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nordsb [41]
3 years ago
5

Flying against the wind, an airplane travels 4000 kilometers in 5 hours. Flying with the wind, the same plane travels 5040 kilom

eters in 4 hours. What is the rate of the plane in still air and what is the rate of the wind? Urgent!!
Mathematics
1 answer:
andriy [413]3 years ago
7 0

Answer:the plane in still air is 904 km/h

the rate of the wind is 104 km/h

Step-by-step explanation:

Let x represent the rate or speed of the plane in still air.

Let y represent the rate or speed of the wind.

Flying against the wind, an airplane travels 4000 kilometers in 5 hours. This means that the total speed of the airplane would be (x - y) km/h

Distance = speed × time

Therefore

4000 = 5(x - y)

4000 = 5x - 5y - - - - - - - - -1

Flying with the wind, the same plane travels 5040 kilometers in 4 hours. This means that the total speed of the airplane would be (x + y) km/h. Therefore,

5040 = 4(x + y)

5040 = 4x + 4y - - - - - - - - - 2

Multiplying equation 1 by 4 and equation 2 by 5, it becomes

16000 = 20x - 20y

20160 = 20x + 20y

Subtracting, it becomes

- 4160 = - 40y

y = - 4160/-40

y = 104

Substituting y = 104 into equation 1, it becomes

4000 = 5x - 5 × 104

4000 = 5x - 520

5x = 4000 + 520

5x = 4520

x = 4520/5 = 904

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Answer:

x=3

Step-by-step explanation:

4x+1 = 5x-2

Bringing all like terms together,

5x-4x = 2+1

x = 3

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3 years ago
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7-5p+3q when p=1 and q=7
Mnenie [13.5K]

Answer:

23

Step-by-step explanation:

7 - 5p + 3q

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Substitute in the values of "p" and "q", and solve;

7 - 5(1) + 3(7)

7 - 5 + 21

2 + 21

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3 years ago
September 6 is a Read Book Day.Polina read 5 times as many pages as Marcus read.Together,the read 108 pages.How many pages did e
Gemiola [76]

Answer:

The number of pages that Polina read was 90 and the number of pages that Marcus read was 18

Step-by-step explanation:

Let

x -----> number of pages that Polina read

y ----> number of pages that Marcus read

we know that

x+y=108 ----> equation A

x=5y -----> equation B

substitute equation B in equation A and solve for y

5y+y=108\\6y=108\\y=18

Find the value of x

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therefore

The number of pages that Polina read was 90 and the number of pages that Marcus read was 18

3 0
3 years ago
Let f(x)=−3x. The graph of f(x) ​is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 u
Naily [24]
So the equation for these types of equations is f(x) = a(x-h)+k with h being a horizontal translation, a being a stretch/compression and k being a vertical translation. So here if you want a stretch of 4 a would be four, g(x)=4(-3x-h)+k. Also, there is a horizontal translation so it would be positive 4 into the equation. Since there is no change in the y-axis there is no vertical translation resulting in g(x) = 4(-3x-4)
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saveliy_v [14]

Answer:

F = $13,802.31

she can finance $13,802.31 with this loan.

Step-by-step explanation:

Given;

Rate r = 7% = 0.07

Time t = 4 years

Payment per month MP = $250

Number of months per year n = 12

This can be solved using compound interest for future value series formula;

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Substituting the given values, we have;

F = $250(((1 + 0.07/12)^(12×4) - 1)/(0.07/12))

F = $13,802.31

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