Finding the minimum value of a2-2a-6 Given that the value of the algebraic formula x2 + y2-14x + 2Y + 50 is 0, find the value of X and y Given x (x + 1) - (x2 + y) = - 3, find the value of x2 + y2-xy ——— two X2 = x square y2 = y square The third problem is known as X (x + 1) - (x2 + y) = - 3 to find (2 / 2 x2 = Y2) - XY

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• 1. Two mathematical problems of probability, When a store holds a celebration activity, customers can randomly select 2 different gifts from the 4 kinds of gifts when their consumption reaches a certain amount. The probability that one of the gifts selected by any two customers has the same variety is zero___ . The startup password of a device is composed of three different numbers from 0 to 9. If the wrong password is input three times in a row, the device will be shut down permanently. The probability that a person who only remembers that the password is composed of three different numbers can start some devices is 0___ .
• 2. In order to reduce the number of matches, 20 teams are divided into two groups (10 teams in each group) for competition, and the probability of (1) the strongest two teams being divided into different groups and (2) the probability of being divided into the same group is calculated.
• 3. There are 10 products in three grades, including 4 first-class products, 3 second-class products and 3 third-class products. If any 2 products are selected from 10 products, the probability of taking out 2 products of the same grade is 0______ ．
• 4. A mathematical problem about probability, the process of solving the problem At present, a, B, C three people participate in a competition, three people have similar strength, and the probability of winning or losing is 50% Q1: A's chance to win two games in a row Probability of Q2: B continuous transmission of two fields Q3: the probability of a losing two games in a row and B losing two games in a row AB AC BA BC CA CB
• 5. Solving mathematical problems! The process of solving problems is required 1. Given that CD is the middle line of triangle ABC, BC = 10cm, AC = 7cm, what is the perimeter difference between triangle BCD and triangle ACD? 2. The perimeter of an isosceles triangle is 25cm. The median line on one waist divides the perimeter into two parts: 3:2? 3. If one internal angle of an isosceles triangle is 80 degrees, then the degrees of the other two internal angles are -? 4. In the triangle ABC, if the angle a is 90 degrees, BD is the bisector of the angle, De is perpendicular to BC and E is the midpoint of BC, then the angle ABC is equal to -? 5. The length of the base of an isosceles triangle is 5cm. If the difference between the two parts is 3cm, the waist length is -? How many significant numbers are there in the approximate number of 24000, accurate to - digits? 7. The 1998 power of minus 2 times its 1999 power equals? 8. Given that the lengths of three sides of a triangle are 14, 4x and 3x respectively, the value range of X is -? 9. For a piece of land with a triangle (acute angle or right angle), it is required to draw a line segment through a certain vertex of the triangle and divide its area into two parts equally. How do you think this line segment should be drawn? How much is the 2005 power of 10.2 multiplied by the 2006 power of 0.5?
• 6. There are 10000 hectares of cultivated land in a certain place. After 10 years of planning, the grain yield per unit area will increase by 20% and the per capita grain share will increase by 10%. If the annual population growth rate is 1%, how many hectares of cultivated land can be reduced at most every year? (accurate to 1 hectare) We should use the permutation and combination quadratic term theorem to solve the problem
• 7. 1. Given that the absolute value of equation x = ax + 1 has a negative number solution but no positive number solution, find the value range of A 2. If a, B and C are all integers, and the absolute value of A-B to the 19th power plus the absolute value of C-A = 1, then what is the absolute value of C-A plus the absolute value of B-C plus the absolute value of B-A
• 8. Tie a cylindrical cake box with plastic rope (as shown in the figure below). The knot is just the center of the bottom. The length of the knot is 25cm (1) How many centimeters does it take to tie this box? (2) How many square centimeters is the area of this part at least?
• 9. How to do this math problem Solving the equation of first degree with one variable One sixth of his life is childhood; He lived one twelfth of his life and grew a beard; He got married and spent another seventh of his life; Five years later, I have a son; But the son lived only half of his father's age; After his son died, he lived for another four years and died 1: His life span 2: The age of a father 3: Age at the time of his son's death
• 10. 1: F (5) = 1, f (1) = 0 for f (x) 2: F (5) = 0, f (1) = 5
• 11. 1. There is a group of numbers arranged according to a certain rule. The order is 2, - 5,9, - 14,20, x, 35 Can you find the value of X? What's the value of X? 2. An ant crawls on a straight line of a chessboard, and the right is the positive direction. For the first time, it climbs one unit to the right from point a, for the second time, it climbs two units to the left to point B, and for the third time, it climbs three units to the right to point C In this way, it has been climbing 20 times to A. point. Given that A. point represents - 18, what number does a point represent? 3. Given that the number represented by point a is - 27 and point B is - 15 on the number axis, find the distance between two points ab To solve this problem, several students put forward the following calculation schemes: A: The larger number minus the smaller number, that is - 15 - (- 27) = 12 B: Subtract the larger number from the smaller number, i.e. - 27 - (- 15) = - 12 C: The absolute value of the difference between the preceding number and the following number, that is | - 27 - (- 15) | = 12 D: The absolute value of the difference between the latter and the former, that is | - 15 - (- 27) | = 12 E: Draw the number axis, actually count the number, that is (here is the number axis), the distance is 12 Which plan do you think is not correct, and explain the reason. Can you think of other plans? What else do you think you should pay attention to the distance between the two points of the ball?
