Which two operations are needed to write the expression that represents "five less than the quotient of a number and
three"?

The Laplace transform of the given integral function is 1/s +4 / (s²+16) .

The integral transform, commonly known as the Laplace transform in mathematics, converts a function of either a real variable t in the time domain into a function of something like a complex variable s.

The Laplace transform is equal to the integral for the suitable functions

[tex]{\displaystyle {\mathcal {L}}\{f(t)\}(s)=\int _{0}^{\infty }f(t)e^{-st}\,dt.}[/tex]

Now we will use this to find the suitable Laplace transform of the trigonometric function:

(sin 2t-cos 2t)²

= sin² 2t + cos² 2t - 2sin 2tcos 2t

= 1 - sin 4t

Now we will use the Laplace transform of  the function.

L [1 - sin 4t] = L[1] - L[sin 4t]

Now L[1] = 1/s

L[sin 4t] = 4/ (s²+4²) = 4 / (s²+16)

Hence the Laplace transform will be

L [1 - sin 4t]  = 1/s +4 / (s²+16)

Pierre-Simon Laplace invented the complex frequency domain, often known as the s-domain or the s-plane. There are numerous uses for the transform, a method for solving differential equations, in both science and engineering.

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The factorization of the expression  [tex]x^3+3x^2+9x+27[/tex] is  [tex](x+3)(x^2+9)[/tex].

What is factorization?

  The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. A factorization is just the procedure by which an algebraic expression gets expanded in the opposite direction. The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. Factorization is the reverse process of expansion of an algebraic statement. If an algebraic expression is a product of prime factors, it has undergone complete factorization.

Here the given polynomial expression is ,

=> [tex]x^3+3x^2+9x+27[/tex]

=> [tex]x^2(x+3)+9(x+3)[/tex]

=> [tex](x+3)(x^2+9)[/tex]

Hence the complete factorization of the given expression is [tex](x+3)(x^2+9)[/tex].

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The interest she is pay total is $2340.822 when Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.

Given that,

For the purpose of buying new equipment for her business of antique restoration, Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.

We have to find will she pay interest at all.

We know that,

i=p×r×t

Here,

i is interest.

p is principal amount.

r is rate of interest

t is time.

So, p is $6380

r is 12.23%

t is 3 years

So,

i= 6380×0.1223×3

i= $2340.822

Therefore, the interest she is pay total is $2340.822 when Angela's bank granted her a 6380 loan with a 3 year add-on interest period. 12.23% is the interest rate per year.

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The missing values for gallons of gasoline remaining is 11,6,1.

Given that equation shown below can be used to find the gallons of gasoline remaining (g) after distance driven (d).

We want to find the missing values for gallons of gasoline remaining.

The given equation is g=16-(1/20)d

When the distance is 100 then we will find the gallons of gasoline remaining by substituting d=100 in given equation, we get

g=16-(1/20)100

g=16-5

g=11

When the distance is 200 then we will find the gallons of gasoline remaining by substituting d=200 in given equation, we get

g=16-(1/20)200

g=16-10

g=6

When the distance is 300 then we will find the gallons of gasoline remaining by substituting d=300 in given equation, we get

g=16-(1/20)300

g=16-15

g=1

Hence, the missing values for gallons of gasoline remaining when distance 100 is 11, when distance 200 is 6 and when distance 300 is 1.

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2/3 is the unit rate of the relationship

A unit rate is defined as the rate for one of something. For example, if 10 oranges cost $50, the unit rate will be $50/10 = $5 i.e.  $5 for one orange.

On a linear graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:

Slope = y2-y1 / x2-x1  

Thus, we can any two convenient points on the graph and use it calculate the slope as shown in the attached image:

Slope = y2-y1 / x2-x1

Slope = 6-2 / 9-3 = 4/6 = 2/3

Therefore, the unit rate for this relationship is 2/3. The 2nd option is the answer

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Answer:

Step-by-step explanation:

21%

The mapping of the function f of g(x) will result to 41

A function in mathematics is a rule that defines a relationship between one variable. This is a mapping whose codomain is the set of real numbers.

By mapping of the functions f and g defined as;

f : x » x + 5 and g : x » 8x

then;

f of g(x) = f of 8(4.5)

f of g(x) = f of 36

f of g(x) = 36 + 5

f of g(x) = 41

Hence, with proper mapping of the defined functions of f and g, the correct value for f of g(x) is 41.

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With a manufacturing cost of $80 per phone, the selling price of $292.5 would result in the largest annual profit.

Profit is the amount of gain realized from a transaction. The profit formula is useful for figuring out the profit from selling a specific product, typically in a business, or for figuring out the gain in any financial transaction. If the selling price is more than the cost price, a profit can be determined.

Given,

q = -6p+3030

p = 505 - q/6

R(q) = 505q - q²/6

C(q) = 80q

Now, the profit function,

P(q) = R(q) - C(q)

      = (505q - (q²/6)) - 80q

P(q) = 425q - q²/6

P(q) = 425 - q/3

q = 1275 units

Now, put it in the demand function,

p = 505 - q/6

  = 505 - 212.5

  = 292.5

Therefore, the selling price is $292.5.

