How do you find the 6th angle of a hexagon?

The utilization of machinery, originally propelled by water or steam and later by electricity, is the primary feature of the factory system.

The cube root of a number x equals a number y, hence in mathematics, y3 = x. Each non-zero real number has exactly one real cube root, three separate complex cube roots, and one set of conjugate complex cube roots. The cube root of a number is produced when it is multiplied three times. The last cube root is denoted by the symbol, which is three cube roots. Finding an integer's cube root is the opposite of cubing it. The cube root of a number can be found using the relatively simple method of prime factorization. A cube root is represented by the symbol.

given

The utilization of machinery, originally propelled by water or steam and later by electricity, is the primary feature of the factory system.

The employment of machinery or economies of scale, the centralization of industries, and the standardization of interchangeable parts are the main sources of the system's additional characteristics.

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The value of the 9 in 964,352 is 90 times greater than the value of the 9 in 290,481 .

The value of the 9 in 964,352 can be written as 900,000

The value of the 9 in 290,481 is 90, 000

Then to know the the number of times that  value of the 9 in 964,352is greater than the value of the 9 in 290,481 , then we can express it as

900,000/90, 000= 90

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A tangent line is a line that intersects a curve at a single point, with the same slope as the curve at that point. A secant line is a straight line that intersects a curve at two or more points.

A line that touches a curve only at one point is called a tangent line, while a line that passes through two points on a curve is called a secant line. A secant line has a slope that is the average of the slopes of the two points it passes through, whereas a tangent line has a slope that is the same as the slope of the curve at the point of tangency.

A secant line can be used to approximate the rate of change of a curve over a range of values, whereas a tangent line can be used to determine the instantaneous rate of change of a curve at a given point. The maximum and minimum values of a curve can be determined using tangent lines, as well as the inflection points where the curve becomes more concave.

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Based on the relative proportion of your position to the first person and last person in line, the total length of the line is 204 feet.

The proportion refers to the ratio or quotient obtained by applying the division operation.

The ratio is the relative size or value of a number to another.

Like ratios, proportions are expressed in decimals, fractions, or percentages.

To obtain the needed value, the proportional size of the distance is equated to the distance of the first person in line.

Distance from the first person in line = 102 feet

102 feet = 0.5 (1/2 or 50%) of the total length of the line

The total length of the line = 204 (102 ÷ 0.5)

Thus, we can conclude that proportionately, the total length of the line is 204 feet.

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Benito and Tamika 2.5 miles apart.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

Given:

Benito walks 1.5 north in a straight path. (Perpendicular)

Tamika walks 2.0 miles east in a straight path (Base)

Using Pythagoras theorem

H² = P² + B²

H² = (1.5)² + 2²

H² = 2.25 + 4

H² = 6.25

H = √6.25

H = 2.5 miles

Hence, both are 2.5 miles apart.

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Triangle properties include triangle inequality, angle sum, congruence, exterior angle theorem, and isosceles triangle theorem.

1. Triangle Inequality: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. Angle Sum of a Triangle: The sum of the angles of a triangle is always equal to 180°.

3. Congruence of Triangles: If two triangles have all three sides equal, then they are congruent (the same size and shape).

4. Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

5. Isosceles Triangle Theorem: If two sides of a triangle are equal in length, then the angles opposite those sides are also equal in measure.

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The five properties of triangle is listed below.

The term triangle is defined as the polygon with three angle, sides and vertices.

Here we have to list down the properties of triangle.

The basic five properties of triangle are as follows:

1) in geometry, total amount of space inside the triangle is called the area of a triangle. And it is measured by square units.

2) The property of perimeter of a triangle is equal to the sum of all three sides of the triangle.

3) And the another property states that sum of the length of the two sides of a triangle is greater than the length of the third side.

4) according to the angle, the property states that sum of the angles of a triangle is always 180 degrees.

5) If angles of an equilateral triangle are equal and has a measure of 60⁰ each.

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The solution is Option C.

The L'Hopital's rule is applied to the equation lim x approaches 0 (1-cosx)/x

L'Hopital's rule then states that the slope of the curve when t = c is the limit of the slope of the tangent to the curve as the curve approaches the origin, provided that this is defined. The limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.The tangent to the curve at the point [g(t), f(t)] is given by [g′(t), f′(t)]

And , lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

The equation is A = lim x approaches 0 (1/x)

On simplifying the equation , we get

The limit diverges as the function diverges and limit does not exist

And ,  lim x approaches 0₊ (1/x) ≠ lim x approaches 0₋ (1/x) = ∞

b)

The equation is A = lim x approaches 0 ( 2x² - 1 ) / ( 3x - 1 )

On simplifying the equation , we get

when x = 0 ,

Substitute the value of x = 0 in the limit , we get

A = ( 2 ( 0 )² - 1 ) / ( 3 ( 0 ) - 1 )

