the length of the altitude to the hypotenuse of a right triangle with legs of length3 and4 is ? (fraction).

Steps are:

Step: 1

Given,

AE ≅ EB

∠DAE ≅ ∠CBE

Step: 2

congruent angles added to congruent angles form congruent angles

∠DAB ≅ ∠CBA

Step: 3

corresponding parts of congruent Triangles are congruent

DA ≅ CB

Step 4:

Vertical angles are congruent

∠DEA ≅ ∠CEB

Step 5:

Reflexive property

AE ≅ EB

Step 6:

In a triangles, angles opposite of congruent sides are congruent

∠EAB ≅ ∠EBA

Step 7:

SAS property

ΔDAB ≅ ΔCBA

Step 8:

ASA property

ΔDEA ≅ ΔCEB

Angles which are equivalent with one another are referred to as congruent angles. As a result, these angles have the same measure. In general, not all congruent angles are supplementary angles. Angles must be additional in order to add up to 180°. Due to the fact that they have the same measure and add up to 180, only right angles and supplementary angles are congruent.

Correct order is as follows:

Step: 1

Given,

AE ≅ EB

∠DAE ≅ ∠CBE

Step: 2

congruent angles added to congruent angles form congruent angles

∠DAB ≅ ∠CBA

Step: 3

corresponding parts of congruent Triangles are congruent

DA ≅ CB

Step 4:

Vertical angles are congruent

∠DEA ≅ ∠CEB

Step 5:

Reflexive property

AE ≅ EB

Step 6:

In a triangles, angles opposite of congruent sides are congruent

∠EAB ≅ ∠EBA

Step 7:

SAS property

ΔDAB ≅ ΔCBA

Step 8:

ASA property

ΔDEA ≅ ΔCEB

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Answer:

2 • 2 = 4 because you multiply numbers by adding groups of a number!

Answer:

Step-by-step explanation:

2x2=4

The two equations would be 1.5x + 2.5y = 30, 3x + 1.5y = 40, when we add both the equations we get, 4.5x + 4y = 70, and the value of x is 10.

To solve a system of linear equations in two variables using the substitution in two variables using the substitution method. First solve one of the equations for one variable. Substitute this in the other equation in terms of a single variable. Then solve it for the variable. Now, substitute it in any of the equations to get the value of another variable.

Given:

Add the two equations together:

1.5x + 2.5y = 30

3x + 1.5y = 40

(1.5x + 3x) + (2.5y + 1.5y) = (30 + 40)

4.5x + 4y = 70

Isolate the x-variable by subtracting 4y from both sides of the equation:

4.5x + 4y = 70

4.5x + 4y - 4y = 70 - 4y

4.5x = 70 - 4y

Divide both sides of the equation by 4.5 to solve for x:

4.5x = 70 - 4y

4.5x/ 4.5 = (70 - 4y)/4.5

x = (70 - 4y) / 4.5

Substitute the value of y from the first equation:

1.5x + 2.5y = 30

2.5y = 30 - 1.5x

y = (30 - 1.5x) / 2.5

Substitute the value of y into the equation for x and solve:

x = (70 - 4y) / 4.5

x = (70 - 4((30 - 1.5x) / 2.5)) / 4.5

x = 10

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The c/a ratio is divided by the density of the material and then multiplied by the square root of two thirds. This gives the atomic radius of the magnesium atom.

The atomic radius of an atom can be calculated by using the c/a ratio and the density of the material. The c/a ratio is the ratio between the lattice parameter c and lattice parameter a. The density is the amount of mass per unit volume of a substance. The formula for calculating the atomic radius of magnesium is

Atomic Radius= (c/a)√((2/3)*density)

Using the provided data for magnesium, the c/a ratio is 1.624 and the density is 1.74 g/cm^3. Plugging these values into the formula above gives an atomic radius of 1.6708 angstroms. To calculate the atomic radius, the c/a ratio of the crystal structure for magnesium is used, as well as the density of the material. The c/a ratio is divided by the density of the material and then multiplied by the square root of two thirds. This gives the atomic radius of the magnesium atom.

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The terms minimum and infimum are both related to the concept of lower bounds in mathematics. A minimum is the smallest value in a set of numbers, whereas an infimum is the greatest lower bound of a set.

A minimum is a value that is less than or equal to all other values in the set, while an infimum is a value that is less than or equal to all other values in the set, but not necessarily the smallest value.

