What are the three forms of split?

Answer:

Step-by-step explanation:

hi yall funny

The Laplace transformation is:

                 [tex]L [f(t)] = \frac{5 - 8e^{-7s} }{2}[/tex]

Rewriting the f in terms of the unit step function:

[tex]\left \{ {{y=5} for 0\leq t\leq 7 \atop {x=-3}for t\geq 7} \right.[/tex]

⇒ f(t) = 5[u(t) - u (t-7)] - 3u(t -7 )

         = 5u(t) - 8u (t-7)

Unit Step Function:

The unit step function, also known as the Heaviside function, is known in engineering applications as a function that can describe the switching process mathematically. We often encounter functions whose values ​​change rapidly over a certain time unit t.

where,

u(t) = [tex]\left \{ {{y=1 for t\geq 0} \atop {x=0 for t < 0}} \right.[/tex]

Recall the time-shifting property of the Laplace transform:

    L{u(t - c) f( t - c)}

= [tex]e^{-es} L{f(t)}[/tex]

Laplace Transformation:

In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace, is an integral transform that transforms a function of real variables (usually t in the time domain) into a function is. Complex variable (complex frequency domain, also called s-domain or s-plane). As transformations are tools for solving differential equations, they have many applications in science and engineering. In particular, it converts ordinary differential equations to algebraic equations and converts convolutions to multiplications.

and the Laplace transform of a constant function,

L[k] = k/s

So we have

L[f(t)] = L[5u(t) - 8u (t-7)]

        =  [tex]5[L_{1} ] - 8e^{-7s} L[1][/tex]

Therefore,

[tex]L [f(t)] = \frac{5 - 8e^{-7s} }{2}[/tex]

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Based on the CPCTC, the statement that is not true is: A. ∠BCA ≅ ∠BCT.

CPCTC stands for "corresponding parts of congruent triangles are congruent". This simply means that if two triangles are congruent to each other, every of its corresponding angles and corresponding sides are equal or congruent to each other.

In the image given, we are told that ∆BAT ≅ ∆CAT. Thus, this implies that all the corresponding angles are congruent to each other, so also are all their corresponding sides.

Therefore:

Therefore, the statement that is not true is:

A. ∠BCA ≅ ∠BCT

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Answer: 10(4z+5)

Step-by-step explanation:

Find the Greatest common factor, which is 10

10(4z+5)

Answer:   -25x + 15

Step-by-step explanation:

Because you asked

Answer:

To simplify the expression, we can use the rules of order of operations, which dictate that we should perform operations in the following order:

Perform any calculations inside parentheses or other grouping symbols, working from the innermost set of parentheses to the outermost.

Perform any exponents or radicals.

Perform all multiplications and divisions, working from left to right.

Perform all additions and subtractions, working from left to right.

Applying these rules to the expression -5(-3 + 5x), we get:

Perform any calculations inside parentheses or other grouping symbols, working from the innermost set of parentheses to the outermost:

$-5(-3 + 5x)$

$-5(-3) + -5(5x)$

$15 + -5(5x)$

Perform any exponents or radicals:

$15 + -5(5x)$

Perform all multiplications and divisions, working from left to right:

$15 + -5(5x)$

$15 + -25x$

Perform all additions and subtractions, working from left to right:

$15 + -25x$

Therefore, the simplified expression is 15 + -25x.

Step-by-step explanation:

The temperature on a cold winter day in Minnesota was - 6ﾟ F. the temperature decreased by 4ﾟ from a high of 2ﾟ earlier in the day situations could explain how the temperature became - 6ﾟF.

A physical number known as temperature expresses the concepts of hotness and coolness in numerical form. With a thermometer, temperature is measured. Thermometers are calibrated using a number of temperature scales that have defined distinct reference points and thermometric substances. The most widely used scales are the Kelvin scale (K), which is mostly used for scientific reasons, the Fahrenheit scale (°F), and the Celsius scale (°C), formerly known as centigrade, with the unit symbol °C. In the International System of Units, one of the seven base units is the kelvin (SI).The temperature was -6ﾟ F. This means that the temperature must have decreased from a higher temperature to reach - 6ﾟF. This can be explained by option C, the temperature decreased by 4ﾟ from a high of 2ﾟ earlier in the day.

