How do you find the first term?.

Answer: Domain and Range. The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Step-by-step explanation:

The three fundamental trigonometric ratios, namely sine, cosine, and tangent, each yield the ratio of the lengths of the two sides of a right-angled triangle.

We are aware that the sides of a right-angled triangle are called the "legs" and the "hypotenuse," respectively. Thus, the longest side of a right-angled triangle is still referred to as the "hypotenuse" in trigonometry, while the other two legs are referred to as the "opposite side" and "adjacent side."

The opposite, adjacent, and hypotenuse sides of a right-angled triangle are used to define the sin, cos, and tan functions in trigonometry. These are the sin, cos, and tan formulae.

sinФ = OppositeHypotenuse

cos Ф = AdjacentHypotenuse

tan Ф = OppositeAdjacent

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Based on the table of values, the slope and y-intercept include the following:

In Mathematics, the y-intercept is also known as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0). Therefore, the y-intercept is equal to -1/2.

From the information provided in the table above, the slope and data points on this line include the following:

In Mathematics and Geometry, the slope of any straight line can be calculated by using this expression;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have;

Slope (m) = (1 - 0)/(1 + 1)

Slope (m) = 1/2

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Answer:

Side length of square = -10b³ + 12

Step-by-step explanation:

Forming the equation,

→ P = 4 × side

→ P = 4a

→ [ a = P/4 ]

Now the side length of square is,

→ a = P/4

→ a = (-40b³ + 48)/4

→ a = (-40b³ ÷ 4) + (48 ÷ 4)

→ a = (-10b³) + (12)

→ [ a = -10b³ + 12 ]

Hence, side length is -10b³ + 12.

Answer:

-10b³ + 12

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

As a square has four sides of equal length, the perimeter of a square is four times the length of one side.

Therefore, to find the expression for the side length of a square, simply divide the expression for the perimeter by 4.

[tex]\begin{aligned}\textsf{Side length of a square}&=\dfrac{\textsf{perimeter}}{4}\\\\\implies \textsf{Side length of the square}&=\dfrac{-40b^3+48}{4}\\\\&=\dfrac{-40b^3}{4}+\dfrac{48}{4}\\\\&=-10b^3+12\end{aligned}[/tex]

The third stanza of Wilfred Owen's poem "Dulce et Decorum Est" is only two lines long, but it creates a gripping and powerful emotional impact.

Through the use of enjambment, the abrupt transition of the first line to the second creates an unsettling feeling, as if the speaker is struggling to express their thoughts and emotions. The imagery of the gas masks and the vivid depiction of the soldiers' "blood-shod" feet further amplify this emotion, providing a stark contrast to the ideals of glory and honor that the poem's title alludes to. This imagery also serves to evoke a feeling of despair and hopelessness, as the reader is confronted with the harsh realities of war. By using such a minimal amount of words, Owen is able to create an intense emotional effect that resonates with the reader and communicates a powerful message about the horrors of war.

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The domain and range are described for a relation, and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively. For example, if the relation is R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then: Domain = {1, 2, 3, 4} and Range  = {2, 3}.

The domain and range of a function are the elements of a function. The domain is the set of all the input elements of a function, and the range is the possible outcome given by the function.

Domain→ Function →Range. If there exists a function f: α → β such that every element of α are mapped to elements in β, then α is the domain, and β is the co-domain.

The image of an element 'p' under a relation R is given by 'q', where (p,q) ∈ R. The function's range is the set of images. The domain and range of a function are denoted in general as follows:

Domain(f) = {x ∈ R} and range(f) = {f(x): x ∈ domain(f)}.

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Answer:

y = −5x − 19

Step-by-step explanation:

Find the equation using slope-intercept form.

y = −5x − 19

Answer:

Circumference = 56.55

Area=254.47

A triangle def is called a "midsegment triangle" and it is formed by connecting the midpoints of the sides of a triangle ABC.

