The figure below is a square. Find the length of side x in simplest radical
form with a rational denominator.

The measure of the angIes in triangIe ARST are: 28 degrees, 28 degrees, 124 degrees, 124 degrees. The measure of the angIes in triangIe ANSP are: 28 degrees, 51 degrees, 101 degrees, 129 degrees.

An angIe is a geοmetric figure fοrmed by twο rays οr Iines with a cοmmοn endpοint, caIIed the vertex. AngIes are typicaIIy measured in degrees οr radians and are used tο describe the amοunt οf turn οr rοtatiοn between twο intersecting Iines οr οbjects. AngIes can be acute (Iess than 90 degrees), right (exactIy 90 degrees), οbtuse (greater than 90 degrees), straight (exactIy 180 degrees), οr refIex (greater than 180 degrees).

Here,

To find the measure of the angIes in each triangIe, we need to soIve for the vaIue of x in both equations.

For the first equation, we can simpIify it as foIIows:

x + 14 = 2x

Subtracting x from both sides, we get:

14 = x

For the second equation, we can simpIify it as foIIows:

3x + 9 = 2x + 23

Subtracting 2x and 9 from both sides, we get:

x = 14

Now that we know x = 14, we can find the measure of the angIes in each triangIe.

In triangIe ARST, we have:

angIe A = x + 14

= 14 + 14

= 28 degrees

angIe R = 2x

= 2(14)

= 28 degrees

angIe S = 180 - (angIe A + angIe R)

= 180 - (28 + 28)

= 124 degrees

angIe T = 180 - (angIe A + angIe R)

= 180 - (28 + 28)

= 124 degrees

In triangIe ANSP, we have:

angIe A = x + 14

= 14 + 14

= 28 degrees

angIe N = 3x + 9

= 3(14) + 9

= 51 degrees

angIe S = 180 - (angIe A + angIe N)

= 180 - (28 + 51)

= 101 degrees

angIe P = 180 - (angIe N)

= 180 - 51 = 129 degrees

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[tex]f'(x) = 21cos(3x)/(1+49sin²(3x)).[/tex] and the outcome is f'(x) = 21cos(3x)/(1+49sin2(3x)). This is the derivative of the function f(x) with respect to x.

We apply the chain rule and the formula for the derivative of the inverse tangent function to determine the derivative of f(x). We first determine that the function contained within the inverse tangent is 7sin (3x). Thus, by differentiating f(x) with respect to x using the derivative of the inverse tangent function, we are able to get an equation in terms of cos(3x) and sin (3x). Trigonometric identities are used to simplify this formula, and the result is[tex]f'(x) = 21cos(3x)/(1+49sin2(3x))[/tex]. This is the derivative of the function f(x) with respect to x.

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The amount of $300 will be $3000 in 70 years with the rate of 5 %

Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.

we have a principal amount is $300 and an interest rate is 5% annually, the amount after compounding is $3000 we have to calculate the time say n.

We know that the formula for the compound interest is-

[tex]A=P(1- \frac{r}{100})^n[/tex]

we have A= $3000

P= $300

r=5% = 0.05

then according to the formula

[tex]3000=300(1+0.05)^n\\\\30=1.05^n\\n=70 years[/tex]

Hence the amount will be 3000 in 70 years.

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Angular speed is approximately 1.36 rad/sec and the linear speed of a point on the rim of the rotating wheel is approximately 28.56 ft/sec.

How to calculate the angular speed and linear speed of a point on the rim of the rotating wheel?

The angular speed of the rotating wheel in rad/sec is given by:

angular speed = 2π × RPM / 60

where RPM is the revolutions per minute. we get:

angular speed = 2π × 13 / 60

≈ 1.36 rad/sec

The linear speed of a point on the rim of the rotating wheel in ft/sec is given by:

linear speed = radius × angular speed

where radius is the radius of the wheel. we get:

linear speed = 21 ft × 1.36 rad/sec

≈ 28.56 ft/sec

Therefore, the angular speed of the rotating wheel is approximately 1.36 rad/sec and the linear speed of a point on the rim of the rotating wheel is approximately 28.56 ft/sec.

