2. If m < 0, n > 0, | m |
4. Let (3x-1) 7 = A7X7+A6X6+…+A1X+A0, and try to find the value of A0+A2+A4+A6. 6. Solve equation 2 | X+ 1 | | X-3 | = 6. 8.
10.x, y and z are non-negative real numbers, which satisfy the following conditions: x+3y+2z = 3, 3x+3y+z = 4, and find the maximum and minimum values of u = 3x-2y+4z.
1 1. Find the quotient and remainder of x4-2x3+x2+2x- 1 divided by x2+x+ 1.
19. Can the sum of the number obtained by arbitrarily changing the order of a three-digit number and the original number be 999? Explain why.
20. There is a piece of paper with 8 rows and 8 columns, in which 32 squares are randomly painted black and the remaining 32 squares are painted white. Next, the color grid paper is operated, and each operation changes the color of each square in any horizontal or vertical column at the same time. Can you finally get a grid paper with only one black square?
2 1. If both positive integers p and p+2 are prime numbers greater than 3, it is proved that: 6 | (P+ 1). 22. Let n be the smallest positive integer satisfying the following conditions, a multiple of 75, and it happens to have.
23. There are several stools and chairs in the room. Each stool has three legs and each chair has four legs. When they are all seated, * * * has 43 legs (including everyone's two legs). How many people are there in the room? 24. Find the integer solution of the indefinite equation 49x-56y+ 14z=35. 25. Eight men and eight women dance in groups. (1) If men and women stand in two rows;
(2) If men and women stand in two rows, in no particular order, only consider how men and women form partners. How many different situations are there? 26. 1, 2, 3, 4, 5, how many numbers are greater than 34 152? 27.A train is 92 meters long and B train is 84 meters long. If they travel in the opposite direction, they will miss each other after 1.5 seconds. If they travel in the same direction, they will miss each other in six seconds. Find the speed of two trains.
28. The two production teams of Party A and Party B grow the same vegetables. Four days later, Team A will finish the rest alone. It will take two more days. If Party A finishes all the tasks by itself three days faster than Party B, how many days does it take to ask Party A to finish it by itself?
29. A ship set out for a port 240 nautical miles apart, and its speed dropped by 65,438+00 nautical miles per hour 48 nautical miles before reaching its destination. The total time it takes after its arrival is equal to the original speed minus 4 knots, so find the original speed.
3 1. It is known that the sum of the original prices of two commodities is 150 yuan. Due to market changes, the price of the first commodity decreased by 10%, and the price of the second commodity increased by 20%. After the price adjustment, the sum of the unit prices of the first and second commodities decreases by 1%. What are the original unit prices of the first and second commodities respectively? Xiaohong bought two children's toothbrushes and three toothpastes in the shop last summer vacation, and just ran out of money with her. It is known that each toothpaste is more than each toothbrush 1 yuan. This summer, she took the same money to the store and bought the same toothbrush and toothpaste. Because each toothbrush rose to 1.68 yuan this year and the price of each toothpaste rose by 30%, Xiaohong had to buy two toothbrushes and two toothpastes, and she got back 40 cents. How much is each toothpaste?
33. If a shopping mall sells goods with a unit price of 8 yuan per piece 12 yuan, it can sell 400 pieces every day. According to experience, if each piece is sold less 1 yuan, you can sell more than 200 pieces every day. How much should each piece be reduced to get the best benefit?
34. The distance from Town A to Town B is 28 kilometers. Today, A rode his bike at a speed of 0.4km/min, and set out from Town A to Town B. After 25 minutes, B rode his bike to catch up with A at a speed of 0.6km/min. How many minutes does it take to catch up with A?
35. There are three kinds of alloys: the first contains 60% copper and 40% manganese; The second type contains manganese 10% and nickel 90%; The third alloy contains 20% copper, 50% manganese and 30% nickel. Now a new alloy containing 45% nickel is composed of these three alloys, and its weight is 1 kg.
(1) Try to express the weight of the second alloy by the weight of the first alloy in the new alloy; (2) Find out the weight range of the second alloy in the new alloy; (3) Find out the weight range of manganese in the new alloy.
Is that enough?