Mathematics in the first year of junior high school, help me in the mathematics of the first year of

1. 5x+1 2x-3 0 is required

It is to find (5x+1)*(2x-3) 0

Solution-1 52, from the known, the original salt weight should be 10x5% = kg, and the total weight of the mixed brine is 25 kg, the concentration is not less than 8%, not higher than 14%, then the mixed salt weight is not less than 25x8% = 2 kg, not higher than 25x14% = kg.

Available equation <=15p<=

Get 10% p 20%.

Synthesis: Solution: First get the salt content of 5% brine 10*5%=8% according to the meaning of the question (15*p + 14% solution to get 10% p 20%.

Question 1: First of all, 2x-3 cannot be equal to 0, then x is not equal to 3 2, and there are 2 cases.

In the first case: 5x+1>0 and 2x-3<0 at the same time, we get -1 50, we get x<-1 5 and x>3 2

Question 2: From the known, the original salt weight should be 10x5%=kg, and the total weight of the mixed brine is 25kg, the concentration is not less than 8%, not higher than 14%, then the mixed salt weight is not less than 25x8%=2 kg, not higher than 25x14%=kg.

Available equation <=15p<=

Get 10% p 20%.

Synthesis: Solution: First get the salt content of 5% brine 10*5%=8% according to the meaning of the question (15*p + 14% solution to get 10% p 20%.

Question 1: 5 11x-3<0,5 11x<3,5 335 33

Question 2: The concentration after mixing satisfies:

8%<(10*5%)+15*p)) (10+15)<14%, i.e. 8%<(14%)

i.e. 8< (2+60p) <14

i.e. 6<60p<12

Finally, the concentration of brine p ranged from 10% to 20%.

Only 1...Determine the positive and negative of x and do it yourself. No, I'll help you.

Solution: Because there are 92 students in School A and School B, there are more students in School A than School B, so there are more than 46 students in School A and less than 46 students in School B.

And because there are not enough 90 students in school A, the way to buy clothing in school A is: 46 to 90 sets, 50 yuan per set. School B can purchase clothing from 1 to 45 sets, and each set is 60 yuan.

If there are x students in school A, there will be 92-x students in school B.

50x+60(92-x)=5000

50x+5520-60x=5000

10x=520

x=52So: 52 students in school A and 92-52=40 students in school B.

If there are 10 students from school A who cannot participate in the performance, the number of students participating in the performance is: 52-10=42 students.

Purchase plan 1: 1 to 45 sets, 60 yuan per set, buy 42 sets.

42*60=2520 (yuan).

Purchase plan 2: 46 to 90 sets, 50 yuan per set, buy 46 sets.

46*50=2300 (yuan).

Therefore: plan 2, that is, buy 46 sets of clothing, each set of 50 yuan plan, more money-saving.

Description: After entering junior high school, it is necessary to discuss it separately according to different situations, and the brain ribs should be more complicated, and no possible situations can be missed, which is the biggest difference between junior high school mathematics and primary school arithmetic. Training in this area should be strengthened.

Analytical idea: If there are x people in school A, then there are (92-x) people in school B. Next, we will analyze the value range of x separately.

1. When x is less than or equal to 45, there is: 60x+50(92-x)=5000 (note: according to the known conditions of this question, this equation does not exist, because "the number of students in school A is more than that of school B").

I'm writing this step here because among other problems, this step may be indispensable, and I'm just giving you ideas for how to solve the problem.)

2. When x is greater than or equal to 46 and less than or equal to 90, I believe you can write the equation.

。I believe you can do the following questions. I wish you progress in your studies!!

X and Y are expressed with m, x=1-my=2m-23, and then brought in x+y=7 to give m=203

Treat a as a known number, denote x, y as a, solve the equation, x=2a-12, y=8-a, back generation, a=26

Let the velocity of A be x and the velocity of B be y

200(x-y)=400

40(x+y)=400

x-y=2x+y=10

x=6m s, y = 4m s

The velocity of A is x, and the velocity of B is y

then according to the topic.

200x-200y=400

40x+40y=400

The solution is x=6, y=4!

Solution: Let the velocity of A be x m s and the velocity of B be y m s

Then the system of equations is derived according to the title:

200x-200y=400

40x+40y=400

The solution is x=6, y=4!

A: The velocity of A is 6m s, and the velocity of B is 4m s

Set B x people:

60x+(92-x)*50=5000

x = 40 A 92-40 = 52

Or set a x: 50x+(92-x)*60=5000

x=52B92-52=40

You can buy it together, a total of 82 * 50 = 4100 yuan, everyone saves money.

Angle three + angle one = 180 degrees, 2 angle three = 3 angle one, so angle three = 108 degrees, angle one = 72 degrees, angle two = angle three, angle four = angle one,

The expression is a little unclear, according to the title, there is angle 1 + angle 3 = 180 (flat angle) and because 2 angle 3 = 3 angle 1, angle 1 = 108, angle 3 = 72 (solve binary equation).

Angle 2 = Angle 1 = 108

Angle 3 = Angle 4 = 72 (equal to the apex angle).

Don't have a diagram? There is no diagram and the angle is not clear, it is difficult to find.

Solution: 1, AD, CF equally divided BAC, BCA ACF=1 2 ACB

dac=1／2∠bac

bac+∠bca=180º-∠abc

acf＋∠dac＝1／2﹙180º－∠abc﹚＝90º－1／2∠abc

fe, fd make up a 60 angle.

efd＝∠caf＋∠dac＝60º

The conclusion of question 1 is valid.

(1) Judgment: EF=FD (no need to explain, just draw a conclusion, and then explain in the second question) (2) Use the theorem that "the distance from the point on the bisector of the angle to the two sides of the angle is equal".

Point F is on the bisector of the angle BAC, so the distance from point F to AB is equal to the distance from point F to AC.

In the same way, point F is on the bisector of the angle BCA, so the distance from point F to BC is equal to the distance from point F to AC. So, the distance from point F to AB is the same as the distance from point F to BC. Then use the "corner corner" to prove EF=FD.

That's it.