1 1. If the linear function y=x+b passes through point A (0 0,3), then b = _ _ _ _ _ _ _ _ _ _ _ _ _
12. A middle school held a broadcast operation competition, and six judges scored a lesson as follows:
7.5, 8.2, 7.8, 9.0, 8. 1, 7.9.
The average score after removing the highest score and the lowest score is _ _ _ _ _ _ _ _ _ _
13. As shown in the figure, in the rectangular ABCD, two diagonal lines AC and BD intersect at point O, and AB=OA=4, then AD = _ _ _ _ _ _ _ _
14. As shown in the figure, in the right-angle ABCDO, the coordinates of C and A are (-4,0) and (0,2) respectively, so the coordinate of B is ().
15. Writing two irrational numbers makes the product of these two irrational numbers rational, so these two irrational numbers can be _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
Fourth, solve the following problems
20. For a positive △ABC with a side length of 2, establish an appropriate rectangular coordinate system and write the coordinates of each vertex.
2 1. In the plane rectangular coordinate system, the points with coordinates (0,4), (1 0), (2,4), (3,0) and (4,4) are connected in turn by line segments to form a pattern.
(1) Draw this pattern in the following coordinate system.
(2) If the horizontal coordinates of the above points remain unchanged, the vertical coordinates are multiplied by-1 respectively, and then the obtained points are connected by line segments in turn. What is the change between the obtained pattern and the original pattern?
22. Candles burn, consuming 4.8 centimeters per hour. It is known that the original length of the candle is 24 cm, and the remaining length after burning X Xiaoming is Y cm.
(1) Write the functional relationship between y and x.
(2) How long will it take to burn out the candles?
23. A sports shoes counter sells the following sports shoes a day:
Size 172 1222324
Quantity 1 152 1
(1) Find the average, mode and median of the sizes of sports shoes sold;
(2) What size sports shoes do you think should be added to this counter?
Fifth, solve application problems with equations.
Xiaoying plays basketball with her father. They agreed that Xiaoying played 1 to get 3 points, and Dad played 1 to get 1. As a result, they hit 20 * *. After calculation, they found that their scores were just equal. Do you know how many they played?
7.24. A closed central symmetrical figure can be divided into two parts with equal area by making a straight line through the symmetrical center.
For example, a straight line passing through the center of the circle divides the circle into two parts with equal area, as shown in the figure.
Please draw a straight line in Figure 2 and Figure 3 to divide them into two parts with equal areas, where Figure 2 is a parallelogram and Figure 3 is ∠ A = ∠ B = ∠ C = ∠ D = ∠ E = ∠ EFD = 90.
A school is going to buy a batch of computers.
Scheme 1: local purchase, each set needs 7000 yuan;
Option 2: It costs 6000 yuan to buy each one in other places, and other expenses, such as transportation, total 3000 yuan.
To set up a school, X computers need to be added, and the cost of scheme 1 and scheme 2 is Y and Y yuan respectively.
(1) Write the relationship between Y and X and the relationship between Y and X respectively.
(2) When how many computers are added to the school, are the costs of the two schemes the same?
(3) If the school needs to buy 50 computers, which scheme will save money? Tell me your reasons.
27. As shown in the figure, in the isosceles trapezoid ABCD, AD∑BC, AB=CD, AD = 1cm, BC=30cm, the moving point P starts from point A and moves along the edge of AD at a speed of1cm per second, while the moving point Q starts from point C and moves along the edge of CB at a speed of 3cm per second. When one of the points reaches the end point,
What is the value of (1)t, and the quadrilateral ABQP is a parallelogram?
(2) Can quadrilateral ABQP become isosceles trapezoid? If yes, find the value of t; If not, please explain why.