For example, if we consider the set {2, 4, 6}, the minimum is 2 and the infimum is also 2. However, if we consider the set {2, 4, 6, 8}, the minimum is 2 and the infimum is 4. In the latter set, 4 is the greatest lower bound, meaning that all other values in the set are greater than or equal to 4.

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The distance from the rock was 11.26 meters.

The formula used to calculate the distance is:

d = h/tan(α)

Where d is the distance, h is the height of the rock, and α is the angle of the sun at 7 77 am.

Using this formula, the distance from the rock can be calculated as follows:

d = 5.55/tan(31∘)

d = 11.26 meters

Rounding the answer to the nearest hundredth, the distance from the rock is 11.26 meters.

Archimedes knew that the sunlight reaches the ground at an angle of 3 1 ∘ 31​∘​​ 31, degree at 7 77 AM. He also knew that the rock beside him was 5 55 meters tall. Using this information, he was able to calculate the distance he needed to go in order to be awakened by the direct sunlight. The formula used to calculate the distance is d = h/tan(α), where d is the distance, h is the height of the rock, and α is the angle of the sun. After plugging in the values, the distance from the rock was calculated to be 11.26 meters. Rounding the answer to the nearest hundredth, the distance from the rock was 11.26 meters.

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The value that a number produces when it is multiplied by itself is known as the square root of the number. The square root is denoted by the radical sign. For instance, 16 Equals 4. The root symbol or surds is another name for the radical symbol.

The result of multiplying a number by itself yields its square value, while the square root of a number can be found by looking for a number that, when squared, yields the original value. It follows that a a = b if "a" is the square root of "b."

The square root of 50 is 7.07106781187.

The square root of 147 is 12.124355653

The square root of 96 is 9.79795897113

The square root of -8 is 2.82842712475i

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Trade in the Vedic Age led to: A,  the rise of kingdoms because of the importance of controlling land and long-distance travel routes

The Vedic Age was a period between 1500 BC and 600 BC. This period was characterized by the next major civilization that occurred in ancient India following the decline of the Indus Valley Civilization by the year 1400 BC. The Vedas were very composed in this age.

Thus, we can say that in this vedic age;

- Indian civilization saw an unprecedented increase.

- Kingdoms were formed that gained riches and prominence.

These kingdoms mostly formed because increased trade in the area gave rise to the need to be controlled and profited from.

In conclusion, option A is correct.

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Answer:

Trade in the Vedic Age led to: A,  the rise of kingdoms because of the importance of controlling land and long-distance travel routes

Step-by-step explanation:

just did the quiz lol

The distance from the point for the line is (0; -1; 1).

A line is a set of points that lie on the same straight path, extending in opposite directions without end.

To find the distance from the point (1; 2; 3) to the line that contains the two points (1; 3; 2) and (5; 7; 4), we can use the vector formula.

First, we need to find the direction vector of the line by subtracting the first point from the second point:

=> (5; 7; 4) - (1; 3; 2) = (4; 4; 2).

Next, we need to find a vector that connects the point to the line, which is

=> (1; 2; 3) - (1; 3; 2) = (0; -1; 1).

Finally, the magnitude of this cross product is the distance from the point to the line.

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The cost of the fence used to make the rectangular sheep pen is £57.6. The result is obtained by multiplying the perimeter by the fencing price.

The cost for fencing a building can be calculated by multiplying the price of a certain size of fence by the perimeter or the length side to be fenced.

Bill builds a rectangular sheep pen.

Find the total cost of the fence!

The total cost of the fence will be

= P × fencing cost

= 24 m × £1.20 / ½ m

= 24 × £2.40

= £57.6

Hence, the fence to make the sheep pen will cost £57.6.

Your question is incomplete. But most probably your full question was

Bill needs to build a rectangular sheep pen. The pen must have a perimeter of 24 m. Every half meter of fencing costs him £1.20. Work out the cost of the fence used to make the sheep pen!

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y = x is the linear regression equation for the given Dot plot.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, a graph of a linear regression that has points (60, 60) and (70, 70) as we can see in the graph.

From the general formula of the linear equation:

Y = mx + b

where m is the slope

b is the y-intercept

Slope m = (y₂ -y₁)/(x₂ - x₁)

In our case,

Slope = (70 - 60)/70 - 60

m = 10/10 = 1

Thus the equation of a line:

y = x + b

Since, the line goes from (60, 60)

60 = 60 + b

b = 0

Thus, the final equation of the line will be y = x

Therefore, the linear regression equation for the given Dot plot is y = x.

