Which postulate or theorem proves triangle SQY~ triangle PTY? 12mm 8mm 45 degrees 2mm 6mm 4mm

The equation of the axis of symmetry of the quadratic function in this problem is given as follows:

x = -4.

The equation of the axis of symmetry of the quadratic function is a vertical line given as follows:

x = xv.

In which xv is the x-coordinate of the vertex of the quadratic function.

The vertex of a quadratic function is the turning point of the quadratic function, hence it has a x-coordinate of 4 and the equation of the axis of symmetry of the quadratic function in this problem is given as follows:

x = -4.

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From the students diagnostic exam, the 43rd Percentile, 3rd Quartile and 8 Decile are 84.5, 138.5 and 140 respectively.

We first need to sort the scores in ascending order:

34, 36, 66, 74, 76, 78, 84, 85, 99, 103, 121, 123, 123, 125, 130, 133, 137, 140, 145, 156

P43 represents the 43rd percentile, which is the score below which 43% of the scores fall. To find P43, we need to calculate the index of the score that corresponds to the 43rd percentile:

P43 = (43/100) * (n + 1)

P43 = (43/100) * (20 + 1)

P43 = 8.44

Since P43 is not an integer, we can take the average of the scores at the indices 8 and 9 (since the index starts from 1):

P43 = (84 + 85) / 2

P43 = 84.5

Therefore, P43 is 84.5.

The third quartile, Q3, represents the score below which 75% of the scores fall. To find Q3, we calculate the index of the score that corresponds to the 75th percentile:

Q3 = (75/100) * (n + 1)

Q3 = (75/100) * (20 + 1)

Q3 = 15.75

Since Q3 is not an integer, we can take the average of the scores at the indices 15 and 16:

Q3 = (137 + 140) / 2

Q3 = 138.5

Therefore, Q3 is 138.5.

D8 represents the score below which 80% of the scores fall. To find D8, we calculate the index of the score that corresponds to the 80th percentile:

D8 = (80/100) * (n + 1)

D8 = (80/100) * (20 + 1)

D8 = 16.8

Since D8 is not an integer, we can round up to the nearest whole number and consider the score at the 17th index:

D8 = 140

Therefore, D8 is 140.

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The area of APT by the given data is 0.65 m^2.

We are given that;

PV = VR 35° 5 cm

Now,

The formula to calculate the area of APOR is to draw RT so that RT bisects ∠PRQ and point T is on PQ. This will create two congruent triangles, PRT and QRT, by the ASA criterion. Then, the area of APOR can be found by subtracting the area of QRT from the area of APT.

The length of the bottom base of APT is 2(1.5) = 3 m and the length of the top base of APT is 2(1.5 - 0.4) = 2.2 m.

You are also given that each step is 0.25 m higher than the previous one. This means that the height of APT is 0.25 m.

Using these values, you can plug them into the formula for the area of a trapezoid:

A = 0.5(a + b)h A = 0.5(3 + 2.2)(0.25) A = 0.5(5.2)(0.25) A = 0.65 m^2

Therefore, by the area answer will be 0.65 m^2.

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The components of the vector with magnitude 8 and a direction angle of 210° are

(-4√3, -4)

To find the components of a vector with magnitude 8 and a direction angle of 210°, we can use the following formulas

x-component = magnitude * cos(angle)

y-component = magnitude * sin(angle)

given that:

magnitude = 8

angle = 210°

convert the angle from degrees to radians:

angle in radians = angle * π / 180

= 210° * π / 180

= 7π/6 radians

calculate the components:

x-component = magnitude * cos(angle in radians)

= 8 * cos(7π/6)

= 8 * (-√3/2)

= -4√3

y-component = magnitude * sin(angle in radians)

= 8 * sin(7π/6)

= 8 * (-1/2)

= -4

Therefore, the components of the vector with magnitude 8 and a direction angle of 210° are (-4√3, -4).

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The volume of the cylinder is 9071.65 cubic centimeters.

We have to find the volume of the cylinder with a height of 25 cm.

The base has a diameter of 21.5 cm.

Radius of cylinder = 21.5/2

=10.75 cm

The formula for Volume =πr²h

Where r is the radius and height is 25 cm.

