set it equal to zero:

dπ/dQ = -8Q + 98 = 0

Solving for Q gives:

Q = 12.25

To check that this is a maximum, we take the second derivative:

d²π/dQ² = -8 < 0

Since the second derivative is negative, we know that Q = 12.25 is a maximum.

Substituting this value of Q into the profit function gives:

π = -4(12.25)^2 + 98(12.25) - 150 = £594.50

Therefore, the manufacturer receives a maximum weekly profit of £594.50 when it produces 12.25 units per week.

c) At the profit-maximizing level of output, the marginal revenue (MR) is equal to the marginal cost (MC). The marginal cost function is given by the derivative of the total cost function:

MC = dTC/dQ = -38

The marginal revenue function is given by the derivative of the demand function:

MR = dTR/dQ = 60 - 8Q

At the profit-maximizing level of output Q = 12.25, we have:

MC = -38

MR = 60 - 8(12.25) = -1

Since MR < MC, the profit function is decreasing at this point and the maximum profit has been achieved. This can be seen in the graph as the profit function peaks at Q = 12.25 and decreases for larger or smaller values of Q.

Here is a sketch of the relationship between the marginal cost (MC), the marginal revenue (MR), and the profit function at the profit-maximizing level of Q:

     |

MR     |

/\    /  

/  _/     _

/              

-------------------> Q

MC

The vertical line indicates the profit-maximizing level of output, where MR = MC. The profit function is maximized at this point, since it is increasing for smaller values of Q and decreasing for larger values of Q.

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The algebraic expression for the scenario is 15 + x = 60

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

Amount saved up = $15

Cost of item = $60

Amount gifted by your grandma = x

The above parameters means that the mathematical statement is an equation statement

So, we have the following representation

Amount saved up + Amount gifted by your grandma = Cost of item

Substitute the known values in the above equation, so, we have the following representation

15 + x = 60

Hence, the algebraic expression is 15 + x = 60

The question does not require that the equation be solved

However, when it is solved, we have:

15 + x = 60

Subtract 15 from both sides

x = 45

So, the amount is 45

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Answer:

Length = 15m

Width = 5m

Step-by-step explanation:

w = 1/3l

p = 2l + 2/3l

40 = 2 2/3 l

l = 15

w = 1/3(15)

w = 5

If my answer is incorrect, pls correct me!

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-Chetan K

The measurement of ∠STU is 20°.

Define Angle

When two rays are connected at their endpoints, they form an angle in geometry. We refer to these rays as the angle's sides or arms.

Components of an Angle

An angle is composed of the arms and the vertex as its two basic components:

Given, ∠STU = \((\frac {1}{4} x+8)\)°

∠UTV = x+2°

Given, that the line TV bisects ∠STU,

∠STV = ∠UTV

Substitute their values,

\((\frac {1}{4} x+8)\)° = x+2°

Calculating,

\(\frac{1}{4}x-x\) = 2-8

\(-\frac{3}{4}x\) = -6

x = \(-6*(-\frac{4}{3})\)

x = 8

So, we know that:

∠STU = ∠STV + ∠UTV

          =  \((\frac {1}{4} x+8)\)° +( x+2°)

          =  \((\frac {5}{4} x+10)\)

Now, substitute the value of x,

∠STU =  \((\frac {5}{4} )*8\)°+10°

          = 10° + 10°

          = 20°

Therefore, the measure of ∠STU is 20°.

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Answer:

D.

s + m=5

1.75 +2.5m = 11.60

Step-by-step explanation:

Equations that I have made without seeing the options:

s + m = 5

1.75s + 2.5m = $11.60

There is a option that matches my answer. that's D.

Answer:s + m=5

1.75 +2.5m = 11.60

Step-by-step explanation:

Answer:

x = 0 and y = -2

Step-by-step explanation:

x - 2y = 4 and X - 1y = 2

you mentioned elemination aka substraction

so you when substract x - x =  0  -2y -( -y) = -y and 4 -2 = 2

so - y = 2

or y = 2

now substitute the numbers

x + 4 = 4

x = 0

and try it with one of the equation  or sometimes trying on both of them can be very helpful

The length of the legs of the right triangle are 2.83 units.