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The area of the triangle is 62.93 cm²

Triangle is a 2-dimensional closed figure that is formed by 3 sides. The area of the triangle is the region that is bounded by the three sides of the triangle. The formula for the area of the triangle is given by

Here we have

a triangle upside down

The base of the triangle = 20.3 cm

Height of the triangle = 6.2 cm  

From the formula,

Area of the triangle = 1/2 base × height  

Area of the triangle = (1/2) × 20.3 × 6.2

= 20.3 × 3.1  

= 62.93 cm²  

Therefore,

The area of the triangle is 62.93 cm²

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As a result, the x-coordinate of the point on the curve closest to the origin is 2.

Coordinates are a pair of integers that are used to locate a point or object in a two-dimensional plane. A point's location on a 2D plane is defined by two integers called the x-coordinate and the y-coordinate. The distance of a point from the y-axis scaled with the x-axis is known as its abscissa or x coordinate. The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate.

Here,

The x-coordinate of the point on the curve that is closest to the origin can be found by minimizing the distance between the point on the curve and the origin. The distance between two points (x1, y1) and (x2, y2) is given by the Pythagorean theorem:

d = √((x2 - x1)^2 + (y2 - y1)^2)

For the origin and a point on the curve, we have x1 = y1 = 0, so the distance between the origin and a point (x, y) on the curve is:

d = √(x^2 + y^2)

Using the equation of the curve, we have y = 2 * √(9 - x), so the distance can be expressed as:

d = √(x^2 + (2 * √(9 - x))^2)

= √(x^2 + 4(9 - x))

= √(x^2 + 36 - 4x)

To find the x-coordinate of the point that minimizes d, we can use calculus. Setting the derivative of d with respect to x equal to zero and solving for x, we obtain:

d' / dx = 2x - 4 = 0

x = 2

So the x-coordinate of the point on the curve that is closest to the origin is 2.

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The area of the triangular region is 1800 square meters.

The area of a triangular region can be calculated by multiplying its base by its corresponding altitude and dividing by 2.

Given a triangular region with a base of 90 m and a corresponding altitude of 40 m, the area of the region can be calculated as follows:

Area = (Base * Height) / 2

Area = (90 * 40) / 2

Area = 3600 / 2

Area = 1800 square meters

Therefore, the area of the triangular region is 1800 square meters.

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The area of the triangular region is 1800 square meters.

The area of a triangular region can be calculated by multiplying its base by its corresponding altitude and dividing by 2.

Given a triangular region with a base of 90 m and a corresponding altitude of 40 m, the area of the region can be calculated as follows:

Area = (Base * Height) / 2

Area = (90 * 40) / 2

Area = 3600 / 2

Area = 1800 square meters

Therefore, the area of the triangular region is 1800 square meters.

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The coordinates of vertex D are (-3 + 1, 5 - 6) = (-2, -1).

What is parallelogram?

A parallelogram is a quadrilateral that has its opposite sides parallel and equal to each other. It has its interior opposite angles equal. Also, the angles on the same side of the transversal sum up to 180 degrees or are supplementary to each other.

To find the fourth vertex of a parallelogram given the coordinates of three vertices, we can use the property that opposite sides of a parallelogram are parallel and equal in length.

If we subtract the vector AB from the vector AC, we obtain the vector AD, which gives us the coordinates of the fourth vertex D.

AB = (1 - (-3), 2 - 5) = (4, -3)

AC = (2 - (-3), -4 - 5) = (5, -9)

AD = AC - AB = (5 - 4, -9 + 3) = (1, -6)

Therefore, the coordinates of vertex D are (-3 + 1, 5 - 6) = (-2, -1).

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After matching each set of values of a function to the pair of points that satisfy the function, we get

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

Given the set of data

(4,3) and (6.7) rate of change = 2, and initial value = -5

k= 7-3/6-4 = 2, y=2x-5

(2,10) and (5, 19) rate of change=3, and initial value = 4

k= 19-10/5-2 = 9/3 = 3, y=3x+4

(2,5) and (5.2)→ rate of change = -1, and initial value = 7.

k= 2-5/5-2 =  -3/3 = -1, y= -x+7

(2.4) and (4,3) →→ rate of change = -0.5, and initial value =5

k= 3-4/4-2 = -1/2 =-0.5, y=-0.5x+5

A function has two sets of values: the set of input values and the set of output values. The set of input values makes up the function's domain. The set of output values makes up the function's range.