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Option (A) true. The box plot for Dog Show 1 shows a smaller interquartile range and a smaller spread of data compared to Dog Show 2

A coordinate graph is a graph that is split up into four quadrants with an x-axis and y-axis. The x-axis runs horizontally, or side to side, and the y-axis runs vertically, or from top to bottom.

A. The box plot for Dog Show 1 has a shorter box, which indicates a smaller interquartile range and less variability in the weights compared to Dog Show 2.

B. This inference is not valid since the range of weights in Dog Show 2 (55-100 lbs) is greater than the range in Dog Show 1 (65-85 lbs).

C. The interquartile range (IQR) for Dog Show 1 is smaller than  for Dog Show 2, indicating that the middle 50% of the weights in Dog Show 1 are closer together than the middle 50% of the weights in Dog Show 2.

D. This statement is false

E. This inference is not valid since the median weight in Dog Show 1 (75 lbs) is higher than the median weight in Dog Show 2 (70 lbs).

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Part 4:  By the theorem of inscribed angle in the circle: arc RP  = 136°.

Part 5: From the central angle theorem: m∠LNM = 54°.

Part 4:

m∠QRP = 68°

By the theorem of inscribed angle in the circle:

Two chords with a shared termination point on the circle make up an inscribed angle in a circle. The vertex of a angle is this common terminal point.

arc RP  = 2 * m∠QRP

arc RP  = 2 * 68°

arc RP  = 136°

Part 5:

From the central angle theorem:

An inscribed angle's measurement is equal to half of an intercepted arc's measurement.

As a result, any two inscribed angles in a circle with identical intercepted arcs remain congruent.

m∠LNM = 1/2 m∠LNP

m∠LNM = 1/2 * 108°

m∠LNM = 54°

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Answer:

Answer: A, C, D, and F are polyhedra.

Chain of thought reasoning:

A. Pyramid: A pyramid is a polyhedron because its base is a polygon with four or more sides and its associated faces are triangles. Therefore, Pyramid (A) is a polyhedron.

B. Sphere: A sphere is not a polyhedron because it is not composed of flat faces connected at straight edges, thus it does not form a shape with flat faces and straight edges. Therefore, Sphere (B) is not a polyhedron.

C. Pentagonal prism: A pentagonal prism is a polyhedron because its base is a polygon with five sides and its associated faces are also polygons, resulting in a shape with flat faces and straight edges. Therefore, Pentagonal Prism (C) is a polyhedron.

D. Cube: A cube is a polyhedron because both its bases and its associated faces are polygons with four sides, resulting in a shape with flat faces and straight edges. Therefore, Cube (D) is a polyhedron.

E. Cylinder: A cylinder is not a polyhedron because it is not composed of flat faces connected at straight edges, thus it does not form a shape with flat faces and straight edges. Therefore, Cylinder (E) is not a polyhedron.

F. Cone: A cone is a polyhedron because its base is a polygon with three or more sides and its associated faces are circles or triangle, resulting in a shape with flat faces and straight edges. Therefore, Cone (F) is a polyhedron.

Heating the water to a temperature of 212°F or higher, which will cause it to boil and transform from a liquid to a gas (water vapor).

Cooling the water down to a temperature of 32°F or lower, which will cause it to freeze and transform from a liquid to a solid (ice).

The temperature range for a stage change in water is either more noteworthy than or equivalent to 212°F or not exactly or equivalent to 32°F, which compares to the bubbling and edges of freezing over of water, separately.

The water is still in its liquid state at 75°F, but it will change phases if it reaches 212°F or is cooled to 32°F or lower.

Therefore, the temperature changes that will produce a phase change in a glass of water at 75°F are:

Heating the water to a temperature of 212°F or higher, which will cause it to boil and transform from a liquid to a gas (water vapor).

Cooling the water down to a temperature of 32°F or lower, which will cause it to freeze and transform from a liquid to a solid (ice).

