A cuboid container with a bottom area of 15 square decimeters contains 3 decimeters of water. After an irregular stone is put into the container (the stone is completely immersed in the water, and the water surface rises by 2 cm). How many cubic decimeters is the volume of the stone?

15 * 0.2 = 3 (cubic decimeter)

1. Throw an irregular stone into a rectangular container with a bottom area of 20 square meters and a water depth of 2 decimeters. The water surface rises to only 5 centimeters away from the container and submerges the stone. What is the volume of this stone in cubic decimeters?

The floor area is 20 square decimeters
20 * (5-0.5-2) = 50 cubic decimeter

A cuboid is 5 decimeters long and 2 decimeters wide. If you want to increase the surface area of the cuboid by 20 square decimeters, how many decimeters will the width, height and length increase
I know it's 2 decimeters, but I don't know how to work it out

20 ÷ (2 + 3) = 4 (decimeter)

As shown in the figure, △ ABC, ab = AC, ad is the middle line on the edge of BC, be ⊥ AC, and the perpendicular foot is e. if ∠ BAC = 45 °, then ∠ EDC = () °

∵AB=AC,∠BAC=45°
The ABC is an isosceles triangle
∠ACB=∠ABC=(180°-45°)÷2=67.5°
∵ be ⊥ AC, ad is BC
In RT △ BCE
DE=CD=BC
∴∠DEC=∠ACB=67.5°
∴∠EDC=180°-∠DEC-∠ACB=180°-67.5°-67.5°=45°

The distance between a and B is 120 kilometers. A bus runs 40 kilometers per hour from a to B, and 60 kilometers per hour when it returns on the same road. What is the average speed of the bus between the two places?

(120 × 2) / (120 / 40 + 120 / 60), = 240 / 3 + 2, = 240 / 5, = 48 km; a: the average speed of this car to and from the two places is 48 km

1x2+2x3+3x4+.+n(n+1)=_____ (n is a natural number)

1*2+2*3+.+N（N+1）
=1*2+2*3+.+(N^2+N)
=(1+2+3+...+N)+(1^2+2^2+...+N^2)
=[N(N+1)/2]+[N(N+1)(2N+1)/6]
=N(N+1)(N+2)/3
1*2*3+2*3*4+.+N(N+1)*(N+2)
=1*2*3+2*3*4+.+(N^3+3N^2+2N)
=(1^3+2^3+...+N^3)+3(1^2+2^2+...+N^2)+2(1+2+...+N)
=[N(N+1)/2]^2+[N(N+1)(2N+1)/2]+N(N+1)
=(N+1)(N^3+3N^2+6N)/4

The road between a and B is 375 km long. A car has driven 150 km from a to B in the first two hours. At this speed, how many hours will it take to reach B?

A: it will take another 2 hours to get to B

If the equation x ^ 2 - (M + 1) x + 1 = 0 about X has two unequal positive roots, find the value range of the real number m; what about two unequal negative roots?
I know the method. For example, the first one is △ > 0, X1 + x2 > 0, X1 * x2 > 0, but there is no solution = =, who can help me calculate~

Let △ 0, X1 + x2 = m + 1 > 0, X1 * x2 = 1 > 0
Solution (M + 1) ^ 2-4 > 0
(m+1)^2>4
M + 1 > 2 or M + 11 or M0 is m > - 1
So m > 1

There is a batch of cement on the construction site. In the first week, 40% of the total cement was used, and in the second week, 20% of the total cement was used. In two weeks, 240 tons of cement were used. How many tons of original cement were used on the construction site
The solution is set up and solved by equation

Original cement of construction site x tons
40%x+20%x=240
60%x=240
x=400
A: 400 tons of cement was used in the construction site

If the quadratic equation x ^ 2 + 3x-m = 0 has a real solution, then the range of M is 0

B ^ 2-4ac = 9-8m, greater than or equal to 0
So m is less than or equal to 9 / 8

A cuboid container with a bottom area of 15 square decimeters contains 3 decimeters of water. After an irregular stone is put into the container (the stone is completely immersed in the water, and the water surface rises by 2 cm). How many cubic decimeters is the volume of the stone?