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Drag the tiles to the correct boxes to complete the pairs. Match each set of values of a function to the pair of points that satisfy the function. rate of change = -1, and initial value = 7 rate of change = 2, and initial value = -5 rate of change = -0.5, and initial value = 5 rate of change = 3, and initial value = 4 (4, 3) and (6, 7) arrowRight (2, 10) and (5, 19) arrowRight (2, 5) and (5, 2) arrowRight (2, 4) and (4, 3) arrowRight

The given coordinates make a right angled triangle.

Scaling is defined as the process of changing the dimensions of the original figure as per some specific proportional rule.

If the initial length is equivalent to {a}. Then, after the scaling by the scale factor of {K}, the length becomes {Ka}. Similarly, if the initial coordinates are (x, y) then after scaling the coordinates would be {Kx, Ky}.

Scale factor is a dimensionless quantity that tells by how much time a specific dimension of a figure is enlarged or reduced. Mathematically, it is the ratio of two similar quantities. In case of length scaling, we can write -

{K} = L{final}/L{initial}

Given are the coordinates of the triangle as -

P(-1, 3)

Q(9, - 1)

R(-3, - 2)

The distance formula is given as -

d² = (x₂ - x₁)² + (y₂ - y₁)²

PQ = 2√29

QR = √145

RP = √29

QR² = RP² + PQ²

145 = 29 x 4 + 29

145 = 145

Therefore, the given coordinates make a right angled triangle.

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The horizontal asymptote of the curve y = 3 + x^4 / x^2 - x^4 is y = 1 and the vertical asymptotes are x = +√(x^4) and x = -√(x^4).

To find the horizontal and vertical asymptotes of the curve y = 3 + x^4 / x^2 - x^4, we need to examine the behavior of the function as x approaches positive and negative infinity.

For the horizontal asymptote, we look at the behavior of the function as x approaches positive and negative infinity. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the leading coefficients of the numerator and denominator. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptotic.

In this case, the degree of the numerator (x^4) is equal to the degree of the denominator (x^4), and the leading coefficients are both 1. Therefore, the horizontal asymptotic is the ratio of the leading coefficients, which is y = 1.

For the vertical asymptote, we look for any x-values that make the denominator equal to zero, since the function is undefined for these values. In this case, x = +√(x^4) and x = -√(x^4) are the roots of the denominator, so they are the vertical asymptotes.

Therefore, the horizontal asymptote of the curve y = 3 + x^4 / x^2 - x^4 is y = 1 and the vertical asymptotes are x = +√(x^4) and x = -√(x^4).

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The height of the model is 2350 cm or 23.5 m.

The concept used in this calculation is scale modeling. In scale modeling, the size of an object is reduced or increased proportionally to match a specified scale.

The height of the roller coaster is being reduced using a specific scale ratio of 1 centimeter to 4 meters. This allows Molly to build a model that represents the real-life roller coaster, but at a smaller size.

The height of the Millennium Force in meters is 94 meters. If Molly uses a scale of 1 centimeter to 4 meters, then 1 meter will be equal to 100/4 = 25 centimeters.

So, the height of the model will be 94 x 25 = 2350 centimeters.

Thus, the height of the model is 2350 cm or 23.5 m.

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The Millennium Force in Cedar Point, which is 94 meters tall. The height of the model will be 94 meters / 4 meters per centimeter = 23.5 centimeters.

Molly is building a model roller coaster that is based on the Millennium Force in Cedar Point, which is 94 meters tall. To create a model of the roller coaster, she is using a scale of 1 centimeter to 4 meters. This means that for every 1 centimeter on the model, it represents 4 meters in the actual height of the roller coaster.

To find the height of the model, we need to divide the actual height of the roller coaster by the ratio of meters per centimeter. That is:

Height of the model = 94 meters / (1 centimeter / 4 meters)

Height of the model = 94 meters * 4 meters / 1 centimeter

Height of the model = 376 meters / 1 centimeter

Height of the model = 376 centimeters

So, the height of the model is 376 centimeters.

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The number of plants in the first row is 8, which corresponds to option "b. 8 plants".

The concept used in this problem is arithmetic sequence or arithmetic progression. An arithmetic sequence is a sequence of numbers in which each term is the previous term plus a constant. In this problem, the constant is 3, and the number of plants in each row increases by 3. By using the formula for the sum of an arithmetic series, the total number of plants in all the rows can be calculated.

Let's assume that the first row has x number of plants.

