A passenger plane flew from Texas to Frankfurt and back. The round trip is 9900 km.
return trip took 4 hours less than the trip to Frankfurt because of the 50 km/hr wind over the ocean on the return trip. Assume there was no wind on the trip to Frankfurt. Let x km/hr represent the average speed of the plane in still air.

Answers

Answer 1

We want to find the average speed of the plane in still air, we will get that the average speed of the plane in still air is 355.3 km/hr

So we know that the total trip is 9900km, so from Texas to Frankfurt the distance is half of that:

9900km/2 = 4950km

Now, The speed of the plane in still air is x km/hr

The speed of the air is 50 km/hr, and it flows from Frankfurt to Texas.

So in the first part of the trip, the wind blows in opposite direction to the motion of the plane, thus the speed of the plane will be:

(x - 50) km/hr

While in the return trip the wind blows in favor of the plane, in this case, the speed is:

(x + 50)km/hr

Then if the first part of the trip lasts for T hours (the second for T - 4 hours) we can write the system of equations:

(x - 50)*T = 4950

(x + 50)*(T - 4) = 4950

Where I removed the units so it is easier to read.

If we isolate T in the first equation we get:

T = 4950/(x - 50)

Now we can replace this in the other equation to get:

(x + 50)*(4950/(x - 50)  - 4) = 4950

If we multiply both sides by (x - 50) we get:

(x + 50)*4950 - 4*(x + 50)*(x - 50) = 4950*(x - 50)

Now we can solve this for x:

(x + 50)*4950 - 4*(x^2 - 2500) - 4950*(x - 50) = 0

100*4950 - 4*(x^2 - 2500)  = 0

495000 - 4*x^2 + 10000 = 0

505000 = 4*x^2

√(505000/4) = x = 355.3

The average speed of the plane in still air is 355.3 km/hr

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13476446


Related Questions

Mr.Jones is building a patio outside of his back door.The patio will be 8.5 ft long and 10.7 ft wide.What is the area of the patio that Mr.Jones is building?

Answers

38.4 is the area. it’s 8.5 ft long so you do 8.5x2 and you get 17, and then for 10.7 you do 10.7x2 and get 21.4, then you add 21.4 and 17 together.

Answer:

90.95

Step-by-step explanation:

Which of the following decimals is equal to 3 1/40
?


please explain why
3.0025

3.025


3.0250

Answers

Answer:

3.025

Step-by-step explanation:

the answer is 3.025 because 1/40 simplified is 0.025 and add the 3 to get 3.025

Answer: 3.0250

Step-by-step explanation: To convert this mixed number (fraction) to a decimal just follow these two steps:

Step 1: divide numerator (1) by the denominator (40): 1 ÷ 40 = 0.025

Step 2: add this value to the the integer part: 3 + 0.025 = 3.025. So,

3 1/40 = 3.025

9
11 (a) Grapes cost £2 per kilogram.
Calculate the cost of 380g of grapes.

Answers

Answer:

£0.76

Step-by-step explanation:

1kilogram = 1000grams

1000g of grapes costs £2

380g costs = (380 × 2)/ 1000

760/1000 = £0.76

On Tuesday morning a school cafeteria served 18 gallons of orange juice during breakfast. How many cups are in 18 gallons?

A.288 cups
B.64 cups
C.2,048
D.128 cups

Answers

Answer:

A

Step-by-step explanation:

288 cups did this before

1985 x 99 I already know the answer: 196515

Answers

Answer:

196515

Step-by-step explanation:

Answer:

196515

Step-by-step explanation:

Emily reads a story book. o the first day, she reads 1/9 of the whole book, and on the second day, she reads 24 pages. The ratio of the number of pages read to the remaining pages in the two days is 1:4. How many pages are there in this book

Answers

Answer:

Step-by-step explanation:

Let P be the number of pages

First day reads P/9 pages

Second day reads 24 pages

two days reading is P/5  (1 page read for every 4 pages left)

         P/9 + 24 = P/5

        P + 24(9) = 9P/5

  5P + 24(9)(5) = 9P

               1080 = 4P

                     P = 270 pages

There are 270 pages in this book.

Given that,

Emily reads a storybook the first day,

She reads 1/9 of the whole book, and on the second day, she reads 24 pages.

The ratio of the number of pages read to the remaining pages in the two days is 1:4.

