1. If the positive integer solution of the inequality about x-k-x+6 > 0 is 1, 2,3, what value should the positive integer k take?
2. It is known that the solution of equation 3 (x-2a)+2 = x-a+ 1 is applicable to inequality 2 (x-5) ≥ 8a, and the value range of a is found.
3. Two sporting goods stores, A and B, sell the same table tennis bat and table tennis. Each pair of ping-pong bats costs 20 yuan, and each box of ping-pong balls costs 5 yuan. Now both stores are engaged in promotional activities. Shop A: Each pair of ping-pong bats is given a box of ping-pong. B shop: 10% off the list price. One party needs to buy 4 sets of rackets and several boxes of table tennis (no less than 4 boxes).
(1) Let the number of ping-pong boxes purchased be X (boxes), and the payment in Store A is Y A (yuan), and the payment in Store B is Y B (yuan). Write the relationship between Y A, Y B and X respectively;
(2) Discuss which store to buy the number of table tennis boxes.
4. A school held a cultural performance to celebrate the 16th National Congress, and awarded 5 first prizes, 25 second prizes 10 and 25 third prizes. The school decided to award prizes to the winning students. The prizes in the same order are the same, and only one of the items listed in the following table can be selected:
Violin sportswear flute dance shoes harmonica photo album notebook piano
Unit price/yuan 120802422 16654
(1) If the higher the prize order, the higher the unit price of the prize, then how much should the school spend on the prize at least?
(2) The school requires that the unit price of the first prize is 5 times that of the second prize, and the unit price of the second prize is 4 times that of the third prize. On the premise that the total cost does not exceed 1 1,000 yuan, how many purchase schemes are there? How much is the most expensive plan?
Answer:
1.x < 6-k, the positive integer solution of x is 1, 2≤k Y B, that is, 5x+60 > 72+4.5x, then X > 24. When Y A < Y B, that is, 5x+60 < 72+4.5x, at this time, X < 24 can be When the number of table tennis boxes is more than 24, it is cost-effective to go to store B; When the number of table tennis boxes is not less than 4 boxes but less than 24 boxes, it is more cost-effective to go to shop A.
4.( 1) According to the meaning of the question, the first, second and third prizes can be set as photo albums, notebooks and pens. At this time, the cost is 5× 6+10× 5+25× 4 =180 (yuan);
(2) If the unit price of the third prize is X yuan, then the unit price of the second prize should be 4x yuan and the unit price of the first prize should be 20x yuan. The meaning of the problem should be 5× 20x+10× 4x+25× x ≤1000, and the solution is x≤6.06 (yuan). So X can be selected from 6 yuan, 5 yuan and 4 yuan. So 4x should be 24 yuan, 20 yuan, 16 yuan, and 20x should be 120 yuan, 100 Yuan, 80 yuan. Looking at the unit prices of various prizes provided in the table, we can see that 120 yuan, 24 yuan, 6 yuan, 80 yuan, 16 yuan and 4 yuan are suitable for the types of questions, so there are two purchase schemes. Scheme 1: The unit price of prizes is 120 yuan, 24 yuan and 6 yuan, and the required expenses are 990 yuan; Scheme 2: The unit price of prizes is 80 yuan, 16 yuan and 4 yuan, and the required expenses are 660 yuan. Thus, the most expensive plan needs 990 yuan.
4.8 Properties of Similar Polygons
Innovative training 2 1:
1. As shown in Figure (a), AB⊥BD, CD⊥BD, and the vertical feet are B, D, AD and BC respectively. If E is taken as EF⊥BD, what can be obtained? If the vertical direction in Figure (a) is changed to the oblique direction, as shown in Figure (b), in which AB∨CD, AD and BC intersect at E, if E, EF∨AB intersects with BD at F, how can you ask:
( 1)? Is it still valid now? Please explain the reason.
(2) Try to find out the relationship between S△ABD, S△BED and S△BDC, and explain the reasons.