1. Use large and small trucks to transport 360 pieces of machinery and equipment.
Option 1: Use large trucks to transport the equipment and the rest in small trucks. trucks are needed. ;
Option 2: The equipment is transported by large trucks, and the rest is transported by small trucks;
Option 3: The equipment is necessary. transported by large trucks, and the rest is transported by small trucks. For transportation, 26 trucks are needed;
(1) How many pieces of machinery and equipment can each large and small truck transport?
(2) If the freight of each large truck is higher than the freight of each small truck by % (>0), please choose a plan to get the lowest freight and explain the reason. p>
2. There are two straight lines 1 and 2 in the rectangular coordinate system of the plane. The analytical formula for the straight line 1 is
If the coordination paperndata is folded so that the straight lines 1 and 2. coincide, then the point ( -2, 0) also coincides with the point (0, 2).
(1) Find the analytical formula of the line 2.
(2) Suppose that the straight lines 1 and 2 intersect at the point M, Q: Is there such a straight line: y=x+t, such that if the graph paper is folded along the straight line, point M falls exactly on the x-axis? If it exists, find the analytical formula for the line; if it does not exist, please explain the reason.
(3) Let the point of intersection of line 2 and the x axis be A, and the point of intersection of the straight line 2 and the y axis is B. Take the point C (0, ) which is the center of the circle and the length of CA is the radius. Draw a straight line through the point. B (does not coincide with the y axis). It intersects ⊙C at two points D and E (point D is below point E) < /p>
①Draw the graph in the rectangular coordinate systemareas as shown in the figure;
②Suppose OD=x, the area of △BOD is S1 and the area of △BEC is S2, find the functional relationship between y and the height image changing with dripping time .< /p>
3.
Give the following correspondence:
(1): (a)——(e) (2): (b)—— (f) (3): (c)——h (4): (d)——(g) The correct ones are
(A) (1) and (2) (B) (2 ) and (3) (C) (1) and (3) (D) (3) and (4)
4. The daily profit of a certain amusement park y The functional relationship between (yuan) and tickets sold The analytical formula is:
When 200≤x≤300 and x is an integer, the analytical formula of the function of y with respect to
(3) Please think about and explain the real meaning of the intersection point (0, -1000) between the image and the y axis.
(4) Based on picture, please provide 2 informationadditional s.
5. As shown in Figure 9, point D is the midpoint of the line segment AB, point C is the vertical plane of the line segment AB
< p>Any point on the bisector, DE⊥AC is at the point E , DF⊥ BC at point F.(1) Check: CE=CF;
(2) When point C moves to what position does the quadrilateral CEDF become a square ?
Please explain the reason.
6. Nanquan Car Rental Company has a total of 30 taxis, including 20 type A cars and 10 type B cars. These 30 cars are now rented to travel agencies in places A and B. 20 of them are sent to location A and 10 are sent to place B. Travel agencies and car rental companies in both locations have agreed on the daily price as follows. :
Rent for each type A car (yuan/day) Rent for each type B car (yuan/day)
Location A 1000 800
Location B 900 600
(1) Suppose vehicles of type B are shipped to location A. The total rent earned by the leasing company for these 30 vehicles per day is (yuan). Find the analytical expression for the function. between and and note the independent variables. Range of values;
(2) If the total rental amount obtained by the leasing company for these 30 cars per day is not less than 26,800 yuan, please explain how many distributions. there are plans and design the different plans. ;
(3) If you want these 30 cars to get the most rent each day, please propose a reasonable distribution plan to the leasing company.
7. There is a container with inlet and outlet pipes, and the amount of water in and out per unit time is certain. We know that the volume of the container is 600 liters. It is also known that the empty container can be filled in 10 minutes by only opening the tuyau water inlet. If the inlet and outlet pipes are opened at the same time, filling is completed in 10 minutes. the full container can be emptied in 20 minutes. Now we know that there are 200 liters of water in the swimming pool, first open the water inlet pipe for 5 minutes, then open the outlet pipe and open both pipes at the same time until until all the water in the container is drained. This can correctly reflect the change in the volume of water Q (liters) in the container with time t (minutes) during this process. ) The image of change is ( )
Question: ⑴ Before buying the water dispenser, how much money eachstudent spend on average to buy pure water to drink throughout the year?