We have to find

How many pages are there in this book?

According to the question,

Let, P is the number of pages,

The first day Emily reads p/9 pages of the whole book,

And the second day she read 24 pages.

The ratio of the number of pages read to the remaining pages in the two days = 1;4 = p/5.

Therefore,

The number of pages reads first day + the number of pages read the second day = The ratio of the number of pages read to the remaining pages in the two days

[tex]\rm \dfrac{p}{9} + 24 = \dfrac{p}{5}\\\\ \dfrac{p}{5} - \dfrac{p}{9} = 24\\\\\dfrac{p \times 9 - p\times 5}{45} = 24\\\\ \dfrac{9p-5p}{45} = 24\\\\\dfrac{4p}{45} = 24\\\\4p = 24\times 45\\\\4p = 1080\\\\p = \dfrac{1080}{4}\\\\p = 270 \ pages[/tex]

Hence, there are 270 pages in this book.

For more details refer to the link given below.

https://brainly.com/question/14505922

Complete the table of ordered pairs for the linear equation

Answers

Answer:

Step-by-step explanation:

See attachment.

y = 30.078(1.003)*.
Question 1
? Question
Use the exponential model to make predictions about closing prices of this stock. Remember that x
represents the number of weeks since the first data point, so the value of x today would be 260.
Type the correct answer in each box. If necessary, round the answers to the nearest cent.
One week from today, the stock is predicted to close at $
One month from today, the stock is predicted to close at $
One year from today, the stock is predicted to close at $

Answers

Using the exponential function, it is found that:

One week from today, the stock is predicted to close at $65,734.37.One month from today, the stock is predicted to close at $66,327.75.One year from today, the stock is predicted to close at $76,584.35.

The exponential function is:

[tex]y(x) = 30078(1.003)^x[/tex]

x  represents the number of weeks since the first data point, so the value of x today would be 260.

Hence, considering today as an starting point, the function is:

[tex]y(x) = 30078(1.003)^{x + 260}[/tex]

One week from now, we have y(1), hence:

[tex]y(1) = 30078(1.003)^{1 + 260} = 65734.37[/tex]

One week from today, the stock is predicted to close at $65,734.37.

One month from now, we have y(4), hence:

[tex]y(4) = 30078(1.003)^{4 + 260} = 66327.75[/tex]

One month from today, the stock is predicted to close at $66,327.75.

One year from now, we have y(52), hence:

[tex]y(52) = 30078(1.003)^{52 + 260} = 76584.35[/tex]

One year from today, the stock is predicted to close at $76,584.35.

To learn more about exponential functions, you can take a look at https://brainly.com/question/25958656

Answer:

One week from today, the stock is predicted to close at $65,734.37.

One month from today, the stock is predicted to close at $66,327.75.

One year from today, the stock is predicted to close at $76,584.35.

Step-by-step explanation:

a) Complete the table of values for y = 6 - 2x
0
1
2
3
Х
4
5
OT
10
-4
y
8
6
co
b) Draw the graph of y = 6 - 2x
on the grid.
4
2.
c) Solve 6 - 2x = 3

Answers

Step-by-step explanation:

the answer as shown in the photo

Elevator 1 in a building moved from ground position to a final position of +13 feet. Elevator 2 in the same building moved from ground to a final position of −10 feet. Which statement best describes the final positions of these two elevators? (5 points)

Question 4 options:

1)

Elevator 1 is 13 feet above ground level, and Elevator 2 is 10 feet below the position of Elevator 1.

2)

Elevator 1 is 13 feet below ground level, and Elevator 2 is 10 feet above the position of Elevator 1.

3)

Elevator 1 is 13 feet below ground level, and Elevator 2 is 10 feet above ground level.

4)

Elevator 1 is 13 feet above ground level, and Elevator 2 is 10 feet below ground level.

Answers

Answer:

Elevator 1 is 12 feet above ground level, and Elevator 2 is 15 feet below the position of Elevator 1. We are given that Elevator 1 is "+12 feet" and Elevator 2 is "-15 feet" meaning 15 feet below that of Elevator 1 (because they said it was where it was at Elevator 1 ground level prior), so this should be your answer "A".

Step-by-step explanation:

1 a

Is 6.32332333... a rational or irrational number? a Choose the correct answer below. O rational number O irrational number​

Answers

Answer:

Irrational number because it cannot be written in fraction form a/b where b is not supposed to be 0

NO LINKS!!!