A right tangle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the legs of the triangle can be found using trigonometric ratios.

Hence,

sin 45 = opposite / hypotenuse

sin 45 = a / 4

cross multiply

a = 4 × 0.70710678118

a = 2.83 units

Therefore,

cos 45 = b / 4

cross multiply

b = 0.70710678118 × 4

b = 2.82842712475

b = 2.83 units

Therefore, the legs are 2,83 units

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The answer  is that the quadratic function is the one that models the situation.

The function that models the situation is a quadratic function in the form of ax² + bx + c.

In this scenario, the engineer is designing a flashlight with a parabolic mirror. A parabolic mirror has a shape that can be represented by a quadratic function. Quadratic functions are typically in the form of f(x) = ax² + bx + c, where a, b, and c are constants.

The explanation for this is that a parabolic mirror reflects light in a way that the reflected rays converge at the focus, which is the vertex of the parabola. This means that the distance between the reflector and the light source should be the same as the distance between the reflector and the focus. The shape of the parabolic mirror is defined by a quadratic function, which is y = ax²

The variable y represents the height of the mirror at a given point, x represents the distance from the vertex, and a is a constant that determines the steepness of the curve. Therefore, the engineer can use this equation to design the parabolic mirror that will maximize the output of the flashlight.
.

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200 divided by 300000 = 0.000666666666667

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

A vector equation of a surface in three-dimensional space is a function that maps a pair of parameters, say u and v, to a three-dimensional point in space (x, y, z) represented as a vector. The vector equation can be written in the form of r(u, v) = <x(u, v), y(u, v), z(u, v)>.

In general, there are different ways to represent the same surface using vector equations. For example, the surface of a sphere of radius r centered at the origin can be represented by the vector equation r(u, v) = <r sin(u) cos(v), r sin(u) sin(v), r cos(u)>, where u is the polar angle (measured from the positive z-axis) and v is the azimuthal angle (measured from the positive x-axis).

Vector equations can be useful in studying the geometry and properties of surfaces, such as determining their tangent planes, normal vectors, curvature, and surface area. They can also be used to parametrize surfaces for numerical calculations and simulations.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

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The statement "a rectangular table can be detrimental by emphasizing status differences between learners" is true.

Rectangular tables, unlike round or oval tables, can make it difficult for all learners to be equal since rectangular tables often have a head or primary position.

Therefore, the person who is sitting in the primary position can quickly become the central focus of the group, causing other members to feel inferior. This is particularly important for learners in a classroom environment, where creating a sense of equality and encouraging everyone to participate and share ideas is crucial.

Learners might feel isolated or overlooked when seated around a rectangular table, particularly if they are at the end of the table or farther from the primary position. This can have an impact on their self-confidence and participation in group activities, as well as their capacity to learn.

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Routh-Hurwitz stability is applied to the system that has been closed with a controller having a constant gain k. If all the coefficients of the first column of the Routh array are positive, the system is stable, and the range of k values required for absolute stability is 2 < k < ∞.

Task 2: Design using Routh-Hurwitz stability

Given, G(s) = K / s(s + 1)(s + 2)

Adding a controller, the transfer function of the closed loop is given by:T(s) = G(s) / [1 + G(s)] = K / [s^3 + 3s^2 + (2 + K)s + K]Applying Routh Hurwitz stability criteria,

[1 2+K K 0]... Eqn (1)

For the system to be stable, all the coefficients of the first column of the Routh array should be positivei. e.

1 > 0, 2 + K > 0 and (2 + K)(K) - K. 0or 2 < K < ∞ for stability.

For a closed-loop system to be stable, it is important to apply a Routh-Hurwitz stability criterion after a controller has been added to the loop transfer function that has constant gain K (G, (s) = K).The transfer function of the closed-loop is given by

T(s) = G(s) / [1 + G(s)] = K / [s^3 + 3s^2 + (2 + K)s + K].