A = ( 0 - 1 ) / ( 0 - 1 )

A = 1

c)

The equation is A = lim x approaches 0 ( 1 - cosx ) / x

On simplifying the equation , we get

Applying L'Hopital's rule , we get

lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

f ( x ) = ( 1 - cos x )

g ( x ) = x

f' ( x ) = sin x

g' ( x ) = 1

So ,

lim x approches 0 [ f' ( x ) / g' ( x ) ] = lim x approches 0 ( sin x / 1 )

when x = 0

sin ( 0 ) = 0

Therefore , the value of lim x approaches 0 (1-cosx)/x = 0

d)

The equation is A = lim x approaches 0 ( cos 2x ) / 2

On simplifying the equation , we get

when x = 0 ,

A = cos ( 2 ( 0 ) / 2

A = cos ( 0 ) / 2

A = 1/2

Hence , the L'Hopital's rule is applied to lim x approaches 0 ( 1 - cosx ) / x

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Answer:

Step-by-step explanation:

Let the length of the smaller piece be l inches. Then the larger piece is 3*l = 3l inches. But l + 3l = 72. Hence, 4l =72. l= 72/4 = 18. Therefore, the smaller piece has a length of 18 inches.

Based on the information provided, to prepare a total of 220 pancakes Kai needs 30 cups of pancake mix.

To prepare 22 pancakes Kai needs a total of 3 cups of pancake mix, which means the ratio is 22 to 3 or 22:3.

To find the total of pancake mix Kai need for this new number of pancakes different methods can be applied:

First method: Rule of three

3 cups of pancake mix = 22 pancakes

            x                        = 220 pancakes

x (number of cups) = 220 pancakes / 22 panckes x 3

x = 10 x 3

x= 30

This means Kai needs 30 cups

Second method: Find the number of cups for 1 pancake

3 cups  / 22 pancakes=  0.13636

220 x 0.13 = 29.9 which can be rounded as 30 cups

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Answer:

Lets get started :)

(3x - 8)²

(3x - 8)(3x - 8)

(3x)² - 8(3x) - 3x(8) + (8)²

9x² - 24x - 24x + 64

9x² - 48x + 64

Your answer will be the second last option

Step-by-step explanation:

The value of a is zero. The value of a can be determine by analysis the expression given.

As per given comparison is 0 ≤ a ≤ 14 and 235935623₇₄-a. We can se the equation is not in the same base number where one is the decimal and another is base 74. So, the first things we have to do is to convert one of them to another base number. Here, I convert base 74 to base 10 or decimal. Hence, the comparison will be will be

0 ≤ a ≤ 14.  1.835.684.416.755.975- a

After that, Use the fact that 74 mod 15 = -1. The result of the mod will be 2-3+5-9+3-5+6-2+3 = 0  or in other words a = 0

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The graph of the equation pass from the points (-2, 3) and (2, 6).

The ratio of the change in y coordinate to the change in the x coordinate is known as a line's slope.

Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate.

Consequently, the connection between a change in y-coordinate and a change in x-coordinate.

Given equation y - 3 = 3/4(x + 2)

the equation of the line for slope is given by

y - k = m(x - h)

from the given equation  m = 3/4

h = -2 and k = 3

coordinates are (-2, 3)

Another point on the line will be 3 units up and 4 units to the right of that,

Slope = (change in y)/(change in x) = 3/4.

coordinates are (-2 + 4, 3 + 3) = (2, 6)

the line should pass from (-2, 3) and (2, 6).

Hence the graph is attached for a given equation.

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The correct equation is y - 3 = 3/4(x + 2)

The equation of the line that is perpendicular to the line y=-3x + 2 and passes through the point (6, 8) will be y = (1/3)x + 6. Then the correct option is D.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given below.

y = -3x + 2

The equation of the line that is perpendicular to y = -3x + 2 will be given as,

y = (1/3)x + c

The equation of the line passes through the point (6, 8). Then we have

8 = (1/3)(6) + c

8 = 2 + c

c = 6

The equation of the line that is perpendicular to the line y=-3x + 2 and passes through the point (6, 8) will be y = (1/3)x + 6. Then the correct option is D.