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Answer:It was not until the eighteenth century that mathematician Leonard Euler (1707-1783) discovered a relationship between the three classical triangle centers.

Step-by-step explanation:

The annual return of the investment is 31.1%.

Given that, person has purchased a single-family home that you intend to rent for $850 per month.

A return, also known as a financial return, in its simplest terms, is the money made or lost on an investment over some period of time.

First find the amount earned per year:

= 850 x 12

= $10,200

The yearly expenses would be:

= (390 x 12) + (60 x 12) + (340 x 2) + 500 + (100 x 12)

= 4,680 + 720 + 680 + 500 + 1,200

= $7,780

The annual ROI is:

= (10,200 - 7,780) / 10,200 x 100%

= 31.1%

Therefore, the annual return of the investment is 31.1%.

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"Your question is incomplete, probably the complete question/missing part is:"

Buying rental property is an investment option that carries a higher risk than some other options. However, the returns can be good. Assume you have purchased a single-

family home that you intend to rent for $850 per month. You will have the following expenses:

Monthly mortgage $390

Monthly insurance $60

Semiannual property taxes $340

Repairs (yearly estimate) $500

Monthly lawn care or snow removal $100

The return on investment for the property is

% (Round to one decimal place.)

Approximately 1700 Americans died of AIDS in 1983. In 2006, 14,260,633,600 individuals would have perished from AIDS if the trend had remained unchecked.

When a population's per capita growth rate remains constant, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.

When people in a population reproduce at a certain pace, exponential growth results. After a time of exponential expansion, a population's growth slows or pauses, which is known as logistic growth.

Exponential growth model Growth factor = 2

model y = a(2)^t

a = initial

y = final

Let 1983 as t=0

y = 1700 × (2)^t

In 2006

t = 2006 - 1983

= 23

y = 1700 × (2)^23

= 1700 × (8388608)

= 14,260,633,600 people would have died

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The percentage of income that a person or corporation must pay or withhold as taxes is known as the effective tax rate. The effective tax rate is 10.15%. Here option A is the correct answer.

The term effective tax rate refers to the average tax rate that an individual pays on both earned and unearned income, such as stock dividends. According to the progressive tax model, when income rises, the tax rate also rises, putting persons in a higher tax bracket.

Here, the presented data shows that the marginal tax rate is 22% for taxable income in the $40,526 to $86,375 income range.

Effective tax rate = total taxes owed/taxable income × 100.

Effective tax rate = $6,847.50/$67,400 × 100.

The tax rate in effect = 10.15%

Complete question:

Having a total tax liability of $6,847.50, a taxable income of $67,400, and a marginal tax rate of 22%. Determine the effective tax rate for a taxable income of $75,400. round the final answer to the nearest hundredth.

A. 10.15%

B. 18.27%

C. 42.00%

D. 64.90%

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The option which says Angle 2 and Angle 3 are Supplementary is the best statment that describes the Alternate Exterior Angle Theorem.

What is an Exterior Angle?

An Exterior Angle is the angle formed by a polygon's side and an extended neighbouring side; an angle generated by a transversal as it cuts one of two lines and located on the line's outside.

Solution:

Using the Alternate Exterior Angle Property we can say

Adjecent Angle of Angle 2 and Angle 3 are equal

Also, Angle 2 + Adjecent Angle of Angle 2 = 180

So, we can write Angle 2 + Angle 3 = 180

The option which says Angle 2 and Angle 3 are Supplementary is the best statment that describes the Alternate Exterior Angle Theorem.

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If the midpoint is M(1, 5). and One endpoint is P(–4, 9) the other point is solved to be

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

solving for Q (x₂, y₂)

1 = (x₂ + -4)/2

2 = x₂ + -4

x₂ = 6

5 = (y₂ + 9)/2

10 = y₂ + 9

y₂ = 19

point Q = (6, 19)

the other point is solved to be Q (6, 19)

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Answer: the answer is C

-4+x2/2 = 1, 9+y2/2 =5

Step-by-step explanation:

Yes, you can solve for the y-intercept using the slope, one ordered pair, and the slope-intercept equation.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Here Rin says that you can solve for the y-intercept using the slope, one ordered pair, and the slope-intercept equation.