Now apply the Routh Hurwitz stability criteria, [1 2+K K 0]. For the system to be stable, all the coefficients of the first column of the Routh array should be positive, that is

1 > 0, 2 + K > 0, and (2 + K)(K) - K. 0 or 2 < K < ∞ for stability.

The range of k values required for absolute stability of the system that has been closed with a controller having a constant gain k is 2 < k < ∞ if all the coefficients of the first column of the Routh array are positive.

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Answer:

Chopped tomatoes

= 3/4 x 800 = 600g

Stock

= 3/4 x 600 = 450 ml

Red wine

= 3/4 x 300 = 225 ml

Answer: See below

Step-by-step explanation:

For this problem, you will need to use proportions to make sure that the ingredients are the correct amounts when the grams of minced beef is decreased.

Chopped tomatoes

\(\frac{400g beef}{800 g tomatoes} =\frac{300g beef}{x}\)             [cross multiply]

\(400x=240000\)                         [divide both sides by 400]

\(x=600g\)

We will need 600 g chopped tomatoes.

------------------------------------------------------------------------------------------

Stock

\(\frac{400g beef}{600ml stock} =\frac{300gbeef}{x}\)               [cross multiply]

\(400x=180000\)                         [divide both sides by 400]

\(x=450\)

We will need 450 ml of stock.

------------------------------------------------------------------------------------------

Red wine

\(\frac{400g}{300ml} =\frac{300g}{x}\)                            [cross multiply]

\(400x=90000\)                           [divide both sides by 400]

\(x=225\)

We will need 225 ml of red wine.

In a competitive market, we need to graph the market demand and supply curves and determine the equilibrium quantity. The equilibrium quantity represents the quantity at which the demand and supply curves intersect.

To sketch the supply and demand curves, we first need to gather information on the market demand and supply. The demand curve represents the quantity of ventilators that the four hospitals are willing to purchase at different prices, while the supply curve represents the quantity of ventilators that the four producers are willing to sell at different prices.

Using the multipoint drawing tool, we can plot the market demand curve based on the data provided for the hospitals. Label this line as 'Demand'. Next, using the same tool, we can plot the market supply curve based on the data provided for the producers. Label this line as 'Supply'.

The equilibrium quantity is determined at the point where the demand and supply curves intersect. It represents the quantity of ventilators that will be sold in the market. To find this point, we identify the quantity at which the demand and supply curves meet on the graph.

By following the instructions and accurately plotting the demand and supply curves, we can determine the equilibrium quantity of ventilators sold in the market.

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Answer:

21.9 m

Step-by-step explanation:

Take the amount for one dress and multiply by 6

3.65*6 =21.9 m

Answer:

21.9m

Step-by-step explanation:

3.65m*6=21.9m

that is how to solve it because one clothe is 3.65m so therfore six clothe will be 3.65*6=21.9m

The chi-square distribution provides a good approximation to the sampling distribution of the chi-square statistic if the expected frequency in each cell is at least 5.

The chi-square statistic is a measure of how different an observed frequency is from the expected frequency. It is calculated by taking the difference between the observed and expected frequency in each cell, squaring it, and then summing the results. This measure can then be compared to a chi-square distribution with degrees of freedom equal to the number of cells minus one. If the calculated statistic is larger than the expected value from the chi-square distribution, then it can be concluded that the observed frequency differs significantly from the expected frequency.
In order to use the chi-square approximation, it is important that the expected frequency in each cell is at least 5. This is because the chi-square approximation only works well when there are large expected frequencies. When expected frequencies are smaller than 5, the chi-square statistic is not an accurate measure of the difference between the observed and expected frequencies.

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As a result of answering the given question, we may state that As a circle result, the value of x is 4.8.

