A store sells a commodity with a purchase price of 8 yuan at 10 yuan per piece, and 200 pieces can be sold every day. Now it adopts the method of increasing the selling price of the commodity and reducing the sales volume to increase the profit. If the selling price of the commodity increases by 0.5 yuan per piece, the sales volume will decrease by 10 yuan. How much yuan should the selling price be set to make the daily profit 640 yuan? How many pieces can be sold every day?

A store sells a commodity with a purchase price of 8 yuan at 10 yuan per piece, and 200 pieces can be sold every day. Now it adopts the method of increasing the selling price of the commodity and reducing the sales volume to increase the profit. If the selling price of the commodity increases by 0.5 yuan per piece, the sales volume will decrease by 10 yuan. How much yuan should the selling price be set to make the daily profit 640 yuan? How many pieces can be sold every day?

If the selling price is set at x yuan, the profit can reach 640 yuan / day (x > 10), then the profit of each commodity is X-8 yuan. If sold every day: 200-10 [(X-10) △ 0.5] = 200-20x + 200 = 400-20x pieces ∧ (X-8) (400-20x) = 640 (X-8) (20-x) = 32x ^ 2-28x + 192 = 0 (X-12) (x-16) = 0x = 12 or x = 16, substitute 400-20x = 16

Probability (22 19:34:11)
From the four line segments of 3cm, 5cm, 7cm and xcm in length (x is an integer), what is the value of line segment x if the probability of forming a triangle is 1 / 4?

The probability is 1 / 4, 3cm, 5cm, 7cm can form a triangle, so x can not form a triangle with others, X12 and X belongs to an integer

In order to organize a basketball league match, the competition system is single circle (one match between two teams), 28 matches are planned, and () teams should be invited to participate in the match
A. 6B. 7C. 8D. 9

There are x teams, each team has to play (x-1) games, but there is only one game between the two teams, X (x-1) △ 2 = 28, the solution is x = 8 or - 7 (discard). Therefore, 8 teams should be invited to participate in the game

Quadratic function (important process) (17 19:37:44)
 
The shape and opening direction of y = -1 / 4x2-3 are all the same, and the vertex coordinates are (2,4) (- 2,4) and the vertex coordinates are the same, the shape and opening direction of y = -1 / 4x2-3, and the vertex coordinates are all the same, and the vertex coordinates are the same, and the coordinates of the vertex coordinates are (- 2,4) and the coordinates of-2,4, and the coordinates of 35; 35\35;#\\106;;; \\\\35\\35\\###\\\\35\\\\\\itwas also shown that the #;; \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\it's 160;                                                                                              
(1) Find the function analytic formula of this parabola? (?) 160; (?) 160; (?) 160; (?) 160; (?) 160; (?) 160; (2) please give a translation scheme for the parabola in question (1) so that the translated parabola passes through the origin?

Y = - 1 / 4 (X-H) & sup2; + K brings the vertex into y = - 1 / 4 (x + 2) & sup2; + 4 so y = - X & sup2; + 4-x + 3 suppose to move down a, then the vertex is up (- 2,4-a) so y = - 1 / 4 (x + 2) & sup2; + 4-A goes through the origin x = 0, y = 0 so + = - 1 / 4 * 2 & sup2; + 4-AA = 3 so move down 3 units

Mathematics probability of junior three, please answer in detail, thank you! (22 19:30:9)
There are 10 red balls and several white balls in a pocket. The number of white balls is estimated by the following experiments: Take 8 balls out of the pocket at a time, find out the ratio of the number of red balls to 8, put the balls back into the pocket, mix them well, repeat the above process, and the average ratio of the number of red balls to 8 is 1 / 4?

The average is 1 / 4, indicating that the probability of a red ball is 1 / 4
The total number of balls is 40, white ball 40-10 = 30

It is known that the reciprocal sum of the two real number roots of the quadratic equation (M2-1) X2 - (2m-1) x + 1 = 0 (M is a real number) with respect to X is greater than zero

Let the two equations be X1 and X2 respectively. According to the relationship between the root and coefficient, we can get: X1 + x2 = 2m − 1m2 − 1, x1 · x2 = 1m2 − 1 ∵ 1x1 + 1x2 = X1 + x2x1x2 > 0, that is, 2m − 11 > 0. The solution is: M > 12 and m ≠ 1 △ = [- (2m-1)] 2-4 (M2-1) = 4m2-4m + 1-4m2 + 4 = - 4m + 5 ∵ the given equation has two real roots, that is, - 4m + 5 ≥ 0 ∵ m ≤ 54

Circle (22 18:19:10)
If the minimum distance between a point and a circle is 4cm and the maximum distance is 9cm, the radius of the circle is_____
 
Please write down the specific process

You first connect this point (assumed to be the H point) with the center of the circle, and set the intersection circle at a and B
Then ha = 4, Hb = 9
1. In the park
Circle radius r = (9-4) / 2 = 2.5
If you want to prove why OA is the shortest, just take a point P (different from a and b) on the circle and connect HP and AP, then in △ HAP, ha

Taking o as the center of the circle, there is a reef within 8 nautical miles. When a ship arrives at a 16 nautical miles west of o point and receives a message, the ship will sail at least to the East and south to avoid hitting the reef

If the line of travel is the tangent line of the circle passing through point a, and the tangent point is B, then the triangle OAB is a right triangle, OA = 16, OB = 8, then the angle OAB = 30 degrees, that is, the ship will sail 30 degrees east by south

Application of quadratic function (229:2:8)
It is known that m, n are two real roots of the equation x ^ 2-6x + 5 = 0, and m
(1) Find the analytical formula of the parabola;
(2) Let the other intersection of the parabola in (1) and the x-axis be C, and the vertex of the parabola be d. try to find out the coordinates of C and D and the area of the triangle BCD;
(3) P is a point on the line OC, passing through P as pH, perpendicular to X axis, and intersecting with the parabola at H point. If the straight line BC divides the triangle PCH into two parts whose area ratio is 2:3, the coordinates of point P are requested

I have done this problem
1) Two real roots X1 = 1, X2 = 5, m of the equation x & sup2; - 6x + 5 = 0

A container is filled with 20 liters of pure alcohol. The first time you pour out several liters, you fill it with water. The second time you pour out the same amount of liquid, and then you fill it with water. This is the remaining pure alcohol in the container. It's 5 jin. Try to find the number of liters of liquid poured out each time

Let X be the first two times inverted
Then pour out for the first time and fill the container with 20-x alcohol + X water
Let's say that water and alcohol are completely fused, and half of the X poured out in the second time is water and half alcohol
Then pour it out for the second time and fill it with 20-x-x / 2 alcohol and X + X / 2 water
20-x-x/2=5
15=3x/2
x=10