Use the Distributive Property to simplify the expression.

$\frac{1}{4}\left(8+x+4\right)=$

This question is incomplete, the complete question is;

A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel consumed at rate r, and the exhaust gases are ejected with constant velocity v(sub e) [relative to the rocket]. A model for the velocity of the rocket at time t is given by the equation:

v(t) = -gt - v(sub e) ln [(m-rt)/m]

where g is the acceleration due to gravity, and t is not too large. If g = 9.8 m/s^2, m = 30,000 kg, r = 160 kg/s, and v(sub e)= 3000 m/s, find the height of the rocket one minute after liftoff.

Answer:

the height of the rocket one minute after liftoff is 14.8441 km

Step-by-step explanation:

Given the data in the question;

Velocity of the rocket at time t is;

v(t) = -gt - [tex]V_{e\\}[/tex] ln( [tex]\frac{m-rt}{m}[/tex])

[tex]\int\limits^t_0 {v(t)} \, dt[/tex] = ₀∫⁶⁰(  -gt - [tex]V_{e\\}[/tex] ln( [tex]\frac{m-rt}{m}[/tex]) )dt

= -g([tex][\frac{t^{2} }{2}]^{60}_0[/tex]  - [tex]V_{e\\}[/tex] ₀∫⁶⁰In( [tex]\frac{m-rt}{m}[/tex]) dt

= -g([tex][\frac{t^{2} }{2}]^{60}_0[/tex]  - [tex]V_{e\\}[/tex] [ t In( [tex]\frac{m-rt}{m}[/tex]) + [tex]\frac{m}{r}[/tex] - t - mr[tex]\frac{1}{r^{2} }[/tex] In |m-rt| [tex]]^{60}_0[/tex]

= -g([tex][\frac{60^{2} }{2}][/tex]  - [tex]V_{e\\}[/tex] [ 60 (In(1 -  [tex]\frac{60r}{m}[/tex])-1) + [tex]\frac{m(In(m^{2})-In((m-60r)^2))) }{2r}[/tex] ]

we input our given values; g=9.8 m/s², m=30000 kg, Ve = 3000 m/s, r = 160 kg)

= -9.8([tex][\frac{60^{2} }{2}][/tex]  - 3000 [ 60 (In(1 - [tex]\frac{60(160)}{m}[/tex])-1) + [tex]\frac{30,000(In(30,000^{2})-In((30,000-60(160))^2))) }{2(160)}[/tex] ]

[tex]\int\limits^t_0 {v(t)} \, dt[/tex] =  14844.10 m

we convert to kilometer

[tex]\int\limits^t_0 {v(t)} \, dt[/tex] =  14844.10 ÷ 1000

[tex]\int\limits^t_0 {v(t)} \, dt[/tex] =  14.8441 km

Therefore, the height of the rocket one minute after liftoff is 14.8441 km

Hope this helps! I had hw similar to this... so..

Answer:

2√5-4(3√5-2)

6√25-4√5-12√5+8

6(5)-16√5+8

30+8-16√5

38-16√5

Answer:

2/5 *(5x+32)

Step-by-step explanation:

Answer:

1 hour 42 minutes

Step-by-step explanation:

Given :

Time table :

BRIGHTON _____ LONDON

0718 __________ 0900

0725 __________0832

0728 __________ 0848

Tine taken by the 0718 train :

Arrival time, London - Departure time

09:00 - 07:18

2 hours (60 - 18) minutes

Answer:

There would be 94 tiles.

Step-by-step explanation:

The number of tiles is given by the following equation:

[tex]n = 6 + 4p[/tex]

In which p is the current position.

How many tiles would there be in position 22?

This is n when [tex]p = 22[/tex]. So

[tex]n = 6 + 4*22 = 6 + 88 = 94[/tex]

There would be 94 tiles.

The number of titles would there be in the position 22 is 94 titles.

Given that,

Based on the above information, the calculation is as follows:

n = 6 + 4p

= 6 +  4(22)

= 6 + 88

= 94

Therefore we can conclude that the number of titles would there be in the position 22 is 94 titles.

Learn more: brainly.com/question/13549064

Step-by-step explanation:

uhhh what set of numbers?

Answer:

X=3 y=-1

Step-by-step explanation:

X+y=2

X-y=4

so that means

y=X-4

substitute it in

X+X-4=2

2x-4=2

2x=2+4

2x=6

x=3

3+y=2

3+-1=2

y=-1

ways to check

3--1=4

double minus equal plus

3+1=4

In response to the question, we may say that It will take Kendra and Joe expression approximately 3.2 hours to paint the room together.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

Let's denote the time it takes Kendra to paint the room as "K" and the time it takes Joe to paint the room as "J". We can use the formula:

[tex]1/K + 1/J = 1/T\\1/7 + 1/6 = 1/T\\13/42 = 1/T\\13T = 42\\[/tex]

Therefore, T = 42/13 ≈ 3.2 hours (rounded to the nearest tenth).

It will take Kendra and Joe approximately 3.2 hours to paint the room together.