The midsegment triangle is always parallel to the original triangle and has half the area. The three sides of the midsegment triangle are called the "midsegments" of the original triangle, and they are always parallel to the corresponding sides of the original triangle and have half the length.

A triangle defined by connecting the midpoints of the sides of triangle ABC is called a "midsegment triangle" or "medial triangle." The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle and is parallel to the third side. The three sides of the medial triangle are the midsegments of the original triangle, and the three angles of the medial triangle are equal to one-half of the angles of the original triangle.

A triangle is a geometric shape that has three sides and three angles. It is a fundamental shape in Euclidean geometry and is one of the basic shapes in geometry. Triangles are classified based on their angles and sides, such as acute, right, and obtuse triangles. The sum of the angles in a triangle is always 180 degrees. Triangles can also be classified as equilateral, isosceles, or scalene based on the lengths of their sides. They are used in a variety of fields such as construction, engineering, and physics.

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A circumference is not, first of all, calculated in square units. Square measurements can only be made for areas.

figuring out the circle's area:

find the circle's radius first

A circle's circumference is determined by

C = 2πr

Given that a circle has a 14π cm circumference

by entering C's value in the formula above, we obtain

14π = 2πr

Divide both sides by 2π

r = 7

Therefore, value of radius ( r ) is 7 cm

The circle's area is defined as :

A = π r^(2)

A = π ( 7 )^2

A = π ( 49 )

Consequently, the circle's area is

49π cm^2

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No, All 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles.

No, not all right triangles are 30-60-90 triangles. A right triangle is a type of triangle that has one right angle (90 degrees) and two acute angles. The other two angles in a right triangle can have any measurement, they don't have to be 30-60-90 degrees.

A 30-60-90 triangle is a special type of right triangle that has specific angle measurements: one angle is 90 degrees (the right angle), one angle is 30 degrees, and one angle is 60 degrees. The ratio of the sides in a 30-60-90 triangle is also fixed, the longest side is opposite the 90-degree angle and it is always twice the length of the shortest side and the medium side is opposite the angle of 60 degrees and it's always the square root of 3 times the length of the shortest side.

For example, if a right triangle has angles of 45 degrees, 45 degrees, and 90 degrees, it is not a 30-60-90 triangle. The angles do not fit the pattern of 30-60-90 degrees.

Therefore, In short, all 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles. A 30-60-90 triangle is a special type of right triangle with specific angle measurements and side ratios.

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4x-2 is added to the given polynomial p(x) to leave the remainder=(-2).

[tex]p(x)=2x^3-7x^2+2x\\g(x)=2x-3\\dviding. p(x) by g(x),\\ we get2x-3)2x^3-7x^2+2x(x^2-2x2x^3-3x^2- +0 -4x^2+2x-4x^2+6x+ -0 -4xq(x)=x^2-2xand, r(x)=-4x\\Now,\\According to division algorithmp\\(x)=g(x)*q(x)+r(x)2x^3-7x^2+2x=(2x-3)(x^2-2x)+(-4x)\\adding 4x-2 on both side,\\ we get\\2x^3-7x^2+2x+4x-2=(2x-3)(x^2-2x)+(-4x)+4x-22x^3-7x^2+6x-2=(2x-3)(x^2-2x)+(-2)[/tex]

4x-2 is added to the given polynomial p(x) to leave the remainder=(-2).

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

what number must be added to[tex]2x^3-7x^2+2x[/tex] so that the resulting polynomial leaves the remainder -2 when divided by 2x-3​

The area over which the signal is transmitted are: a.[tex]\pi[/tex] b. [tex]25\pi[/tex] c. CB transmits 25 times more signal to walkie talkie.

When two quantities of the same units are compared, the ratio shows how much of one quantity is included in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, while part to part ratio is the other.

The area of the circle is given by the formula:

[tex]A = \pi r^2[/tex]

For the walkie-talkie the signal is received up until 1 mile. Substitute the value of r = 1.