It is important to note that the temperature of the water will not change during the phase change until the entire change is complete. To put it another way, when water is boiling, it will remain at 212°F until all of the liquid has evaporated, and when it is frozen, it will remain at 32°F until all of the liquid has frozen solid.

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To find the height of Sophia's fig tree, we subtracted 38 from 74 and got the result that the height of her fig tree is 36 inches.

In this problem, we are given information about the height of Sophia's lemon tree and the relationship between the heights of her lemon and fig trees. We are asked to find the height of the fig tree.

First, we use "f" to represent the height of the fig tree. We are told that the fig tree is 38 inches shorter than the lemon tree, which we know is 74 inches tall. To find the height of the fig tree, we can subtract 38 from 74:

We know from the problem that Sophia's fig tree is 38 inches shorter than her lemon tree, which is 74 inches tall. So we can write the following equation:

f = 74 - 38

Simplifying this equation, we get:

f = 36

Therefore, the height of Sophia's fig tree is 36 inches.

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Answer:

The data set represented by the modified box plot is:

116, 118, 114, 117, 151, 126, 122, 114, 124

Step-by-step explanation:

The ability to edit a transaction depends on the specific platform or software that you are using to manage your transactions.

However, in general, there are two options when it comes to editing a transaction:

Edit the existing transaction: This option allows you to modify the details of a transaction that has already been recorded in your system. You may be able to edit the date, amount, category, or any other relevant details of the transaction. This is typically done within the transaction history or ledger of the platform or software you are using.

Void and re-enter the transaction: This option involves voiding or deleting the original transaction and then entering a new transaction with the corrected details. This may be necessary if the original transaction was recorded with incorrect information that cannot be easily edited, or if you want to keep a clear record of the changes made to the transaction.

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Answer:

electronic funds transfer

Thus, the rational inequality formed for the given solution is found as:

x - 3 ≤ 0

A rational inequality is a specific type of statistical inequality statement that typically has a ratio of two polynomials (commonly known as a "rational expression") on the left side and a zero on the right.

Given expression is:

−1 + x ≤ 2

Subtract both side by 2

−1 + x - 2 ≤ 2 - 2

x - 3 ≤ 0

Thus, the rational inequality formed for the given solution is found as:

x - 3 ≤ 0

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Correct question:

Create a rational inequality for which −1 + x ≤ 2 is the solution.

The missing information for both parts below include the following:

mVYW = 162 degrees.

m∠XZY = 140 degrees.

In Mathematics and Geometry, the theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

Additionally, the inscribed angle of a circle is equal to half of the central angle of a circle;

mVXW = 1/2(mVYW)

81 = 1/2(mVYW)

mVYW = 162 degrees.

By applying the theorem of intersecting secants, the value of m∠XZY can be calculated as follows:

m∠XZY = 1/2(m∠VW - m∠YX)

m∠XZY = 1/2(106 - 36)

m∠XZY = 140 degrees.

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In the 1st part the correct option is B and in 2nd part A.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

Hence, In the 1st part the correct option is B and in 2nd part A.

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Answer:

False. Kant's notion of empirical intuition refers to the immediate awareness of particular objects or experiences, which he believed was necessary for gaining knowledge of the world. However, sweetness is not an example of empirical intuition as it is a subjective experience that cannot be directly observed or measured.

It is false that sweetness is an example of empirical intuition, according to Kant.

Immanuel Kant introduced the concept of empirical intuition, which refers to the mind's ability to organise and structure sensory experience. It enables us to perceive objects and events in our surroundings and form opinions about them. However, it has nothing to do with sweetness.

Kant defines empirical intuition as sensory information received through our senses, such as colours, shapes, and sounds.

Empirical intuition, according to Kant, refers to the a priori knowledge we have about space and time that shapes our experience of the world.

It excludes abstract concepts like sweetness, which are derived from our perception and interpretation of sensory data.

Thus, the given statement "Sweetness is an example of empirical intuition, according to Kant" is false.

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The value of x for the intersecting chords is derived to be 4 and the segment AV is equal to 8.