To know more about expression visit :-

https://brainly.com/question/14083225

#SPJ1

Answer:

-10

Step-by-step explanation:

f(2) = 2 x -5

= -10

The answer is -10

Answer:

im pretty sure its y=1/3x

Step-by-step explanation:

rearrange for y to be subject

its perpendicular so then the gradient will be the negative reciprocal (-1 / -3= 1/3) so thats your new gradient

then when you substitute the (3,-1) into that equation get -1=1 + c so then c is 0  and your whole equation is y=1/3x

Answer:

32 plates

Step-by-step explanation:

If the pottery class has 16 pounds  of clay and each student got 1/2 of a pound;

then;

1 plate = 1/2 pounds

xplate = 16pounds

Divide both expressions

1/x = 1/2÷16

1/x = 1/2*!6

1/x = 1/32

x = 32

Hence the student will make 32 plates

36 cookies are left

Step-by-step explanation:

to do this problem all you have to do is do the equation 48*0.25 and when you do that you get 12. after that you subtract 12 from 48 to get 36

Answer:

g o f = [tex]g(f(x)) = 32x^2 + 32x + 4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 4x +2[/tex]

[tex]g(x) =2x^2 - 4[/tex]

Required:

Find g o f

This is calculated as:

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

[tex]g(x) =2x^2 - 4[/tex]

So:

[tex]g(f(x)) = 2(4x+2)^2 - 4[/tex]

[tex]g(f(x)) = 2(4x+2)(4x+2) - 4[/tex]

[tex]g(f(x)) = 2[ 16x^2 + 16x + 4)] - 4[/tex]

[tex]g(f(x)) = 32x^2 + 32x + 8 - 4[/tex]

[tex]g(f(x)) = 32x^2 + 32x + 4[/tex]

Answer:

Cups at $3.20

Step-by-step explanation:

Gallon - $3.99

Quarts - $5,00

Pints - $5.20

Cups - $3.20

Step-by-step explanation:

(3×6) + (2×6)

= 18 + 12

= 30 in²

Answer:

David decorated the cookies at a faster rate than Colton.

Step-by-step explanation:

David decorated one cookie every 3 and 1/3 minutes. Colton decorated one cookie every 3.5 minutes. The way to find the answer to your question is by dividing the number of minutes by the number of cookies decorated.

Answer: the equation for SU is 2(lb+bh+hl)

Step-by-step explanation: L stands for length B stands for base. H stand for height multiply that by 2

Answer:

There were 20 questions

19/20 = 0.95

Hope that helped!

Answer:

20 questions on the quiz

Step-by-step explanation:

Let x = the number  of questions on his quiz

95/100 of x = 19,

95/100x = 19 [multiply both sides by 20]

19x = 380 [divide both sides  by 19]

x = 20 questions  

Answer:

2x² + 13x + 15

Step-by-step explanation:

| 2x | 3

x | 2x*x = 2x² | 3*x = 3x

5 | 2x*5 = 10x | 3*5 = 15

We have, 2x² + 3x + 10x + 15

Combining like terms, we would have the final expression as:

2x² + 13x + 15

Answer:

2, 70

Step-by-step explanation:

It is given that :

At Nolan's Car rentals, if a customer rents a car, he or she has to pay $60 for the car for the first day and more $ 5 for every additional days.

Therefore this gives the equation :

y = 5x +60 ..........(1)

At Westford car rental, the price of the car for first day is $ 50 and additional $10 for every additional day.

So the equation will be :

y = 10x + 50.......(2)

Solving (1) and (2), we get

 5x + 60 = 10x + 50

⇒ 60 - 50 = 10x - 5x

⇒ 10 =  5x

∴ x = 2

Now putting the value of x = 2 in equation (1), we get

y = 5x +60

y = 5(2) +60

y = 70

Therefore, (x, y) = (2, 70)

Answer:

Theres 3, 8 8 8

or 111, 111*8=888.

Two correct answers

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

1+3(6-3n)= -6-4n

1+18-9n= -6-4n

1+18+6= 9n-4n

25=5n

25/5=n

5=n

Answer:

The answer is "0.30%"

Step-by-step explanation:

To assign employees to work, we have to select 6 out of 20 to do work, instead select 4 out of another 14 jobs, 2 to do, and 5 out of another 10 works 3. The other five were going to go do work four. They may decide how often ways of making each of these options. Their service would be how many forms to allocate those four positions to staff. The random sample is from the height.

There are equally estimated that numbers of arrangements with both the four in Job 1.They then allocate all four to work 1. In this situation We must then select 2 out from the 16 existing spaces in job 1, 4 out from the 14 remaining spaces in job 2, 5 out of the 10 existing spaces in job 3 as well as the ones remaining in job 4.

The possibility of any four being at 1 is that they've been all divided by the overall amount of circumstances in 1 task.

[tex]\to \frac{[ \frac{16!}{(2!4!5!5!)}]}{[\frac{20!}{(6!4!5!5!)}]}\\\\\to [ \frac{16!}{(2!4!5!5!)}] \times [\frac{(6!4!5!5!)}{20!}]\\\\\to [ \frac{16!}{(2!)}] \times [\frac{(6!)}{20!}]\\\\\to [ \frac{16!}{(2!)}] \times [\frac{(6\times 5 \times 4 \times 3 \times 2!)}{20!}]\\\\\to 16! \times [\frac{(360)}{20 \times 19 \times 18 \times 17 \times 16!}]\\\\\to \frac{(360)}{20 \times 19 \times 18 \times 17 }\\\\\to \frac{(360)}{20 \times 19 \times 18 \times 17 }\\\\\to \frac{360}{116,280}[/tex]

[tex]\to 0.00309597523 \approx 0.30 \%[/tex]

Answer: 16/5 or 3.2

Steps:

=> 1× 2 + 2× 2 + 3× 2 + 4× 1 + 5 ×2 + 6 ×1/ 2+2+2+1+2+1

=> 16/5 or 3.2 (answer)