[tex]A _1= \pi (1)^2\\\\A_1 =\pi[/tex]

For the CB radio the signal is received up until 5 miles. Substitute the value of r = 5.

[tex]A_2 = \pi (5)^2\\\\A_2= 25 \pi[/tex]

a. The area over which a walkie-talkie can transmit its signal is [tex]\pi[/tex] miles.

b. The area over which a CB radio signal can transmit its signal is [tex]25\pi[/tex] miles.

c. The ratio of the transmitted signals are:

[tex]\frac{CB}{WT} = \frac{25\pi}{\pi} \\\\CB = 25 (WT)[/tex]

Hence, the CB signal transmits 25 times more than the signal transmitted by the walkie-talkie.

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Answer:

200 students vote in the election

Step-by-step explanation:

We know

120 votes = 60%

1% = 2 votes

To find how many students vote in the election, we take

2 x 100 = 200 votes

So, 200 students vote in the election

Answer:

Mai needs 4/3 cups of strawberries in order to make the whole cake.

Step-by-step explanation:

1 cup of strawberries being equal to 3/4 of the cake is also the same as 1 cup of strawberries equaling 75% of the cake. So, what times 0.75 is equal to 1? That is 4/3.

In the context of mathematics, a series has a stagnant difference between terms. Therefore , we can find out the sum of the terms in arithmetic series by multiplying the number of times the average of the very last and first terms.

Thus we can observe that series and knowing the sum of the terms of series is a very crucial task in mathematics. In this head, we will talk about some very known series and series formulas with instances.

Actually, a series in math is very easy the sum of the different numbers or elements of the series. For instance, to make a series from the channel of the first five positive integers 1, 2, 3, 4, 5 we will simply sum   them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.

So, the series of a sequence is the sum of the sequence to some given number of terms, or occasionally til infinity. It is frequently written as S_n.

If the series is 2, 4, 6, 8, 10, … , then the sum of the first 3 terms:

S

3

=2+4+6

S3=12.

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Answer:

Step-by-step explanation:

In the context of mathematics, a series has a stagnant difference between terms. Therefore , we can find out the sum of the terms in arithmetic series by multiplying the number of times the average of the very last and first terms.

Thus we can observe that series and knowing the sum of the terms of series is a very crucial task in mathematics. In this head, we will talk about some very known series and series formulas with instances.

Actually, a series in math is very easy the sum of the different numbers or elements of the series. For instance, to make a series from the channel of the first five positive integers 1, 2, 3, 4, 5 we will simply sum   them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.

So, the series of a sequence is the sum of the sequence to some given number of terms, or occasionally til infinity. It is frequently written as S_n.

If the series is 2, 4, 6, 8, 10, … , then the sum of the first 3 terms:

S

3

=2+4+6

S3=12.

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n +2 represents that number is increasing by 2.

A horizontal line with evenly spaced numerical increments is called a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Given, n + 2

to put something with something else to increase the number or amount or to improve the whole: Beat the butter and sugar together and slowly add the eggs. She's added a Picasso to her collection.

that means the number is increasing by 2

Therefore, n +2 represents that number is increasing by 2.

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By taking the quotient between the distance and the time, we will see that the speed is 16 miles per hour.

Remember that the speed is defined as the quotient between the distance traveled and the time in which that distance is traveled.

Such that:

speed = (distance)/(time)

Here we know that the ship can travel 48 miles in 3 hours, so:

distance = 48 mi

time = 3 hours

Then the speed is:

S = 48mi/3h

S = 16 mi/h

So the speed of the ship is 16 miles per hour.

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The cost of the shoes is $19.