The total number of plants in all rows is 70, so we can write an equation using x to represent the number of plants in each row:

x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 70

5x + 30 = 70

5x = 40

x = 8

So, the number of plants in the first row is 8, which corresponds to option "b. 8 plants".

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The number of plants in the first row is 8, which corresponds to the option "b. 8 plants".

The concept used in this problem is an arithmetic sequence or arithmetic progression. An arithmetic sequence is a sequence of numbers in which each term is the previous term plus a constant. In this problem, the constant is 3, and the number of plants in each row increases by 3. By using the formula for the sum of an arithmetic series, the total number of plants in all the rows can be calculated.

Let's assume that the first row has x number of plants.

The total number of plants in all rows is 70, so we can write an equation using x to represent the number of plants in each row:

x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 70

5x + 30 = 70

5x = 40

x = 8

So, the number of plants in the first row is 8, which corresponds to the option "b. 8 plants".

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The confidence interval narrows as the sample standard deviation gets smaller.

The width of a confidence interval depends on the sample size, the confidence level, and the sample standard deviation. The formula for a confidence interval is given as (sample mean - z-score * (sample standard deviation/square root of sample size)) to (sample mean + z-score * (sample standard deviation/square root of sample size)), where z-score depends on the confidence level.

Since the sample standard deviation is in the denominator of this formula, a smaller sample standard deviation results in a smaller value in the denominator and thus a narrower interval.

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The total number of respondents and x would be the total number of respondents who rate the product a 5.

A survey asking respondents to rate a product on a scale of 1 to 5

In this scenario, a binomial distribution should be used to model the response y. A binomial distribution is a discrete probability distribution that is used to model the probability of a certain number of successes in a given number of trials. The formula for a binomial distribution is P(x) = nCx * p^x * (1-p)^(n-x) where n is the number of trials, x is the number of successes, and p is the probability of success in a single trial. In this case, n would be the total number of respondents and x would be the total number of respondents who rate the product a 5.

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Answer: you got it right

Step-by-step explanation:

The reasoning of Percy is incorrect because there is one mode for the data set.

Mode of a data set is the value that occur most frequently in a data set.

There may be no mode, one mode or more than one mode for a data depending on the number of times values are repeating.

Given data is {5, 0, 4, 0, 0}.

Here the value 0 is repeating three times.

No other number has repeated three times.

So there is only one mode for the data set and is 0.

This does not mean that there is no mode for the set.

A data set has no mode if and only if all the numbers in the set are repeated same number of times.

Hence the reasoning of Percy is incorrect.

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Answer:

approximately 256 popcorn bags

Step-by-step explanation:

the cost of popcorn machine is $15. So we should add it to 100$

Then it is 115$. This is the amount that team A need

The cost of additional supplies for the popcorn is $0.05 per bag & team A will sell the bags of popcorn for $0.50 each. then the profit that the team A can gain by selling a bag is,

[tex]0.50 - 0.05 = 0.45[/tex]

Then,

[tex] \frac{115}{0.45} = 255.55[/tex]

Answer:

271.498934853

Step-by-step explanation:

Answer:

The answer is 0.039.

Step-by-step explanation:

The first term of the sequence is 156. Then the 46th term of the sequence is 156.

What are sequence and series?

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after. In mathematics, a series can be generally described as the sum of an infinite sequence of values.

Given

The first three terms of a sequence are shown.

156,153,150 and so on.

The given sequence is repeating every three terms, and the repeating terms are 156, 153, 150.

So, to find the 46th term, we need to determine which set of repeating terms it belongs to.

Dividing 46 by 3 gives us a quotient of 15 with a remainder of 1, meaning the 46th term belongs to the 16th set of repeating terms and will be the first term in that set, which is 156.

So, the 46th term of the sequence is 156.

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The first term of the sequence is 156. Then the 46th term of the sequence is 156.

What are sequence and series?

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after. In mathematics, a series can be generally described as the sum of an infinite sequence of values.

Given

The first three terms of a sequence are shown.

156,153,150 and so on.

The given sequence is repeating every three terms, and the repeating terms are 156, 153, 150.

So, to find the 46th term, we need to determine which set of repeating terms it belongs to.

Dividing 46 by 3 gives us a quotient of 15 with a remainder of 1, meaning the 46th term belongs to the 16th set of repeating terms and will be the first term in that set, which is 156.

So, the 46th term of the sequence is 156.

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Answer:

Step-by-step explanation: