Question

1.Упростите выражение 9(2x-3y)-8(y-x) 2 . Решите уравнение 7(4-3x)-(8,5-x)=4-3(x-8) 3. Расстояние между двумя городами автомобиль преодолевает за 3 часа а автобус скорость которого на 18 км в час меньше за 3,75 ч. определите скорость автомобиля и расстояние между городами 5. Стоимость железнодорожного билета 1800 рублей билеты на самолет по тому же маршруту 2700 рублей а) на сколько процентов билет на самолет дороже железнодорожного билета б) на сколько процентов железнодорожный билет дешевле билета на самолет

Answer 1

1. Упростите выражение 9(2x-3y)-8(y-x)

To simplify the expression 9(2x-3y)-8(y-x), we can distribute the coefficients and combine like terms:

9(2x-3y)-8(y-x) = 18x - 27y - 8y + 8x

Combining like terms, we get:

18x + 8x - 27y - 8y = 26x - 35y

Therefore, the simplified expression is 26x - 35y.

2. Решите уравнение 7(4-3x)-(8,5-x)=4-3(x-8)+3

To solve the equation 7(4-3x)-(8.5-x)=4-3(x-8)+3, we can follow these steps:

7(4-3x)-(8.5-x)=4-3(x-8)+3 28 - 21x - 8.5 + x = 4 - 3x + 24 + 3

Simplifying both sides of the equation:

28 - 8.5 + 4 + 24 = 21x + x + 3x + 3x - 21x 48.5 = 7x

Dividing both sides of the equation by 7:

48.5/7 = x x = 6.928571428571429

Therefore, the solution to the equation is x = 6.93.

3. Расстояние между двумя городами автомобиль преодолевает за 3 часа, а автобус, скорость которого на 18 км/ч меньше, за 3.75 часа. Определите скорость автомобиля и расстояние между городами.

Let's assume the speed of the car is represented by c km/h and the speed of the bus is represented by b km/h.

Given that the car covers the distance between the two cities in 3 hours and the bus covers the same distance in 3.75 hours, we can set up the following equations:

Distance = Speed * Time

For the car: Distance = c * 3 For the bus: Distance = (b - 18) * 3.75

Since the distances are the same, we can equate the two equations:

c * 3 = (b - 18) * 3.75

Simplifying the equation:

3c = 3.75b - 67.5

To solve for the values of c and b, we need another equation. However, the given information does not provide any additional equations or information about the relationship between the speeds of the car and the bus. Therefore, it is not possible to determine the specific values of the car's speed (c) and the distance between the cities.

5. Стоимость железнодорожного билета 1800 рублей, билеты на самолет по тому же маршруту 2700 рублей.

а) На сколько процентов билет на самолет дороже железнодорожного билета? б) На сколько процентов железнодорожный билет дешевле билета на самолет?

To calculate the percentage difference between the cost of an airplane ticket and a train ticket, we can use the following formulas:

a) Percentage increase = ((New Value - Old Value) / Old Value) * 100 b) Percentage decrease = ((Old Value - New Value) / Old Value) * 100

Given that the cost of a train ticket is 1800 rubles and the cost of an airplane ticket is 2700 rubles, we can calculate the percentage difference:

a) Percentage increase = ((2700 - 1800) / 1800) * 100 = 50% b) Percentage decrease = ((1800 - 2700) / 2700) * 100 = -33.33%

Therefore: a) The airplane ticket is 50% more expensive than the train ticket. b) The train ticket is 33.33% cheaper than the airplane ticket.