Plug in the values of radius and height in to the volume formula.

=3.14×10.75²×25

=9071.65 cubic centimeters.

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The equation of graph is y= 1√(x-5) - 2 .

The equation of graph is y= 1√(x+3) + 4.

We have to write the equation in the form of y= a√(x-h) + k

From the graph 1, the value of h and k is

h = 5

k = -2

and, the value of a is

= rise/ run

= 1/1

= 1

So, the equation of graph is y= 1√(x-5) - 2

From the graph 1, the value of h and k is

h = -3

k = 4

and, the value of a is

= rise/ run

= 1/1

= 1

So, the equation of graph is y= 1√(x+3) + 4.

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Answer:

23.90 years

Step-by-step explanation:

To find the half-life of a radioactive substance, we can use the formula:

[tex]\boxed{\begin{minipage}{10 cm}\underline{Half-life formula}\\\\$ t_{1/2} =\dfrac{\ln 2}{k}$\\\\where:\\\\ \phantom{ww}$\bullet$ $t_{1/2}$ is the half-life. \\ \phantom{ww}$\bullet$ $k$ is the decay constant (percentage decay rate per year)\\ \end{minipage}}[/tex]

In this case, the decay constant is 2.9% or 0.029 (expressed as a decimal). Therefore, substitute k = 0.029 into the formula:

[tex]t_{1/2} =\dfrac{\ln 2}{0.029}[/tex]

[tex]t_{1/2} =23.9016269...[/tex]

[tex]t_{1/2} =23.90\; \sf years\; (2\;d.p.)[/tex]

Therefore, the half-life of the radioactive substance, rounded to 2 decimal places, is approximately 23.90 years.

Answer:

Hi

please mark brainliest ❣️

Thanks

Step-by-step explanation:

10 + x / 3 = 12

Cross multiply

10 + x = 12× 3

10 + x = 36

Collect like terms

x= 36 - 10

x = 26

Answer: 113.04

Step-by-step explanation:

btw, the question is

What's the surface area of a circle with a radius of 6.

Grammar XD

Anyways, the formula for an area of a circle is [tex]\pi r^2[/tex], where [tex]\pi[/tex] is approx 3.14

6 square is 36

36*3.14 is 113.04

Please mark brainliest! :)

Answer:

The length of the third side is approximately ≈ 14.79 inches

Step-by-step explanation:

A piece of wire is bent into the shape of a triangle. Two sides have lengths of 16 inches and 23 inches. The angle between these two sides is 40°. What is the length of the third side to the nearest hundredth of an inch?

Use the law of cosines to find the length of the missing side.

Let C be the third side.

A = 18

B = 23

Angle C = 40^∘

c^2  =  a^2  +  b^2 - 2ab  cos C

c =  √a^2 + b^2 - 2ab cos C

c =  √18^2 + 23 ^2 - 2 (18) (23) cos 40^∘

c = √583 - 828 cos40^∘

≈ 14.79

Thus, The length of the third side is approximately  14.79 inches.

Hope this helps!

Answer: Order of operations

Answer: 0.6156 or in fraction form, 62%

Step-by-step explanation: To find the probability that at least one of the two people does not go on vacation, we subtract the probability that both of them go on vacation from 1. The probability that both go on vacation is 0.62 * 0.62 = 0.3844.

Therefore, the probability that one or both of them does not go on vacation is 0.6156, or about 62%.

Answer: 0.2356 and 0.1444

Step-by-step explanation:

62% of Americans go on Vacation

So out of 100 Americans, 62 go on vacation

The chance of one of them NOT going on vacation is 100-62 or 38%, however, the other person has to go on vacation, so it's 38%*62% or 0.2356, approx 40%*60% or 0.24

The chance of both of them do not go on vacation is 38%*38%, or 0.1444 or approx 40%*40% or 0.16 (very rough calculating)

Answer:

2/5

Step-by-step explanation:

4 raspberry / 10 total

4/10

2/5

The value of x is:

x = -32/3

Here, we have,

EF = ½(BC + AD) => Trapezoid Midsegment theorem

Substitute

21 = ½(24 + (-3x-14))

21 = ½(10 -3x)

Multiply both side by 2

42 = 10 -3x

Collect like terms

- 3x = 42 - 10

-x = 32/3

Divide both sides by -1

x = -32/3

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The interquartile range for the data-set in this problem is given as follows:

IQR = 22.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

The data-set in this problem has 10 elements, divided into two halves as follows:

The first quartile is the middle element of the first half, hence it is given as follows:

45.