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If the distance from P to R is 3 units, then the distance from Q to S is; 3 units

We are told that quadrilateral PQRS is a scaled copy of quadrilateral ABCD. Thus, this means that;

P → A

Q → B

R → C

S → D

We are also told that the length of PR = 3 units.

Now, from the given image, we see that;

AC = 6 and BD = 6

We also know that;

AC corresponds to PR

BD corresponds to QS

Due to the fact that AC and BD have the same side lengths, then it means that PR and QS will have the same side lengths.

Therefore, the value of QS is: QS = 3

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Complete question is;

Here is Quadrilateral ABCD.

Quadrilateral PQRS is a scaled copy of Quadrilateral ABCD Point P corresponds to A.

Q to B. R to C. and S to D.

1. If the distance from P to R is 3 units, what is the distance from Q to S?

Answer:

y = 1.2·x

x = 1;  y = 1.2·1 = 1.2

x = 2;  y = 1.2·2 = 2.4

x = 3;  y = 1.2·3 = 3.6

The equation that models the cost of the van rental is V = $183 + (m - 120)0.39. (first option)

The number of miles that Tim and Jessica can travel roundtrip on vacation is Ashville MC (second option)

The equation that represents the total cost of renting the camper van is a linear equation. A linear equation is an equation that has single variable that is raised to the power of one.

The general form of a linear equation is: y = mx + b

Where:

The form of the linear equation is:

total cost = cost of renting the van + [(total miles driven - 120) x cost per mile)

V = $183 + (m - 120) x 0.39

V = $183 + (m - 120)0.39

Total miles that can be driven if they have to spend $598.74

$598.74 = $183 + (m - 120)0.39

$598.74 = $183 + 0.39m - 46.80

$598.74 = $136.20 + 0.39m

$598.74 - $136.20 = 0.39m

$462.54 = 0.39m

m = $462.54 /0.39

m = 1186

Distance Tim and Jessica can travel from the rental company to the destination = 1186 / 2 = 593 miles

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Answer: The correct answer is x=−1/5  and y=−1/5

Step-by-step explanation:

Solve the System by substitution:

y=6x+1 and 7x−2y=−1

Solve y=6x+1 for y:

y=6x+1

Substitute 6x+1 for y in 7x−2y=−1:

7x−2y=−1

7x−2(6x+1)=−1

−5x−2=−1 (Simplify both sides)

−5x−2+2=−1+2 (Add 2 to both sides)

−5x=1

−5x/−5 = 1/−5  (Divide both sides by -5)

x=−1/5

Substitute −1/5 for x in y=6x+1:

y=6x+1

y=6(−1/5)+1

y=−1/5   (Simplify both sides)

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The range of the function is y ≤ 3.

The set of a function's potential output values is known as its range.

Given, the graph of the function.

The range of a function is the set of values of y the function can take.

The maximum y value of the function is 3, and the graph is going down both sides infinitely.

Therefore, the range of the function is y ≤ 3.

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Answer:5/9

Step-by-step explanation:

Answer:

huhh

Step-by-step explanation:

Hi im new can u guys tell me how this work pease??

Answer:

Step-by-step explanation:

idek idek

Answer:

(∞,-3) and (1,-∞)

Step-by-step explanation:

Decreasing means going down or in math terms, going toward the negatives.

When you are talking intervals in math, you only want to use the x-axis for the interval points. We write the interval as if it was a coordinate point though.

Looking at the graph it looks like it is going from infinity to -3 or written as (∞,3) and from 1 to negative infinity or written as (1, -∞)

The interval(s) for which the function shown below is decreasing are (∞,-3) and (1,-∞).

A function is a relationship between two sets of values in mathematics where each input value (or "argument") corresponds to a certain output value.

In most cases, the input values come from a set referred to as the function's domain, while the output values come from a set referred to as the function's range.

Declining is the mathematical phrase for decreasing or moving towards the negatives.

Mathematicians only use the x-axis to represent interval points when discussing intervals. Yet, we express the interval as if it were a coordinate point.

If you look at the graph, it appears to be traveling from infinity to -3, which is written as (,3), and from one to negative infinity, which is written as (1, -).

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Answer:

There isn't one. There is no solution.

Step-by-step explanation:

There are multiple ways to solve this system, but here's what I did:

Solve the both equations for s:

   s/2 + 5t = 3 + 5t  ⇒  s = 6

   3t - 6s = 9 + 3t  ⇒  s = -3/2

Since s cannot equal both 6 and -3/2 at the same time, there is no real solution to this system.