The statement is right because for the calculation of the y-intercept we need one point to pass through the line and the slope of the line.

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To write an area, you need to know the shape and the measurements of the sides.

For example, if you have a square, you can calculate its area with the formula A = s², where A is the area and s is the length of a side.

If the side is 10 cm, then the area would be written as A = 10² = 100 cm².

1. Identify the shape of the area you are trying to calculate.

2. Calculate the measurements of the sides.

3. Use the appropriate formula to calculate the area. For example, for a square, use the formula A = s², where A is the area and s is the length of a side.

4. Plug in the measurements and calculate the area.

5. Write the area using the correct unit of measurement. For example, if the side was 10 cm, the area would be written as A = 10² = 100 cm².

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The slope of the points passes through the two points [tex](1,1)[/tex] and [tex](2,2)[/tex] is [tex]1[/tex].

When the equation of the line passes through the two points [tex](1,1)[/tex] and [tex](2,2)[/tex]

Then we can find the slope m is

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{2-1}{2-1} \\m=1[/tex]

The value of the slope is [tex]1[/tex].

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Answer:

x = 44°

Step-by-step explanation:

The sum of the three angles is 180°.

So, x + x + 5 + 2x -1 = 180

4x + 4 = 180

4x = 176

x = 44°

Answer:

The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

Step-by-step explanation:

umm....I really hope this helps u

Answer:

5

Step-by-step explanation:

(20/12)(3)=5

Yes. The matrix A-2I is invertible because 2 is an eigenvalue for matrix A.

When the matrix (transformation) is applied to some vectors (eigenvectors), the eigenvalues of the matrix are scalars. In other words, if A is a square matrix of order n x n and v is a non-zero column vector of order n x 1, and Av = v (the product of A and v is just a scalar multiple of v), then the scalar (real number) is called an eigenvalue of the matrix A that corresponds to the eigenvector v.

The eigenvalues can be determined by formula,

[tex]|A-\lambda I|=0[/tex]

Where, [tex]\lambda[/tex] = eigenvalues.A square matrix with an inverse is known as an invertible matrix. A square matrix is said to be invertible if and only if the determinant is not equal to zero. In other words, a 2 x 2 matrix is only invertible if its determinant is not zero.

Given,

A is a 4x4 matrix whose eigen values are λ=1,2,3,4

we need to determine that A-2I is invertible or not.

We know that 2 is an eigen value of matrix A, so, if we substitute 2 to find determinant of A-2I, then we will get zero as answer.

So, when determinant of A-2I is zero then the matrix is invertible.

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Answer: x<-9

Step-by-step explanation:

4x-45<[tex]x^{2}[/tex]

x^2+4x-45<0

factor

(x+9)(x-5)<0

x<-9,x<5

the negative solution is x<-9

The parallel line has an equation of y = 1/3x + 2

The equation is given as

3y-x=-12

Make y the subject in the equation

So, we have

y = x/3 - 4

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = 1/3

The slopes of parallel lines are equal

This means that the slope of the other line is 1/3

i.e. m = 1/3

Recall that:

The equation of a line can be represented as

y = mx + c

Where

slope = m = 1/3

Also, we have

(x, y) = (6, 4)

So, we have

4 = 1/3 * 6 + c

This gives

c = 4 - 2

Evaluate

c = 2

So, we have

y = 1/3x + 2

Hence, the equation of the parallel line is y = 1/3x + 2

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Answer:38.4615384615% (increase)

Step-by-step explanation:Percent change = 180 - 130 |130| × 100% = 50 130 × 100 = 38.4615384615% (increase). Where: 130 is the old value and 180 is the new value.

Answer:

y=14x−3 .