• 12. [1/3-(-1/9)+5/12]×(-36) 19 and 15 / 16 × (- 8) (1 and 1 / 2) × (- 1 and 1 / 3) × (- 1 and 1 / 4) × 1 and 1 / 5) × (- 1 and 1 / 6) × (- 1 and 1 / 7)
• 13. Solving three math problems 1. It is known that a and B are opposite to each other, m and N are reciprocal to each other, and C = 2. Find the value of 2A + 2B + Mn / C 2. If a is less than 0, B is less than 0 and a is less than B, try to determine whether the numbers represented by the following expressions are positive or negative? (1)a+b (2)a-b (3)-a-b (4)b-a 3. Given A-3 + B-4 = 0, find the value of a + B / ab
• 14. 1. The lengths of two sides of a triangle are 8cm and 12cm respectively. Find the perimeter of the triangle 2. The length of three sides of an isosceles triangle is 4cm, (3x-2) cm, (x / 2 + 1) cm respectively. Find the value of X and the length of three sides of the isosceles triangle 3. In triangle ABC, ∠ B is 15 ° smaller than ∠ a, and ∠ A is 15 ° smaller than 2 times of ∠ C. calculate the size of each internal angle —— Write the third question clearly, and it's better to solve three questions together
• 15. Yes, I will- 1. A plane flies in the two cities with a wind speed of 24 km / h. It takes 2 hours and 50 minutes to fly along the wind and 3 hours to fly against the wind. The speed of the ball seamless aircraft is the same as the distance between the two cities 2. It takes 3 hours for a ship to go back and forth between wharf A and wharf B. It takes 30 minutes more for a ship to sail upstream than downstream. If the speed of the ship in still water is 26 km / h, calculate the current speed 3. A ship sails downstream from wharf a to wharf B, and then reverses to wharf C for 9 hours. It is known that the speed of the ship in still water is 7.5 km / h, and the water flow speed is 2.5 km / h. If the distance between wharf A and wharf C is 15 km, the distance between wharf A and wharf B is calculated Find the answers to these three questions I hope I can finish it by the end of the evening
• 16. ① The route from a city to B city is 9750km long. It takes 12.5h for an aircraft to fly from a City downwind to B city, and 13h for it to fly against the wind. The average speed and wind speed of the aircraft can be calculated ② : a unit marches 4 hours a day and 5 hours the next day. It marches 98 km in two days, and the first day is 2 km less than the second day. What is the average speed of the first day and the second day? ③ Objective: to prepare 18kg antiseptic liquid containing 50% medicine with 30% and 75% antiseptic liquid?
• 17. Three math problems, how many can be solved 1. The total weight of the two barrels of oil a and B is 60 kg. The weight ratio of the remaining oil and B is 3:7. How many kg of oil was there in barrel a? 2. To process a batch of parts, the time ratio of a, B and C is 3:4:5? 3. There are three granaries a, B and C, with a total grain weight of 96 tons. If 3 tons are transported from each of the two granaries AB to C, the grain storage ratio of the three granaries is 4:3:1. How many tons of grain were stored in each of the three granaries
• 18. Mathematics problem solving! Urgent! Detailed problem solving process! 1. Calculate the values of 2,2 + 4,2 + 4 + 6,2 + 4 + 6 + 8 respectively 2. According to the calculation of 1., we guess the expression of 2 + 4 + 6 +... + 2n Prove your conjecture by mathematical induction Can you answer the third question in detail
• 19. 1. The number of boys in a class is 5% less than 4, and the number of girls is more than 40%? 2. It takes 6 hours for ship a to travel from the east port to the West Port, and 4 hours for ship B to travel from the West Port to the east port. Now the two ships start from the east port and the West Port at the same time. As a result, they meet at the place 18 kilometers away from the midpoint. How many kilometers is the distance between the east port and the West Port? 3. There are 162 more male workers than female workers in a factory. Now one eleventh of the male workers and 12 female workers are selected to participate in the speech contest. The number of male workers is twice that of female workers. How many female workers are there in this factory? 4. It costs 5.6 yuan to buy three pencils, two erasers and two exercise books in a shop. If it costs 5.9 yuan to buy two pencils, three erasers and three exercise books, how much is each pencil? 5. For a batch of square bricks, if they are put together into a large rectangle with the ratio of length to width of 5:4, the remaining 38 pieces will be left. If they are changed into a large rectangle with the length and width increased by one piece each, the remaining 53 pieces will be left behind. So, how many square bricks are there in total?
• 20. 1. If a, B, C ∈ R +, a + B + C = 1, then the minimum value of A2 + B2 + C2 is_____________ 2. Let x, y ∈ R +, and X + 4Y = 4, find the maximum value of XY__________ 3. Let a = {(x, y) y ≥ 0.5 X-2}, B = {(x, y) y ≤ - x + B} a ∩ B ≠ & # 61638; (1) The value range of B is________ (2) If (x, y) ∈ a ∩ B, and the maximum value of X + 2Y is 9, then the value of B is_________ All three questions should be explained in detail,