⑵ Please calculate: After purchasing water dispensers to solve the students' drinking water problem, how many yuan will each class spend in total this year?
⑶ After implementing this measure to facilitate students, Dongpo Middle School will save a total of yuan for all students per year
9 (the total score for this question is 12. points) As shown in Figure 12, the equilateral △ABC of side length 2 is a cross section of a triangular prism. A beam of light arrives at point D on side BC in the direction perpendicular to side AB (point D does not). coincide with points B and C. ), the reflected light is emitted on the AC side. NSP is the normal line. Let the length of BE be x and the length of AF be y.
(1) Find the functional relationship between y and x and writez the range of values of the independent variable x;
(2) In the rectangular coordinate system of the given plane Draw the graph of this function.
Figure 26
10. Xiao Wang, a salesman from Shijiazhuang Xingda Company, went to Harbin to negotiate business. The company first sent a car to take him to Beijing (this is known). from Shijiazhuang to Beijing Airport (the distance is 360 kilometers), then transferred to a plane to Harbin. However, after leaving for a while, he found that an important document had been left at the company, so the company sent car B to deliver it. the document. At the same time, Xiao Wang returned to Car A to greet him, and then continued to move forward. In the figure, the broken line O-A-B-D- and the line segment CB respectively represent the image of the distance y (km) of car A and car B from Shijiazhuang changing with time t (time). Ranswer the questions based on the images:
⑴When did Xiao Wang find out that the files had been left at the company and start returning them?
⑵ When will truck B sent by the company deliver the documents to Xiao Wang?
⑶ If the plane takes off at 1:00 p.m., ask Xiao Wang if he can take the plane?
11． A newsstand in a certain city buys an evening newspaper from a media company for 0.30 yuan per copy and resells it for 0.50 yuan. Unsold newspapers can be returned to the newspaper company, but the amount of money returned per copy. is the same as the amount returned. The quantity relationship of newspapers is as follows:
Returned quantity 5 10 15 20 25 30 or more
Price (yuan/copy) 0.25 0.20 0.15. 0.10 0.05 0.02
A market study revealed that in a month (counted over 30 days), 150 copies/day can be sold for 20 days, and only 100 copies/day can be sold for 10 days, and the newspaper company stipulates that newspapers are sold in bulk at the stands every day. The quantities must be the same.
(1) By drawing points in the coordinate system (taking the amount of money returned as the ordinate and the number of newspapers reported as the abscissa), the points are distributed in Analyze the functional relationship between the amount of money returned y (yuan) and the number of newspapers returned k (copies).