Step-by-step explanation:

We know that the equation of a line is y=mx+b with m being the slope and b being the y-intercept. We can plug in your slope ( 14 ) and your y-intercept ( −3 ). This simplifies to y=14x−3 .

The permutation combination is 120 for 3 different topping pizzas are available.

Permutation Combination:

A variety of ways to select objects from a set, usually forming a subset without replacement. The selection of this subset is called a permutation if the order of selection is a factor, and a combination if the order is not a factor. The French mathematicians Blaise Pascal and Pierre de Fermat, in the 17th century, used many chances in his game of combinatorics and probability by considering the ratio of the number of required subsets to the number of all possible subsets stimulated the development of the theory.

The concepts of permutations and combinations and their differences can be illustrated by examining all the different ways of selecting pairs of objects from five identifiable objects such as the letters A, B, C, D and E.

According to the Question:

Given that :

Number of different toppings = 10

Number of Pizzas = 03

therefore,

The permutation  combination are :

                = 10!/7! 3!

                = 15 × 8

                = 120.

Therefore, there are 120 different combinations of toppings.

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Original shape will contract when scale factor is less than 1 , expand when scale factor is greater than 1 and it doesn't change when scale factor is 1

A scale factor is a number that can be used to change the size of any geometrical figure or shape in relation to its original size. It is the ratio of the sizes of the original and dilated figures.

It is denoted by "k"

The magnitude of the scale factor is taken into account, and it cannot be zero. The scale factor has the ability to either increase or decrease the size of an object.

The basic formula for calculating the scale factor of a dilated figure is as follows:

Scale = dimension of preimage / dimension of image

According to the question,

(a) If scale factor is less than 1 , k < 1 then the original shape will contract means It's size will decrease

(b) If scale factor is greater than 1 , then image will enlarge and it would expand

(c) If scale factor is equal to 1 , then No change in shape nor in size

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The speed of 150 kilometres in five hours is 30 kilometres per hour.

The speed is calculated by the formula -

Speed = total distance covered ÷ total time taken

The distance covered is 150 kilometres and time taken is five hours.

Keep the values in formula to find the speed -

Speed = 150/5

Performing division on Right Hand Side of the equation to find the speed

Speed = 30 kilometres per hour

Hence, the speed of mentioned data covering the distance 150 kilometres in time duration of five hours is 30 kilometres per hour.

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The required volume of the right circular cone is 135.83409in³.

A right circular cone is one whose axis is the line between the vertex and the circular base's midway.

In other words, a right angle is formed when the center point of the circular base and the cone's peak are united.

So, the right circular cone volume formula:

V=1/3hπr²

Diameter = 8.8 in

Radius = 8.8/2 = 4.4 in
Now, calculate the volume as follows:

V = 1/3hπr²

V = 1/3(6.7)π(4.4)²

V = 135.83409 in³

Therefore, the required volume of the right circular cone is 135.83409in³.

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The dimension of a rectangle is 23m and 23m.

Here we have to find the area of a rectangle as large as possible.

Data given:

Perimeter = 92m

The formula for the perimeter of the rectangle:

perimeter = 2(length + breadth)

92 = 2( l + b)

l + b = 46

We have to find the largest area, so when we will take the length and breadth same then we get the largest area.

So length = breadth

2 length = 46

length = 23m

length = breadth = 23m

Therefore the dimensions are 23m and 23m.

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Answer:

7

Step-by-step explanation:

4x+7=4x+7

-4x-7=-4x-7

The value of the function h(f(x)) for x = 3 is h(f(3)) = 348.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is

  [tex]f(x)=x^3+8x\\\\g(x)=\sqrt{2x}\\\\h(x)=7x-9[/tex]

Now we have to find the value of the function h(f(x)),

            [tex]h(f(x))=7(f(x)) - 9\\\\h(f(x))=7(x^3+8x)-9\\\\h(f(x))=7x^3+56x-9\\\\$at x = 3, $\\\\h(f(3))=7(3)^3+56(3)-9\\\\h(f(3))=7*27+168-9\\\\h(f(3)) = 348[/tex]

Hence, the value of the function h(f(x)) for x = 3 is h(f(3)) = 348.

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