Which inequality is correct?
0.22<0.18
0.22>0.22
0.41<0.08
0.41>0.02

This is made easy if you know the Laplace transform pair

[tex]u(t - c) y(t - c) \mapsto e^{-cs} Y(s)[/tex]

where u(t) is the Heaviside step function and Y(s) is the Laplace transform of y(t).

We rewrite f, g, and h in terms of u :

[tex]f(x) = (x^2+2x+1) (u(x) - u(x-3)) + e^{-5x} u(x-3)[/tex]

[tex]g(x) = \sin(3x) (u(x-5) - u(x-10))[/tex]

[tex]h(x) = (u(x) - u(x-4)) + 2(u(x-4)-u(x-8)) + 3 (u(x-8)-u(x-16))[/tex]

and we also rearrange terms to get the right shift in argument:

[tex]f(x) = (x^2+2x+1) u(x) - ((x-3)^2+8(x-3)+16) u(x-3) + e^{-15} e^{-5(x-3)} u(x-3)[/tex]

[tex]g(x) = [\cos(15) \sin(3(x-5)) + \sin(15) \cos(3(x-5))] u(x-5) \\\\ ~~~~~~~~~~- [\cos(30) \sin(3(x-10)) + \sin(30) \cos(3(x-10))] u(x - 10)[/tex]

[tex]h(x) = u(x) + u(x-4) + u(x-8) - 3 u(x - 16)[/tex]

Now we can apply the known transform pair, along with

[tex]x^n \mapsto \dfrac{n!}{s^{n+1}}[/tex]

[tex]e^{ax} \mapsto \dfrac1{s-a}[/tex]

[tex]\sin(ax) \mapsto \dfrac{a}{s^2+a^2}[/tex]

[tex]\cos(ax) \mapsto \dfrac{s}{s^2+a^2}[/tex]

The transforms of f, g, and h are then

[tex]F(s) = e^{-s} \left(\dfrac2{s^3} + \dfrac2{s^2} + \dfrac1s\right) - e^{-3s} \left(\dfrac2{s^3} + \dfrac8{s^2} + \dfrac{16}s\right) + \dfrac{e^{-15} e^{-3s}}{s + 5} \\\\ = \boxed{e^{-s} \left(\dfrac2{s^3} + \dfrac2{s^2} + \dfrac1s\right) - e^{-3s} \left(\dfrac2{s^3} + \dfrac8{s^2} + \dfrac{16}s\right) + \dfrac{e^{-3(s+5)}}{s + 5}}[/tex]

[tex]G(s) = \dfrac{3\cos(15) e^{-5s}}{s^2+9} + \dfrac{s \sin(15) e^{-5s}}{s^2+9} - \dfrac{3\cos(30)e^{-10s}}{s^2+9} - \dfrac{s \sin(30) e^{-10s}}{s^2+9} \\\\ ~~~~~~~ = \dfrac{3(\cos(15)-\cos(30)) + s(\sin(15) - \sin(30))}{s^2+9} \\\\ ~~~~~~~ = \boxed{\dfrac{6\sin\left(\frac{45}2\right)\sin\left(\frac{15}2\right) - 2s \cos\left(\frac{45}2\right)\sin\left(\frac{15}2\right)}{s^2+9}}[/tex]

[tex]H(s) = \boxed{\dfrac{e^{-s} + e^{-4s} + e^{-8s} - 3 e^{-16s}}s}[/tex]

Answer:

[tex]\huge\boxed{\bf\: 83 \: yd^{2}}[/tex]

Step-by-step explanation:

Consider rectangle ABCD.

Here,

AB = DC = 9 yd (length = l)

AD = BC = 7 yd (width = w)

Area of this rectangle:

= l * b

= 9 * 7

= 63 yd²

[tex]\rule{150pt}{2pt}[/tex]

Now, take rectangle DEGF.