Here are the system of equations that represent the question:

x + y = 46 equation 1

y = x - 8 equation 2

The substitution method would be used to solve these equations

Substitute for y in equation 1

x + x - 8 = 46

Combine similar terms: x + x = 46 - 8

Add similar terms together: 2x = 38

Divide both sides of the equation by 2: x = 38/2

x = 19

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Answer:

Follow the equations from the person above me, but instead the cost of the shoes is 27.

Step-by-step explanation:

Answer:

The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). In this example, the value "5" is the Y Coordinate.

Answer:

  B(-π/3, 1/2), D(7π/6, -√3/2), E(11π/12, -1/2)

Step-by-step explanation:

You want the coordinates of various points marked on the graph of the sine and cosine functions.

The horizontal divisions on the graph are multiples of π/6. That is, there are 6 divisions between 0 and π. This means the x coordinates of interest are ...

  B = -π/3

  D = 7π/6

  E = 11π/6

Points B and D lie on the red curve, which the graph tells you is a plot of cos(x). Then the coordinates are ...

  B = (-π/3, cos(-π/3)) = (-π/3, 1/2)

  D = (7π/6, cos(7π/6) = (7π/6, -√3/2)

Point E lies on the blue curve, which is a plot of sin(x). Its coordinates are ...

  E = (11π/6, sin(11π/6)) = (11π/6, -1/2)

__

Additional comment

The attachment shows the coordinates of points on the unit circle as (cos(θ), sin(θ)). On the given graph, θ is on the horizontal axis (x), and sine and cosine are on the vertical axis. To make use of the attachment, you find the angle, then look for the (cos, sin) coordinates at that angle.

Negative angles are clockwise from θ=0. To find the corresponding angle on the attachment, add 2π to any negative angle.

An increase of 1 on the Richter scale means that the scale has increased by approximately 31 units in terms of Richter scale.

A 1.0 increment in the Richter magnitude scale results in a 31-unit difference in the intensity of an earthquake. The Richter scale (ML), a numerical measure of an earthquake's size, was devised by American seismologists Charles F. Richter and Beno Gutenberg in 1935.

The magnitude of an earthquake is determined by taking the height of the largest seismic wave and dividing it by the logarithm of its amplitude. The original Richter scale has been replaced in modern science by newer, more accurate scales, yet it is still routinely misrepresented in news reports of earthquake intensity as the logarithmic scale on which earthquakes are measured.

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The value of x when solving for the alternate angles is; x = 20 degrees

Alternate angles are defined as angles that occur on the opposite sides of the transversal line and thus have the same size. There are two different types of alternate angles namely alternate interior angles and alternate exterior angles 3x + 50 degrees and 6x - 10 degrees are alternate angles and as such;

3x + 50 = 6x - 10

Rearrange to collect like terms to get;

6x - 3x = 50 + 10

3x = 60

x = 60/3

x = 20 degrees

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We can see here that the different orders that she can wear the shorts is 25.

In mathematics, an order refers to the degree or highest exponent of a term in a polynomial equation. For example, the equation y = 3x^2 + 2x + 1 is a polynomial of order 2, because the highest exponent of x is 2.

In computer science, an order is a set of instructions for a computer to perform a specific task. For example, an order can be used to sort a list of numbers in ascending or descending order.

We see here that if the 5 pairs of basketball will go round on every day of the five days. Thus, it is: 5 x 5 = 25.

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An earthquake with a Richter scale value of 4.0 is 10 times more powerful than one with a value of 3.0.

On the Richter scale, every whole-number rise in magnitude corresponds to a 10-fold increase in observed amplitude.

In order to evaluate the size of different earthquakes, the Richter scale was initially developed to quantify the magnitude of earthquakes of moderate size (i.e., magnitude 3 to magnitude 7). The scale was created for earthquakes that occurred in southern California, were detected by the Wood-Anderson seismograph, and had epicenters that were less than 600 km (373 miles) away from the seismograph's position.

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The rectangular pool has a width of 80 feet and a length of 68 feet. The area is 640 square feet and the length is 12 feet shorter than the width.