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Answer:

s= -3

Step-by-step explanation:

Given 18=-6s

We need to figure out what the variable "s" is

18=-6s  Divide both sides by -6

18/-6=-3 Simplify

Answer: s=-3

Hope this helps :)

Answer:

s=-3

Step-by-step explanation:

Im not completely sure what the quotation marks mean but ill try my best :)

18=-6s

18/-6=-3

-3=s

The equation of the perpendicular line is y = 1/2(x + 4) - 5

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

y = 1/2x + 1

Also, from the question;

We have the following points

Point = (-4, -5) i.e.  (x, y) = (-4, -5)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 1/2

This means that the slope is 1/2

The slopes of parallel lines are equal

This means that the slope of the other line is 1/2

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

m = 1/2

(x₁, y₁) = (-4, -5)

So, we have

y = 1/2(x + 4) - 5

Hence, the line has an equation of y = 1/2(x + 4) - 5

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The relation given by the set of ordered pairs {(5,2),(4,2),(3,2),(2,2),(1,2)} is not a function. This is because there are multiple y-values (2) for the same x-value (5, 4, 3, 2, 1).

A function is a relation where each input (x-value) has one and only one output (y-value).

To further illustrate this, let's look at a more concrete example. Consider the following set of ordered pairs:

{(1,2), (2,4), (3,6), (4,8), (5,2)}

Here, we can see that the x-value 5 is paired with the y-value 2, but the x-value 1 is paired with the y-value 2 as well. This means that there is more than one y-value associated with a single x-value, which means this relation is not a function.

To better understand why this relation is not a function, let's look at the mathematical definition of a function. A function is defined as a relation between two sets of values (x and y) such that each x-value has one and only one y-value associated with it. Mathematically, this can be expressed as:

f: X → Y,

where X is the set of all x-values and Y is the set of all y-values.

In our example, the relation between the x-values and y-values does not satisfy this definition, as there is more than one y-value associated with a single x-value. Therefore, this relation is not a function.

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Yes, the line shown on the scatter plot is a good line of fit because the line follows the pattern.

What is a line of best fit?

The straight line that best depicts the overall picture of what the collected data is showing is known as the line of best fit, also known as a trendline or a linear regression. It aids in determining whether the two things under study are related or have a correlation. This trendline aids in our ability to forecast upcoming developments involving the data under study.

The line models a positive association is incorrect, because the plot has a negative slope which means that it has a negative association.

The data does not have a linear association is wrong because it can seen that the plot does show that most of the points are clustered around a path that would be a line through the points.

It is not necessary for a line of best fit to go through any of the original points so line does not pass through any of the data points is also incorrect.

Therefore, the line is a good fit as it follows the pattern.

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Answer:

Hope this help :)

Step-by-step explanation:

The two functions are inverse of one another using the composition function.

It is suggested that we replace one function with another using the composition operator. The result will be reversed if two functions are inverses of one another.

According to the composition function if f(g(x)) = g(f(x)) = x; then f(x) and g(x) are inverse of one another.

The composition of f(g(x)) is given as follows:

Substitute  [tex]x= g(x) = \frac{x-2}{5}[/tex] in f(x):

[tex]f(g(x)) = 5 (\frac{x-2}{5}) + 2[/tex]

[tex]f(g(x)) = x -2 +2[/tex]

[tex]f(g(x)) = x[/tex]

The composition of g(f(x)) is given as follows:

Substitute x= f(x) = 5x + 2 in g(x):

[tex]g(f(x)) = \frac{5x+2 -2}{5}[/tex]

[tex]g(f(x)) = \frac{5x}{5}[/tex]

[tex]g(f(x)) = x[/tex]

Hence, f(g(x)) = g(f(x)) = x and according to composition function the two functions are inverse of one another.

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The graph of the two linear inequalities is given below with its own color region.

The possible combinations of pounds of salads that Lu can make are:

4 pounds of macaroni salad.

2 pounds of potato salad.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

Macaroni salad costs $4 per pound and potato salad costs $2 per pound.

Let x = pounds of macaroni salad

Let y = pounds of potato salad

Now,

The system of linear inequalities is:

x + y ≤ 6 ____(1)

4x + 2y ≤ 20 ______(2)

Now,

x + y = 6

x = 6 - y

Substituting in 4x + 2y = 20.

4(6 - y) + 2y = 20

24 - 4y + 2y = 20

24 - 2y = 20

24 - 20 = 2y

4 = 2y

y = 2

And,

x = 6 - y

x = 6 - 2

x = 4

The graph of the linear inequalities is given below.

The blue region is equation (1).

The red region is equation (2).

Thus,

The graph of the linear inequalities is given below.

The possible combinations of pounds of salads are:

4 pounds of macaroni salad.

2 pounds of potato salad.

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The equation of the line in slope intercept form that is perpendicular to y=-5x+3 and passes through (2-0) is  y = 1 / 5x - 2  / 5.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Hence, the line is perpendicular to y = -5x + 3  and passes through (2, 0).

Therefore, perpendicular lines have slopes that are negative reciprocals of one another.

Hence, the slope of the line is 1 / 5.

