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50 math problems in the first volume of the second day of junior high school
7. (Ziyang, 2008) It is known that A, B and C are three sides of a triangle, so the root of equation (a+b)x2+2cx+(a+b)=0 is ().

A. there is no real number root b, and there may be only one real number root.

C. there are two equal real roots. D. there are two unequal real roots.

A: A.

13. (Yangzhou, 2008) If two quadratic equations ax2+2x-5=0 about x exist and only one of them is between 0 and 1 (excluding 0 and 1), then the value range of a is ().

a、a3 C、a-3

Answer: b

9. (Taiwan Province Province in 2008) Which of the following statements is correct about the solution of equation 49x2-98x- 1 = 0? ( )

(a) No solution (b) There are two positive roots (c) There are two negative roots (d) There is one positive root and one negative root.

Answer: d

2. (Weifang City, Shandong Province, 2008) It is known that the inverse proportional function, when x > 0, y increases with the increase of x, then the root of the equation about x is ().

A. There are two positive roots B. There are two negative roots C. There is one positive root and one negative root D. There is no real root.

Answer: c

1. (Weihai, Shandong, 2008) About the root of the quadratic equation of X, it is

A. There are two unequal real roots B. There are two equal real roots.

C. there is no real root d, so it cannot be determined.

9. (Jingzhou, Hubei, 2008) The sum of the two real roots of the equation about X is m, and the inequality about Y has a real number solution, then the value range of K is _ _ _ _ _ _ _ _ _ _ _ _ _.

2. There are several ways to judge the congruence of two triangles besides definitions. Can be abbreviated as _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _______; _______; _________.

1. The right sides of a right triangle are 3cm and 5cm respectively. After proper cutting, this right triangle can be put together into a square without weight and leakage. Excuse me, what is the side length of this square?

(The result is accurate to 0.0 1cm)

2. Xiao Ming and Xiao Fan got different answers when they answered "Simplify first, then evaluate: the square of1-2a+ A under the radical A+,where a=9". Xiao Ming answered: the square of (1-a) under the radical A+=a+ (65438+).

(1). Whose answer is wrong?

(2) The wrong answer is what is the nature of quadratic radical?

It is proved that the midline of the hypotenuse of a right triangle is equal to half of the hypotenuse.

Proof that half of the hypotenuse of a right triangle is equal to the midline of the hypotenuse

It is proved that the right angle side opposite to the 30 angle is half of the other side.

1. It is known that the square root of 2a- 1 is +-3, and the arithmetic square root of 3a+b- 1 is 4. Find the square root of a+2b.

2. The volume of a cube is 8 times that of the original one, and how many times is its side length? 27 times the original volume? 1000 times of the original sound volume? Use the law you found to solve the following problems: If the cube root of 0.00000526 =0.0 1739, the cube root of X = 17.39, and the cube root of -5.26 =y, find the values of X and Y. ..

1. Xiaohua wants to design a ball-touching game so that the probability of hitting the red ball is equal to 1. But his mother wants his design to meet the following requirements: (1) At least four colors of balls (2) At least one yellow ball (3) It embodies the fairness of the game.

How should the floret be designed?

2. A newly-built four-story teaching building in a middle school has eight classrooms on each floor, and there are four doors in and out of the building, two of which are the same size and two side doors are the same size. During the safety inspection, four doors were tested: when one main entrance and two side doors were opened at the same time, 560 students could pass through in 2 minutes; When a colleague opens a front door and a side door, 800 students can pass in 4 minutes.

(1) How many students can pass through a main entrance and a side door every minute?

(2) During the inspection, it was found that the efficiency of going out was reduced by 20% due to the crowded students in an emergency. According to the safety inspection regulations, in case of emergency, students in the whole building should be evacuated safely through these four doors within 5 minutes. Suppose there are at most 45 students in each classroom of this teaching building. Excuse me: Do these four doors meet the safety requirements? Please explain the reason.