The third quartile is the middle element of the second half, hence it is given as follows:

67.

Then the IQR is given as follows:

IQR = 67 - 45

IQR = 22.

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The following would be filled in the boxes using the distributive property:

(4 × 3 ) + (4 × 7 )

The distributive property is a mathematical concept that describes how multiplication distributes between addition and subtraction. It provides a rule for word expansion and expression condensing.

The distributive property allows us to factor polynomials, simplify expressions, and solve equations in algebra and arithmetic more quickly.

Having said that,

4 × (3 + 7) =(4 × 3 ) + (4 × 7 )

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The probability of drawing a King and then another King is 1/221. Hence, the correct option is d. 1/221.

Number of favorable outcomes: There are 4 Kings in a deck of 52 playing cards. After drawing the first King, there will be 3 Kings remaining in the deck.

Number of possible outcomes: After drawing the first card, there will be 51 cards left in the deck. For the second card, any one of the remaining 51 cards can be drawn.

Thus, the probability can be calculated as follows:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

           = (4/52) * (3/51)

           = 12/2652

           = 1/221

Therefore, the probability of drawing a King and then another King is 1/221. Hence, the correct option is d. 1/221.

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The rectangular prism has a greater volume than the cylinder.

Here, we have,

Volume of shapes:

The rectangular prism has a greater volume than the cylinder. This is because the rectangular prism fully occupies the space within its boundaries, while the cylinder has empty space above and below it.

The cylinder's rounded shape leaves gaps between its curved surface and the boundaries of the rectangular prism.

Therefore, the rectangular prism can hold more volume than the cylinder as it utilizes the entire space within its shape efficiently.

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The correct statement is: ii. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space. Option D

We have from the information given that;

I. The set of all second-degree polynomials with the standard operations is a vector space

II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space

III. The set of second quadrant vectors with the standard operations is a vector space

Then , we should know that;

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The image of point (-1, 3) after the translation by vector (5, 2) is the point (4, 5).

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They

The image of D(-1, 3) along the translation vector (5, 2) can be obtained by adding the vector (5, 2) to each point in D(-1, 3).

This results in the translated point

D(-1, 3) → (-1+5, 3+2) → D(4, 5).

Therefore, the image of point (-1, 3) after the translation by vector (5, 2) is the point (4, 5).

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The domain and the range of the graph are

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

(-2, -1), (0, 1), (2, 3)

The above are a list of ordered pairs

The rule of a function is that

Using the above as a guide, we have the following:

Domain = (-2, 0, 2)

Range = (-1, 1, 3)

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The basic charge refers to a fixed fee or cost that is charged for a service or utility regardless of the actual usage or consumption.

In the given context, the term "basic charge" refers to a fixed fee or cost that is charged for a particular service or utility regardless of the actual usage or consumption.

It is a standard or minimum charge that is applied uniformly to all customers or users, typically to cover the basic infrastructure or administrative costs associated with providing the service.

The basic charge is often separate from any variable charges based on usage or additional services.

It is a recurring fee that customers are required to pay regardless of their specific usage level.

The purpose of the basic charge is to ensure a baseline revenue for the service provider and to contribute to the maintenance and operational costs of the service infrastructure.

It provides a consistent source of income and helps to distribute the costs among all customers fairly.

The basic charge is usually set at a fixed amount or a predetermined rate and may vary depending on the type of service or utility being provided, such as electricity, water, internet, or telecommunications.

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The complete question may be like: Define the basic unit of currency in the United States and explain its significance in the context

The amplitude of the function is 1/2, and the period of the function is π.

We know that,

The general form of a sine function is,

⇒ f(x) = A sin(Bx + C) + D,

where:

A is the amplitude

B is the angular frequency or 2π divided by the period

C is the horizontal shift

D is the vertical shift

Now, We have;

The function is,

⇒ f (x) = 1/2 sin 2x

Hence, By Comparing this to the function f(x) = 1/2 sin 2x, we can see that:

A = 1/2, which means that the amplitude of the function is 1/2.

B = 2, which means that the angular frequency is 2,

Or equivalently, the period of the function is 2π/2 = π.

Therefore, the amplitude of the function is 1/2, and the period of the function is π.

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The two expressions are not equivalent.

The expression "fraction numerator log 25 over denominator log 3 end fraction" is equal to log 25 divided by log 3.

This is because the numerator represents the logarithm of 25 and the denominator represents the logarithm of 3, resulting in the ratio of the two logarithms.

On the other hand, the expression "fraction numerator ln 25 over denominator ln 3 end fraction" is not equal to log subscript 3 25. The numerator represents the natural logarithm (ln) of 25, and the denominator represents the natural logarithm of 3.

The natural logarithm uses the base e (2.71828), whereas the logarithm with subscript 3 uses the base 3.

Therefore, these two expressions are not equivalent.

log 25 divided by log 3 is equal to log subscript 3 25.

fraction numerator ln 25 over denominator ln 3 end fraction is not equal to log subscript 3 25.

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The point (x, y) = (- 1, 2) (Point A) is the solution to the system of linear equations.

In this problem we find the representation of two linear equations set on Cartesian plane, the system consists in two equations with two variables. We are asked to find the solution to the system of linear equations. Graphically speaking, the solution to the system of linear equations is represented by a point of intersection.

Then, by direct inspection, we find that the solution to the system of linear equations is (x, y) = (- 1, 2). (Point A)

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The missing length x = 18. 4

To determine the value of the missing side, we need to take note of the following;

The different trigonometric identities are expressed as;

The sine identity is represented with the fraction;

sin θ = opposite/hypotenuse

From the information given, we have;

θ = 61 degrees

x is the opposite side

21 is the hypotenuse

Substitute the values, we have;

sin 61 = x/21

cross multiply the values, we have;

x = 0.8746(21)

Multiply the values, we have;

x = 18. 4

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The complete question:

Find the missing length x. Round your answer to the nearest tent

theta = 61°

Hypotenuse = 21

Opposite = X

The statement that will help Melody determine the amount of water needed to fill the tank is D . Find the volume by using the formula V = lwh

The amount of water that Melody needs to be able to fill up the tank would be the volume of the tank .

To find the volume of a rectangular prism, the formula is:

V  = L × W × H

Which is length x width x height. This is the exact formula shown in option D so this is the correct option .

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Options include:
A Find the surface area by using the formula SA = 2hw + 2lh + 2wh

B Find the surface area by using the formula SA = pi * r ^ 2 * h

C. Find the volume by using the formula V = 2lw + 2lh + 2wh

D Find the volume by using the formula V = lwh

h can be written as the composition of:

f(x) = x⁴ and  g(x) = 8x - 6

We know that the function h is written as:

h(x) = (8x - 6)⁴

And we want to write h(x) as a composition of other two functions, such that:

h(x) = f(g(x))

Then we can define f(x) as a quartic power, f(x) = x⁴, and g(x) as the argument g(x) = 8x - 6, then we will get:

f(g(x))  = g(x)⁴ = (8x - 6)

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The period and the amplitude of the given function is 4π and 2.

To find the amplitude and period of a function using its graph, you can follow these steps:

Identify the highest point and the lowest point on the graph. These points represent the maximum and minimum values of the function.

The amplitude is equal to half the difference between the maximum and minimum values of the function. In other words, it is the distance from the midline (average value) of the function to either the highest or lowest point on the graph.

Locate two consecutive peaks or troughs on the graph. A peak is a point where the graph reaches its highest point, and a trough is a point where the graph reaches its lowest point.

Measure the horizontal distance between these two consecutive peaks or troughs. This distance is called the period of the function.

If the distance between the two peaks or troughs is not explicitly marked on the graph, you can estimate it by counting the grid lines or using the scale of the x-axis.

Hence the period and the amplitude of the given function is 4π and 2.

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