Let's find the y-intercept using (2, 0).

y = 1  /5 x + b

0 = 1  /5(2) + b

b = - 2  /5

Therefore, the equation of the line is y = 1 / 5x - 2  / 5

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Note that where the archaeologist rode east on a donkey from the Great Gate, at (-11,4), to the Royal Road. Then he rode south to the palace, which means that the Archeologist Rode for 15 km. Note that

Note that from the original graph given, the palace is situated at (0,0). Thus, If the archaeologist rode from (-11, 4) to the east to the royal road which is situated on the y-axis, it means that the distance stretches for 11 units or kilometers).

From that point (0, 4) to the palace (0,0) is another 4 units (or kilometers). Thus, the total distance ridden is:

11 + 4

= 15 Kilometers.

It is thus correct to state that the archaeologist rode for 15 Kilometers to the Palace.

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Full Question:

An archaeologist is digging at an ancient city. The map shows the locations of several important finds. Each unit represents 1 kilometer. Use the map to answer the question below:

The archaeologist rode east on a donkey from the Great Gate, at (-11,4), to the Royal Road. Then he rode south to the palace. How far did the archaeologist ride?

The change in height to keep the volume constant is 19.11 cm/s.

The volume of a right circular cylinder is equal to the product of the area of its base and its height.

V = πr2h

Given,

Diameter = 10 cm

Height = 20 cm

Change in diameter = 3 cm/s

We need to find change in height to keep the volume constant.

V = πr2h

V = π(10/2)2h

V = π(25)h

Let the change in height be h cm/s.

Therefore,

π(25)h + 3h = π(25)(20)

⇒ h = 60/π  ≈ 19.11 cm/s

Hence, the change in height to keep the volume constant is 19.11 cm/s.

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The correct option to make the triangle prism by net will be;

⇒ First option.

A triangular prism is also known as a pentahedron which comprises of two triangle bases and three rectangular sides.

Since, The net of the triangular prism is formed as a result of unfolding that occurs along the edges and faces as they are laid out in a pattern of two dimensions.

Hence, From the given question ;

We would see that the first option matches and correlates with triangular prism in question.

Thus, The ''first option'' from the diagram given represents the triangular prism in the question.

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The figure of the question is shown in image.

The size of XYZ in the triangle based on the application of trigonometry ratio is 66.4°.

Based on the information given, it should be noted that we can apply trigonometry to solve the triangle.

In this case, the hypothenuse is 15cm and the adjacent is 6cm. The trigonometry ratio will be:

cos = adjacent / hypothenuse.

cos x = 6 / 15

cos x = 0.4

x will be the inverse cos to find the value. This will be 66.4°.

Therefore, the angle is 66.4°.

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The probability that a randomly chosen test taker had a score greater than 1,127 is 0.1587.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below

z-score = (x – μ) / σ

where x = individual data value = 1,127

μ = mean = 896

σ = standard deviation = 231

z-score = (1,127 - 896) / 231

z-score = (231) / 231

z-score = 1

Find the probability that corresponds to the z-score in the z-table. (see attached images)

at z = 1,     p = 0.8413

Since the probability we have calculated is for the scores less than and including 1,127, subtract the calculated probability from 1.

probability = 1 - 0.8413 = 0.1587

Hence, the probability that a randomly chosen test taker had a score greater than 1,127 is 0.1587.

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An angle is a shape formed by two lines or rays, which start at the same point and extend in different directions.

Angles are measured in degrees, with a full circle being 360°. Depending on their size, angles can be classified as acute (less than 90°), right (90°), obtuse (more than 90° but less than 180°) and reflex (more than 180°).

Angles are important to mathematics because they can be used to measure distances and calculations between objects. They can also be used to calculate the area of a triangle, a quadrilateral or any other closed form. Angles are also an important part of trigonometry and can be used to help solve problems involving triangles.

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Answer:

Step-by-step explanation:

Sorry, but Ummm the question doesn't make sense

Answer:

A line segment joining any two points on the circle is called a chord.

Step-by-step explanation:

A chord is a line segment with both endpoints on the same circle.

Answer:

The meaning of segment joining is ⇔ A line segment joining any two points on the circle is called a chord.

Line segment joining midpoints of opposite sides of quadrilateral.

Step-by-step explanation:

I hope this helps and have a wonderful day!

Answer:

Step-by-step explanation:

= 8^3+7+8+(9*2/3)*2= 8^3+7+8+(18/3)*2= 8^3+7+8+(6)*2= 8^3+7+8+6*2= 512+7+8+6*2= 512+7+8+12= 519+8+12= 527+12= 539

Answer:

The difference in temperature is 16 degrees. To find the difference, you subtract the initial temperature from the final temperature: 5 - (-11) = 16.

Step-by-step explanation:

Answer:

The difference in temperature is 16 degrees. You can find the difference by subtracting the initial temperature from the final temperature: 5 degrees - (-11 degrees) = 5 + 11 = 16 degrees