Here,

DE = FG = 5 yd (length = l)

DF = EG = 4 yd (width = w)

Area of this rectangle:

= l * b

= 5 * 4

= 20 yd²

[tex]\rule{150pt}{2pt}[/tex]

Total area of the compisite figure:

= Area of rectangle ABCD + Area of rectangle DEGF

= 63 yd² + 20 yd²

= 83 yd²

[tex]\rule{150pt}{2pt}[/tex]

Answer:

$600

Step-by-step explanation:

This can be modeled as an exponential equation.

General form of an exponential function: [tex]y=ab^x[/tex]

where:

Therefore:

[tex]\implies 75=a(0.5)^3[/tex]

[tex]\implies 75=0.125a[/tex]

[tex]\implies a=\dfrac{75}{0.125}[/tex]

[tex]\implies a=600[/tex]

Therefore, the computer initially cost $600.

Answer:

9 4/12

Step-by-step explanation:

Just add the mixed numbers 4 + 5 = 9

Add the fraction numerators 1 +3 = 4

*Since the denominator is the same, we just add the numerators

9 4/12

Answer:

as decimal 9.33333

Step-by-step explanation:

4 1/12 + 5 3/12 = 28/3 = 9 1/3

Answer:

A = 0

__________________________________________________________

Although the question says not to assume A is 0, that is the only possible option, since any nor prime or composite is going to be the higher number, because it stays the same.

0 ÷ a(0) = 0

a(0) ÷ a(0) = 0

__________________________________________________________

Ask in the comments.

Answer:

Step-by-step explanation:

gerald=2x

guy=x

gill= aproximately 0.3x

2x+x+0.3x=99

2.3x=99

x=43.04

The age of the guy is 29.72 years, the age Gerald is 59.44 years and the age of gill is 9.8 years.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given data in the question,

The equation according to the given statement will be,

The age of Gerald is 2x,

The age of the guy is x and the age of the gill is 0.33x.

So, the equation will be,

x + 2x + 0.33x = 99

3.33x = 99

x = 99/3.33

x = 29.72

Age of Gerald, 2x = 2(29.72) = 59.44 years.

Age of guy, x = 29.72 years and,

Age of gill, 0.33x = 0.33(29.72) = 9.8 years.  

To know more about arithmetic operations:

https://brainly.com/question/13585407

#SPJ2

A straight line is 180 degrees in measure

The straight line is made up of three angles

           --> angle 1

           --> angle 2

           --> angle with a little square on it

                     (angle with a little square means it is 90 degrees in measure)

Let's set up an equation

    [tex]angle1 + angle2 + 90 = 180\\angle1 + 87 + 90 = 180\\angle1 = 3[/tex]

Thus angle 1 is 3 degrees or the second choice

Hope that helps!

Assuming  He wants to earn interest on this money rather than keep extra money he does not need. The choice that would be the best for his situation is  $250 to open a regular savings.

A regular savings account is a saving acount that enables you to save and earn interest based on the amount saved because it is an interest bearing account.

Although this account gives you interest but the interest rate is low. Since Tim has $1200 in his checking account  assuming he withdraw $100 twices, Tim will have $1,000 ($1,200-$200).

Now if he open a regular saving with $250 he will have $750 left ($1,000-$250) with which he can earn interest with.

Inconclusion the choice that would be the best for his situation is  $250 to open a regular savings.

Learn more about regular account here:https://brainly.com/question/25787382

Step-by-step explanation:

87 and z are opposite so the are equal. The x equation is on the same line as the 87 degree angle so those 2 added together have to equal 180 so subtract 87 from 180 and get 93 and set 93 equal to 9x-87 and solve to get x=20

Answer:

=> z = 87° { vertically opposite angle }

=> 87° + (9x-87) = 180° { linear pair }

=> 87 +9x-87 = 180

=> 9x = 180°

=> x = 180/9

=> x = 20°

The correct answer for this question is 30 students

Sure hope this helps you :)

Answer:

100 square feet (100 ft²)

Step-by-step explanation:

Formula

Area of stage

Area of trapezoid:-

Area of parallelogram

Total:-

Answer:

I BELIEVE the answer would be 30

Answer:

You multiply the exponents and or to keep the base the same.

Step-by-step explanation:

I apologize if it is incorrect-

I hope it helps! Have a great day!