Purchasing a TV that is 30% off will save $250.
a. What is the part, percent, and whole.
b. What is the original price of the TV?

Answers

Answer:

  a. part: $250; percent: 30%; whole: $833.33

  b. $833.33

Step-by-step explanation:

a. The part is given as $250; the percentage that represents is given as 30%.

The whole is the ratio of the part to the percent:

  $250/30% = $250/0.30 = $833.33 . . . whole

__

b. The original price is the "whole" of which 30% is the part.

  original price: $833.33

B(14, 12)
A(-5,-2)
A. Find the midpoint of Segment AB

Answers

the midpoint formula is (x1+x2/2, y1+y2/2
so you would do (-5+14)/2=4.5. (-2+12)/2=5
(4.5, 5)

integrate (1-x³)² with respect to x​

Answers

Answer:

Start off by expanding the square:

x^6 -2x³ + 1.

Now, we can integrate it in dx:

∫x^6 - 2x^3 + 1 dx = ∫x^6 dx - 2∫x^3 dx + ∫1 dx = (x^7)/7 - 2((x^4)/4) + x = (x^7)/7 - (x^4)/2 + x.

That's the result!

[tex]\\ \sf\longmapsto {\displaystyle{\int}}(1-x^3)^2dx[/tex]

[tex]\\ \sf\longmapsto {\displaystyle{\int}}(1-x^6+2x^3)dx[/tex]

[tex]\\ \sf\longmapsto x-\dfrac{x^{6+1}}{6+1}+2\dfrac{x^{3+1}}{3+1}[/tex]

[tex]\\ \sf\longmapsto x-\dfrac{x^7}{7}+2\dfrac{x^4}{4}[/tex]

[tex]\\ \sf\longmapsto x-\dfrac{x^7}{7}+\dfrac{x^4}{2}[/tex]

Solve the following equation 2x-17=-53

Answers

Step-by-step explanation:

2x - 17 = - 53

2x = - 53 + 17

2x = - 36

x = - 36/2

x = - 18

Answer:

x = -18

Step-by-step explanation:

2x - 17 =  -53

    +17 = + 17            Add 17 to both sides

2x       =   -36            

  x = -36 ÷ 2           Divide by 2

   x = -18

Elsa is selling bracelets at craft shows to raise money for an animal shelter.

She is also accepting additional cash donations. She plans to give 75% of the

money from all bracelet sales and donations to the shelter. She will use the

remaining money to buy more supplies. Bracelet sales and donations from

the first craft show are represented by the expression 24n + 32, where n

represents the amount Elsa charges for each bracelet. The second craft

show sales and donations is represented by the expression 40n + 56. If Elsa

charges $4 for each bracelet, how much money will she donate to the

Answers

Answer:

$258

Step-by-step explanation:

75% = 0.75 when we divide by 100 to convert a percentage to a decimal

75% of total sales = money donated

Total sales = sales from first show + sales from second show

                  = 24n+32 + (40n+56)

                  = 64n + 88

0.75 of (64n+88) = money donated

                            = 0.75 * (64n+88)

                            = 48n + 66

substitute 4 for n, as she charges $4 for each bracelet

money donated = 48*4 + 66 = 258

Three polygons have been divided
into triangles by drawing a
segment from one vertex to all nonadjacent vertices. If n is the
number of sides in the polygon, which expression shows the
number of triangles created by each polygon?
A.n
B.(n + 2)
C.(n - 2)
D.3n, 4n, 8n

Answers

The relationship between the sides of the polygon and the triangle follows an arithmetic sequence

The expression that represents the number of triangles is (c) n - 2

From the diagrams, we have:

Sides           Triangles

  5                    3

  6                    4

  8                    6

The above can be represented as functions as follows:

[tex]f(5) = 3[/tex]

[tex]f(6) = 4[/tex]

[tex]f(8) = 6[/tex]

Express 6 as 8 - 2

[tex]f(8) = 8 - 2[/tex]

Express 8 as n

[tex]f(n) = n - 2[/tex]

So, the expression that represents the number of triangles is (c) n - 2

Read more about sequence and patterns at:

https://brainly.com/question/24050043

i need help fast plz

Answers

Answer:

27/16

Step-by-step explanation:

[tex]12 \div \left(2 + \dfrac 23 \right)^2\\\\\\=12 \div \left(\dfrac 83 \right)^2\\\\\\=12 \div \dfrac{64}9\\\\\\=12 \times \dfrac{9}{64}\\\\\\= \dfrac{3 \times 9}{16}\\\\\\=\dfrac{27}{16}\\\\\\=1\dfrac{11}{16}[/tex]

The answer to this question?

