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Special topics on big math problems
First of all, functional exercises:

1, and the straight line y=kx+b intersects the x axis at point (2,0), then the solution of the equation about x -kx+b=0 is _ _ _ _ _

2. The solution of the given equation kx+b=0 is x=- 1, and the intersection of the straight line y=-kx-b and the X axis is _ _ _ _ _.

3. It is known that the solutions of equation mx+2=0 and equation nx- 1=0 are both x=2, so the area of the triangle surrounded by straight line y=mx+2, y=nx- 1 and Y axis is _ _ _

4. Find the value of n/m by knowing the point where the straight line y=mx+ 1 intersects with the straight line y=nx+4 on the X axis. (process)

5. It is known that the solution of the equation kx+b=0 about X is x=2, and the linear function y=kx+b is shifted to the left by two unit lengths, and then the analytical expression of the linear function is obtained through the point (4, 1).

Second, one-dimensional linear inequality.

1. An aquatic product market management department plans to build a greenhouse with an area of 2,400 square meters. There are 80 type A and B shops in the greenhouse. The average area of each A-type store is 28 square meters, and the monthly rental fee in 400 yuan is 20 square meters. The monthly fee is 360 yuan, and the construction area of all storefronts is not less than 85% of the total area of greenhouses.

(1) Try to determine the number of Type A stores?

(2) The greenhouse management department understands that the occupancy rate of Type A storefront is 75%, and that of Type B storefront is 90%. How many types of stores should be built to make the monthly rent of stores the highest?

2. A furniture store sells tables and chairs, and the unit price is one in 300 yuan and one in 60 yuan. The furniture store has made two preferential schemes: (1) buy a table and get two chairs; (2) Pay 87.5% of the total price. A company needs to buy five tables and several chairs (not less than 10). If it is known that X chairs are to be purchased and the company purchases the same number of chairs, which scheme is more economical?

3. A logistics company wants to transport 300 tons of materials to a certain place, and there are two kinds of vehicles, A and B, which can be used. It is known that each Type A car can carry 20 tons, and each Type B car can carry 15 tons. Shipment of 300 tons of materials without overloading each vehicle. Q: When five A-cars are called, how many B-cars should be called at least?

The school allocated several dormitories to the girls in Class 1, Grade 7. It is understood that there are less than 35 girls in this class. If there are five people in each room, the remaining five people will have no place to live. If there are 8 people in each room, one room will be vacant and one room will be unsatisfactory. How many dorms and girls are there?

5. The planned construction area of aquatic product market management department is 2,400 square meters? Market. There are 80 A-type and B-type stores in the shed. The average area of each type A storefront is 28m? Monthly fee 400 yuan; The average area of each B-store is 20m? Monthly fee 360 yuan. The construction area of all storefronts shall not be less than 80% of the total greenhouse area and shall not exceed 85% of the total greenhouse area. Try to make sure that there are several schemes to establish two types of stores, A and B.