A circle is a two-dimensional form defined as the collection of all points in a plane that are equidistant from the centre. A circle is commonly represented by the letter "O" for the centre and the lowercase letter "r" for the radius, which is the distance from the centre to any point on the circle. Circles have various essential qualities, including circumference (the distance around the circle), which is given by the formula 2r, where (pi) is a mathematical constant roughly equal to 3.14159. The formula r2 gives the area of a circle, which is the amount of space inside the circle.

We have two intersecting chords in the given circle, and their lengths are given:

\(AC = 8 \sBD = 6\)

We must calculate the value of x, which reflects the length of the CD section inside the circle.

We can use the following formula to find x:

AC * BD = AB * CD

where AB is the length of the other chord in the circle intersected by CD.

We can deduce from the information provided that AB = 10. (since it is the diameter of the circle).

When we substitute the values in the formula, we get:

10 * x = 8 * 6

10x = 48

x = 4.8

As a result, the value of x is 4.8.

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Answer:

B

Step-by-step explanation:

The inscribed angle Q is half the measure of its intercepted arc , so

arc RS = 2 × 75° = 150°

The sum of the 3 arcs = 360° , then

arc QR = 360° - (150 + 133)° = 360° - 283° = 77° → B

Answer:

$3.12

Step-by-step explanation:

31.20 divided by 10 = 3.12

Answer:

21+9=27+x

30=27+x

30-27=x

x = 3

Answer:

Data A - 5

Data B - 5

Data C - 5

Data D - 6

Step-by-step explanation:

Data A,

Graph for the data shows that there is a distinct value of y (output value) for every input value of x.

Therefore, Data A is a function.

Data B,

Each ordered pair shows exactly one output value for each input value.

Therefore, Data B represents a function.

Data C,

For each input value there is exactly one output value.

Therefore, Data C represents a function.

Data D,

From the given table,

For x = -1 there are two output values y = 27, 39

For x = -2 output values are y = 45, 21

Since for these input values there are two output values, Data D will not be a function.

Answer:

  (a)  3x² -5

Step-by-step explanation:

The shift down is accomplished by subtracting 5 from the function value. (Eliminates choices B and D.) The function graph is made narrower by a vertical expansion or a horizontal compression. Either way, the coefficient of the x² term will be greater than 1. (Eliminates choice C.)

The transformed function g(x) = 3x² -5 will be narrower and shifted down from the parent function.

Answer:

The two angles are congruent or estimated to be congruent because of the "≅" that is showed in the statement.

Step-by-step explanation:

Congruent/Congruence: Having the same size and shape or matching in size and shape: congruent figures.

≅ --> Means to be congruent of seen to be congruent

≈ --> About the same, or seems equal

I hope this helped <3

It will take approximately 7.27 years for your mother's investment to become worth $1,000,000 when invested in a well-diversified, low-cost mutual fund returning 10% per year.

To determine the number of years it will take for your mother's investment to become worth $1,000,000, we can use the future value formula:

FV = PV * (1 + r)^n

Where:

FV = Future value ($1,000,000)

PV = Present value ($500,000)

r = Annual interest rate (10% or 0.10)

n = Number of years (unknown)

Substituting the given values into the formula:

$1,000,000 = $500,000 * (1 + 0.10)^n

Simplifying the equation:

2 = (1.10)^n

Taking the logarithm of both sides:

log(2) = log(1.10)^n

Using the logarithmic property:

log(2) = n * log(1.10)

Solving for n:

n = log(2) / log(1.10)

Using a calculator:

n ≈ 7.27

Therefore, it will take approximately 7.27 years for your mother's investment to become worth $1,000,000 when invested in a well-diversified, low-cost mutual fund returning 10% per year.

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The term central location or central tendency relates to the way data tend to cluster around some middle or central value

It is a number located towards the center of the distribution of the values of a series of observations, that are called measures, in which the set of data is located. The most commonly used measures of central tendency are: mean, median and mode.

Statistics is a branch of mathematics that allows you to collect, organize and analyze data according to the need you have, for example: to obtain a result, compare information, make better decisions, among many other things.

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