Anygays-

Answer: question 1 equals 31 Over 8 or 3.875 .

question 2 equals 425 over 24 .

question 3 equals 41 over 6 or 6.83333333

question 4 equals 55 Over 14

Step-by-step explanation: hope it helps you .

Answer:

Step-by-step explanation:

The given relations can be used to write three equations for the angle values.

  t + y + z = 180 . . . . . sum of all angle measures

  y + z = 5t . . . . . . . . second and third total 5 times the first

  y + 30 = z . . . . . . third angle is 30 more than the second.

__

Using the third equation to substitute for z in the first two equations gives ...

  t + y + (y +30) = 180   ⇒   t +2y +30 = 180

  y + (y +30) = 5t   ⇒   2y +30 = 5t

Using the second of these equations to substitute for (2y+30) in the first, we have ...

  t +5t = 180

  t = 180/6 = 30 . . . . . . divide by the coefficient of t

Using this value in our equation for 5t gives ...

  2y +30 = 5(30)

  2y = 120

  y = 60

Then the value of angle z is ...

  y +30 = z = 60 +30

  z = 90

The first, second, and third angles are 30°, 60°, and 90°, respectively.

Answer:

No slope.

Step-by-step explanation:

There is no such thing as a vertical slope, meaning that there is no slope. I hope this helps! :)

Answer:

No slope

Step-by-step explanation:

The line is going straight up :)

Brainliest pls?

Answer:

-3y

Step-by-step explanation:

-15(y2)4 ÷5y3y4

Rewrite the division as a fraction

-15(y2)4

 5y3y4

Multiply y3 by y4 by adding the exponents

-5(y2)4

  5y7

Cancel the common factor of -15 and 5

-3(y2)4

  y7

Multiply the exponents in (y2)4

-3y8

 y7

Cancel the common factor of y8 and y7

Factor y7 out of -3y8

y7(-3y)

 y7

Multiply by 1

y7(-3y)

 y7 × 1

Cancel the common factor which is y7 and y7

Rewrite the expression

-3y

 1

Divide -3y by 1

-3y

[tex]"20cm"[/tex]

[tex]Area\ of\ rq=a^2[/tex]

[tex]a=\sqrt{200}=10\bullet \sqrt{2}[/tex]

[tex]d\ iargul=\sqrt{2}9[/tex]

             [tex]=10\times \sqrt{2}\times \sqrt{2}[/tex]

             [tex]=20cm[/tex]

I hope this helps you

:)

Step-by-step explanation:

for me it is best as a first step to combine this all to one big fraction, and then simplify the whole expression.

you do know that when multiplying the same variable with exponent we simply add the exponents. and she we divide the same variable with exponents, we subtract them from each other (as the overlapping exponent parts cancel each other out).

(3ac³f³)/(8a²bcf⁴) × (12ab²c)/(18ab³c²f) =

= (3×12a²b²c⁴f³)/(8×18a³b⁴c³f⁵) =

= (3×12c)/(8×18ab²f²) = 12c / (8×6ab²f²) =

= 2c / (8ab²f²) = c / (4ab²f²)

Answer:

15.75 is 6.3% of 250.

Formula:
[Percentage] x [Number Given] = [New number]

Answer:

They both have a y intercept of 0

Step-by-step explanation:

Linear equations are written in the form y = mx + b. m is the slope and b is the y-intercept. It also states that they intersect at the origin, so they must have a y-intercept of 0.

A) 144 in

is your answer. good luck

Answer: You should try to multiply and divide try then question me back. But the answers are neither of them.

Step-by-step explanation:

Answer:

The answer is 4x² – x – 4 = 0

Step-by-step explanation:

Where,

So, one quadratic polynomial satisfying is given condition is 4x² – x – 4 = 0

Sum of zeroes = 1/4

Product of zeros = 1

Remember this formula

x² – (α + β)x + αβ

x² – 1/4x + 1

4x² – x – 4 = 0

Thus, The quadratic polynomial is

4x² – x – 4 = 0.

Answer:

33

Step-by-step explanation:

For 4 triangles area 4*(1/2)*4*3=24

base square area 3*3=9

all together 24+9= 33