Answers

Answer:

1. 59  2.90  4.31   3. Sorry I dunno

Step-by-step explanation:

1. the 59 degrees is the same.

2. It's a perfect angle

3. Sorry

4.180-90-59=31

use order of operations 7-2(-7-4)

Answers

Answer:

29

hope this helps

How can a person best reduce the risk of sustaining permanent injuries?

Wear protective clothing while sleeping at home.
Secure a seat belt only when riding in the front seat.
Wear a cracked bicycle helmet while riding a bicycle.
Put away guns in a lockbox that is secure and in a discrete location.

Answers

Answer:

Put away guns in a lockbox that is secure and in a discrete location.

Have a good day <3

The backyard of a new home is shaped like a trapezoid with a height of 44 nt and bases of 86ft and 106ft What is the cost of putting sod on the yard, if the
landscaper charges $0.25 por square foot for sod?

Answers

Answer:

Step-by-step explanation:

Area of a trapezoid is the average length of the bases times the height

C = A(0.25)

A = ½(86 + 106)(44) = 4224 ft²

C = 4224(0.25) = $1056.00

Determine the slope from the given graph below:

The slope is−17
The slope is 5
The slope is 7
The slope is -5

Answers

Answer:

The slope is positive 7

Step-by-step explanation:

The y-intercept is -5, and the next point going upwards is positive 2. (Sorry I'm bad at explaining)

Answer:

The slope is 7

Step-by-step explanation:

(1,2)(0,-5)

[tex]m=\frac{-5-2}{0-1} ==\frac{-7}{-1} =7[/tex]

Hope this helps

Question 3 help pls

Answers

Answer:

< greater than

Step-by-step explanation:

u need to turn each one into decimals than find out which ones greater that's how you'll get your answer

Answer: The answer would be D

Can yall please help me it isn't college work it is 6th grade math

Answers

Answer:

C) 1,250

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer: To answer this we have to remember how to find the total amount of cash he will be spending. Since 19.2% is 240, we multiply that by 100. We end up with 24,000 which you will then divide by the percentage. After that, you have your final answer which is 1,250. To double-check you can make sure that 19.2% of 1,250 is 240, which it is. Therefore, your final answer is $1,250.

A family of 6 used 5400l of water in 7 days. Each member of the family used the same amount of water each day. How many litres of water did each person use in a day?

Answers

Answer:

Hello! The answer for this is 900 liters a day

Step-by-step explanation:

Look at the sheet for answer.

the first person to get this right earns breainlesit!!!!!!!!
witch expressions are evculient to 4b?

Answers

Answer:

B,C,D,F, those are yhe right answer

What is the relationship between vertices and edges in a pyramid? In a prism?

Answers

Answer: depends on the shape of it but mostly equal

Step-by-step explanation: hope it helps

PLS HELP BEST ANSWER=BRAINLIEST

3a² - ac + 2c - 6a/ 3a - c = a - 2

i have been looking everywhere but i cannot find the steps on how to simplify/solve this
PLS SHOW STEPS

Answers

Answer:

a-2=a-2

Step-by-step explanation:

Here it is, you just have to notice that the numerator has common factors alternated. You will then collect the same parentheses and simplify with the denominator.

Answer:

Step-by-step explanation:

Parentheses are missing in your problem statement if you intend to simplify ...

  [tex]\dfrac{3a^2-ac+2c-6a}{3a-c}\\\\=\dfrac{a(3a-c) -2(3a-c)}{3a-c}\qquad\text{factor pairs of terms}\\\\=\dfrac{(a-2)(3a-c)}{(3a-c)}\\\\=\boxed{a-2}\qquad\text{cancel common factors}[/tex]

The "steps" are ...

factor numerator (and denominator, if necessary)cancel common factors

Simplify
O A. 6^16
O B. 6
O C. 6^4
O D. 1/6

Answers

the answer for this question is B
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