(2) If the newsstand buys x copies of newspapers every day at newspaper (Satisfactory 100 12． The Guangming farm currently has 10,000 kg of some plants and plans to use them all to produce high-tech medicines and health foods. If high quality medicationstechnology are produced, 1 kg of this plant can extract 0.01 kg of high-tech drugs, which will produce 0.1 kg of pollutants; if health food is produced, 1 kg of this plant can be transformed into 0.2 kg of health food. which will produce 0.04 kg of pollutants. It is known that a profit of 5,000 yuan can be obtained for each kilogram of high-tech medicine produced, and a profit of 100 yuan can be obtained for each kilogram of health food produced. To ensure that the total profit is not less than 410,000 yuan and the total amount of pollutants produced does not exceed 880 kg, determine the weight range of the factory used to produce high-tech medicines. 13． If the point P rotates 180° around the fixed point M and then coincides with the point Q, then the point P and the point Q are said to be symmetrical with respect to the point M, and the fixed point M is called the center of symmetry. At this moment, M ist the midpoint of the line segment PQ. As shown in the figure, in the rectangular coordinate system, the coordinates of vertices A, B and O of ⊿ABO are (1,0), (0,1) and (0, 0) respectively. Two adjacent points in the sequence of points P1, P2, P3,... are symmetrical with respect to a vertex of ⊿ABO: Point P1 and point P2 are symmetrical with respect to point A, and point P2 and point P3 are symmetrical with respect to point B., Points P3 and P4 are symmetrical with respect to point O, point P4 and point P5 are symmetrical with respect to point A, point P5 and point P6 are symmetrical with respect to point B, point P6 and point P7 are symmetrical with respect to point O is symmetrical,…. The centers of symmetry are A, B, O, A, B, O,..., and these centers of symmetry rotate in sequence. We know that the coordinates of point P1 are (1, 1). Try to find the coordinates of points P2, P7 and P100. 14． During the "May 1st Golden Week", Xiao Ming and his parents took a cruise from point A to point B for sightseeing. When they saw table (1) in the ticket hall, his father said to Xiao Ming, “I’m here.” to test yourself. Can you find out the mileage?" Is there any relationship between this and the fare?" Xiao Ming nodded and said: "The relationship between mileage and fare is a linear function, in particular... ". On the cruise ship, he noticed the table (2), thought about it and said to his father: "If the speed of the cruise ship remains unchanged in calm water, then I can also calculate its speed and the speed of the water flow. » Dad said, “You are so smart! » Dear classmate, do you know how Xiao Ming found out? Please work with Xiao Ming to find out: (1) The functional relationship between fare (yuan) and mileage (kilometers); Departure time and arrival timearrival
B→A 9:20 a.m. 10:00 a.m.
A→B 10:20 a.m. 11:20 a.m.
… … …
(2) The speed of the cruise ship in still water and the speed of the water flow.
Mileage (km) Fare (yuan) Departure time and arrival time
A→B 16 38 A→B 8:00 a.m. 9:00 a.m.
A → C20 46 B→A 9:20 a.m. 10:00 a.m.
A→D 10 26 A→B 10:20 a.m. 11:20 a.m.
… … … … …
Table (1) Table (2)
Departure time and arrival time
A→B 8:00 a.m. 9:00 a.m.
B→A 9:20 a.m. 10:00 a.m.
A→B 10:20 a.m. 11:20 a.m.
… … …
Departure time arrival time
A →B 8:00 a.m. 9:00 a.m.
B→A 9:20 a.m. 10:00 a.m.< /p>
A→B 10:20 a.m. 11:20 a.m.
… … …
First, air quality is important. Since all the decoration materials of the finely decorated house are purchased by the developer, the owner has no way to monitor them. Particular attention must therefore be paid to the materials used.
Thus, when handing over a house, it is preferableThe to carry testing tools to test the air quality in the house. It is best to research online in advance to see how well the air quality meets standards. Only in this way can we treat developers calmly.
Secondly, the decoration materials used should be inspected. Materials used by developers must comply with national standards. In order to make more money, some developers use substandard materials and hazardous substances far exceed standards.
After completion, you can ask a professional team to check whether they are qualified. At the same time, it is very important to require the developer to issue the relevant acceptance documents.
Third, pay special attention to some hidden projects. For example, if the tightness of the mthe house is in place, how the water circuits are installed, what materials are used for sanitary ceilings, etc.
These locations are relatively detailed and hidden, and can easily be overlooked by everyone. When checking receipt, everyone usually focuses on the places visible at a glance, but these places will only be exposed after being used for a period of time.
So you can bring a few “experts” with you to the receiving inspection to help you review it together. If there is a problem, you can report it on site.
Fourth, in addition to being inside your own home, you should also pay special attention to things outside your home. Includes public stands, location, stairwells, greening, etc. must also be reviewed. Do not rush to confirm acceptance, otherwise it will beIt is difficult to modify it after signing.