1. 640 divided by 12 = 53.33

2. 53.33 + 12 = 65.33

3. Width = 65.33 feet

4. Length = Width - 12 = 65.33 - 12 = 53.33 feet

The area of the rectangular pool is 640 square feet. To find the width, we divide 640 by 12 because the length is 12 feet shorter than the width. 640 divided by 12 gives us 53.33. We add 12 to this number to get the width of the pool, which is 65.33 feet. To find the length, we subtract 12 from the width, which gives us 53.33 feet. Therefore, the width of the pool is 65.33 feet and the length is 53.33 feet. The area of the pool is 640 square feet and the length is 12 feet shorter than the width.

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Answer:

[tex]a_4 = 154[/tex]

Step-by-step explanation:

In this problem, we are asked to find the fourth term ([tex]\square_4[/tex]) of a sequence [tex]a[/tex] given that [tex]a_1 = 5[/tex] and [tex]a_n = na_{n-1} + 2[/tex].

To solve for this, we can first find the second term in the sequence by inputting [tex]a_2[/tex] into the sequence definition.

[tex]a_2 = 2a_{2-1} + 2[/tex]

Then, we can replace [tex]a_{2-1}[/tex] with the value that we were given: [tex]a_1 = 5[/tex].

[tex]a_2 = 2(5) + 2[/tex]

[tex]a_2 = 10 + 2[/tex]

[tex]a_2 = 12[/tex]

Next, we can solve for the third term in the sequence.

[tex]a_3 = 3a_{3-1} + 2[/tex]

And we can replace [tex]a_{3-1}[/tex] with the value that we just solved for: [tex]a_2 = 12[/tex].

[tex]a_3 = 3(12) + 2[/tex]

[tex]a_3 = 36 + 2[/tex]

[tex]a_3 = 38[/tex]

Finally, we can solve for fourth term in the sequence.

[tex]a_4 = 4a_{4-1} + 2[/tex]

We can again replace [tex]a_{4-1}[/tex] with the value that we just solved for: [tex]a_3 = 38[/tex].

[tex]a_4 = 4(38) + 2[/tex]

[tex]a_4 = 152 + 2[/tex]

[tex]a_4 = 154[/tex]

Answer:

  a₄ = 154

Step-by-step explanation:

You want the value of a₄ given the recursive sequence definition ...

  [tex]\begin{cases}a_1=5\\a_{n}=n\cdot a_{n-1}+2\end{cases}[/tex]

The easiest way to find the first few terms of a recursively-defined sequence is to use the recursive definition directly:

  [tex]a_2=2\cdot a_1 +2 = 2(5) +2 = 12\\\\a_3=3\cdot a_2+2=3(12)+2 =38\\\\a_4=4\cdot a_3+2=4(38)+2=154[/tex]

The value of a₄ is 154.

__

Additional comment

The terms of this sequence get rapidly larger. The 10th term is 23,357,002. The general term can be defined in terms of the Euler gamma function and the incomplete gamma function:

  [tex]a_n=\Gamma(n+1)+2e\Gamma(n+1,1)[/tex]

The length of the rectangle is 18 feet and width is 8 feet .

The perimeter of a rectangle is the sum of the lengths of all four sides of the rectangle. It is calculated by adding twice the length and twice the width. The formula to calculate the perimeter of a rectangle is

P = 2(L + W), where P is the perimeter, L is the length and W is the width of the rectangle. In simpler terms, it is the total distance around the rectangle.

The perimeter of rectangle is given by  2 ( l + b)

where l is length of rectangle and b is width of the rectangle

given that perimeter of rectangle is 52

so 2 (l+b)= 52

=>  l+b=26  ---(i)

given l = b +10

=> l -b = 10 ---(ii)

adding equation (i) and (ii) we get :

2l = 36

=> l =36/2

so length = 18 and breadth = 18 - 10 =8

so the length is 18 and breadth is 8.

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