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

UA × AS = VA × AT

10 × 12 = 2x(3x + 3)

120 = 6x² + 6x

dividing through by 6 and equating to 0, we have a quadratic equation;

x² + x - 20 = 0

by factorization;

(x - 4)(x + 5) = 0

so;

x = 4 or x = -5

using x = 4, the value of the segment AV is derived as;

AV = 2(4) = 8.

Therefore, the value of x for the intersecting chords is derived to be 4 and the segment AV is equal to 8.

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Answer:

you are correct keep going

transformation

rigid motion

Answer: 6000

Step-by-step explanation:

10 times 600
10 x 600

6000

Answer:

80

Step-by-step explanation:

In this sequence, every number increases by 6 units:

4; 10; 16; 22; 28 (first five terms)

The sum:

4 + 10 + 16 + 22 + 28 = 80

Answer:

Step-by-step explanation:

Let's start by defining a coordinate system where the horizontal axis represents the number of weeks that Gildong has been saving (and spending), and the vertical axis represents the amount of money he has in savings.

During the first 15 weeks, Gildong saved 20,000 won per week, so his savings increased linearly from week 0 to week 15. We can represent this with the equation:

y = 20,000x

where x is the number of weeks since the beginning (x = 0 corresponds to the start of the saving period) and y is the amount of money Gildong has saved after x weeks.

During the next 15 weeks, Gildong spent 20,000 won per week on eating Maratang, so his savings decreased linearly from week 15 to week 30. We can represent this with the equation:

y = -20,000(x - 15) + 20,000(15)

where x is the number of weeks since the beginning (x = 15 corresponds to the start of the spending period) and y is the amount of money Gildong has saved after x weeks.

To represent the total amount of money Gildong had in savings at any given time, we can combine the two equations above using an absolute value:

y = |20,000x| - 20,000(x - 15)

where x is the number of weeks since the beginning, and y is the amount of money Gildong has in savings after x weeks.

This function represents the absolute value of the difference between the amount of money Gildong has saved and the amount of money he has spent on Maratang, taking into account the fact that his savings increased linearly during the first 15 weeks and decreased linearly during the next 15 weeks.

Answer:

x=8

Step-by-step explanation:

|x+8|=x+8

x+8=x+8

x^2+8=8

x^2=16

√x^2=√16

x=8

Answer: 4

Step-by-step explanation:

Lets first start with the expression:

[tex]m^2+5m-2[/tex]

and m = -6

this means by using substition and plugging in the value -6 for all the m's in the expression, you'll be able to evaluate it.

in other words the expression will now like this when doing substition:

[tex](-6)^2+5(-6)-2[/tex]

36 - 30 - 2

= 4

Answer:

[tex]30 - x = 4x \\ 30 = 4x + x \\ 30 = 5x \\ x = \frac{30}{5} \\ x = 6[/tex]

The measure of a length, you would typically need to know the two endpoints of the length and use the distance formula to calculate the distance between them.

[tex]d = √((x₂ - x₁)² + (y₂ - y₁)²)[/tex]

the formula can also be extended to three-dimensional space by adding an additional term for the z-coordinate, as follows:

[tex]d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)[/tex]

The measure of an angle, you would typically need to know the two rays or line segments that form the angle and use trigonometry or geometry formulas to calculate the angle measure.

[tex]sin(A)/a = sin(B)/b = sin(C)/c[/tex]

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The cost for 100 shares at the 52-Week Low is $5228.  Therefore the correct option is option A.

We need to look at the table or chart that shows the data on stock prices at the 52-week low in order to respond to this question. The question alone does not provide the response.

After gaining access to the table, we may calculate the price for 100 shares by multiplying the price for 1 share at the 52-week low by 100.

Let's use $52.28 as an example of the price per share at the 52-week low. The price for 100 shares would be as follows:

$52.28 x 100 = $5,228

Thus, $5228 is the correct response (A).

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Answer:

Step-by-step explanation:

the answer is c because all those numbers are even and less than 12 its not a because yes all the numbers are greater than two but that answer must include 3,4,5,6,7 and on and on is not d because some numbers are prime and it's not d because the only numbers less than three are 2,1 so that's why the answer is c