Answer:

y2−5y=750 

750 -y(y-5)=0750−y(y−5)=0  and (y+25)(y-30)=0

Answer:

Step-by-step explanation:

90

Answer:

value of x are 2 and 3 which make the inequality true

The resulting value of the the expression 6769 x 925 by first rounding each number so that it has only 1 nonzero digit is 63,000

Round off

Round off refers a number is made simpler by keeping its value intact but closer to the next number. And it is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

Given,

Here we need to estimate  6769 x 925 by first rounding each number so that it has only 1 nonzero digit.

Here we have to take individual terms to round off then we get,

By rounding 6799 so that it has only one non-zero digit is rounding it to nearest thousand.

6769 rounds to nearest thousand as 7000 as hundreds digit 7 > 5.

Similarly, by rounding 925 so that it has only one non-zero digit is rounding it to nearest hundred.

925 rounds to nearest hundred as 900 as tens digit 2 < 5.

Now, the estimated value after rounding each number so that it has only one non-zero digit is

=> 7000 x 900

=> 63000.

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Answer:

x=7

Step-by-step explanation:

these 2 triangle sides are equal to each other so just set them equal to find x

X+3=3x-11

-x.  -x

3=2x-11

+11. +11

14=2x

=2. =2

7=x

Hopes this helps please mark brainliest

Answer:

option c

y = -1

Step-by-step explanation:

2x - y = 3 -----------------(1)

x - 3y = 4 ------------------(2)

from equation (2)

x = 4 + 3y-------------------(3)

substituting the value of x in equation (1)

2(4+3y) - y = 3

8 + 6y - y = 3

5y = 3-8

5y = -5

y = -1

substituting the value of y in equation (3)

x = 4 - 3

x = 1

Answer:

Account A is incorrect the interest that you would earn is $8.60, not $860.00

Step-by-step explanation:

Answer:

1.3000

Step-by-step explanation:

To Round Numbers...

1 ) Decide which is the last digit to keep ( In this case it would be the hundredths )

2 ) Leave it the same if the next digit is less than 5 (this is called rounding down)

3 ) But increase it by 1 if the next digit is 5 or more (this is called rounding up)

Hope this helps! :)

The first five terms of the sequence defined by the given function are f(1) = 10 f(2) = 22  f(3) = 48.4 f(4) = 106.48 and f(5) = 234.256.

What is a sequence?

A collection of events or items that occur one after the other in a specific order is referred to as a sequence.

Here, we have

Given the function is f(n) = 2.2 [ f(n-1) ] Here, f(1) = 10 then we have to create the first five terms of the sequence defined by the function.

Since f(1) = 10

f(2) = 2.2 [ f (2-1) ] = 2.2× [ f (1) ]

    = 2.2 × 10 = 22

f (3) = 2.2 [ f (3-1)] = 2.2 × [ f (2) ]

       = 2.2 × 22 = 48.4

f(4)  = 2.2 [ f(4-1) ] = 2.2× [ f(3)]

       = 2.2 × 48.4 = 106.48

f(5)  = 2.2 [ f(5-1) ] = 2.2× [ f(4)]

        2.2× 106.48 = 234.256

Hence the first five terms of the sequence defined by the given function are f(1) = 10 f(2) = 22  f(3) = 48.4 f(4) = 106.48 and f(5) = 234.256.

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Answer:

Pedro can buy 4 pounds of pears and 3 pounds of apples.

Step-by-step explanation:

Pedro has a total of $18, Apples cost $2 a pound, and Pears cost $3 a pound.

$2×3lb + $3×4lb=$18

The equation of line q is  y = x/10 - 9/10.

What is equation of straight line?

   A line that does not curl or bend is said to be straight. A line has length but no width, making it a one-dimensional figure. A line consists of points that extend infinitely in opposite directions. Two points in a 2D plane determine it. A, B, and C are real-based constants in the formula Ax + By + C = 0, A, B 0. The geometric representation of the equation is always a straight line.

Here the given line P,

=> y+5=-10(x+2)

=> y+5=-10x-20

=> y = -10x-25

Here in the given line y=mx+c , where m=slope. Then,

=> Slope of line P = -10.

Here line P is perpendicular to line q.

Then, slope of line q = -1/ slope of line p = -1/-10 = 1/10

Now the line passes through the point [tex](x_1,y_1)=(-1,-1)[/tex] then,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y+1 = 1/10 (x+1)

=> 10y+10 = x+1

=> 10y=x-9

=> y = x/10 - 9/10.

Hence the equation of the line q is  y = x/10 - 9/10.

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The values from the parent function are a = 1, b = -6, h = 3, and k = -4.

What is the vertex form of quadratic equations?

The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

The given parent function is f(x) = (x - 3)² - 4.

comparing with the standard vertex form of the parabola, we get

                  a = 1, h = 3 and k = -4.

Now to find 'b', we have to simplify the given function in the form of f(x) = ax² + bx + c

                  f(x) = (x - 3)² - 4

                  f(x) = (x² - 6x + 9) - 4

                  f(x) = x² - 6x + 5

Comparing with f(x) = ax² + bx + c we get, c = -6.

Hence, The values from the parent function are a = 1, b = -6, h = 3, and k = -4.

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