Two math problems, not made in a summer vacation, worth studying!

In the second problem, according to the symmetry, it is obtained that point b (2m-3,-1) intersects the parabola with a straight line at point b, so point b is on the parabola, so the point b is substituted into the parabola equation and m=2

So b(1,-1) parabola y=x 2-4x+2, so there are two straight lines, one with no slope and one tangent of the parabola.

If the slope does not exist, it is x=1

The tangent can be derived to find the slope k=-2 (or set a straight line and connect it with a parabola, using b 2-4ac=0 to find the slope), so the other straight line is y=-2x+1

1x-1 = plus or minus 40 = plus or minus 2 times plus or minus 10

x = 1+2 times with 10 or 1-2 times with 10

24x+1 = plus or minus 48 = plus or minus 4 times plus or minus 3

4x = -1+4 times with 3 or -1-4 times with 3

x=-1 4+3 or -1 4-3

(1) x-1 = plus or minus 2 root number 10

x = 1 + (plus or minus 2 root number 10).

2) 4x+1 = plus or minus 4 root number 3

4x=(plus or minus 4, root number 3)-1

x = (plus or minus root number 3) - (1 4).

1. Solution: Let Xiaoduo have 3x yuan, then Xiaohong has 4x yuan, Xiao Ming has 3x+5 yuan, and 3x+4x+3x+5=185 according to the title

10x+5=185

10x=180

x=18 so 3x=54,4x=72,3x+5=59Answer: Xiaoduo has 54 yuan.

2. Solution: If there are x footballs bought by Mr. Wang, there are 1 3x volleyballs bought, and 1 3x-10=(x+10) (1 7) is obtained according to the title

1/3x-10=1/7x+10/7

1/3x-1/7x=10/7+10

4/21x=80/7

x=60, so 1 3x=20

Answer: Mr. Wang bought a total of 60 + 20 = 80 volleyballs and footballs.

1. If Xiao Ming and Xiao Duo money are the same, that is, subtract 5 yuan from Xiao Ming, then the three of them have a total of 180 yuan, then the ratio of Xiao Ming, Xiao Duo, and Xiao Hong's money is 3:3:4, Xiao Duo's money is 180 10 3 = 54 yuan, and Xiao Hong's is 180 10 4 = 72 yuan.

Xiao Ming is 54 + 5 = 59 yuan.

2. Suppose that the total number of all balls is unit 1, the original volleyball accounts for 1 4 of the total, now volleyball accounts for 1 8 of the total, and the volleyball is reduced by 1 8 of the total, which is 10.

So the total is 80.

1.Let Xiaoduo x yuan, then Xiao Ming x+5, Xiaohong 4 3*x, so: x+(x+5)+4 3*x=185 solution x=54 yuan 2If soccer x is set to be volleyball, then volleyball x 3

x 3-10)*7=x+10 to get x=60, volleyball has 1 3*60=20.

1. Xiao Duo: (185-5) (3+3+4) 3=54 Xiao Ming: 54+5=59

Xiaohong: (180-5) (3+3+4) 4=722, volleyball accounted for 1 4 of the total at the beginning, and later 1 8 (10+10) (1 4-1 8) of the total

1. (185+5) (3+4+3)*3=57 (yuan) Xiaoduo Yo 57 yuan.

185 + 5 is the total amount of "Xiao Ming is equal to Xiao Duo", 3 + 4 + 3 is the total number of copies 2, solution: let the number of volleyballs be x, then the number of soccer balls is 3x

x-10)/(3x+10)=1/7

7x-70=3x+10

7x-3x=10+70

4x=80x=20

The number of volleyballs is 20 and the number of soccer balls is 60. 80 in total. (I believe the questioner can understand the equation, so I won't explain it here).

1: Solution: Let Xiao Duo have x yuan, Xiao Hong (4 3x) yuan, Xiao Ming (x + 5) yuan.

x+4 3x+(x+5)=185 solution: x=54, so, Xiaoduo is 54 yuan, Xiaohong is 72 yuan, and Xiao Ming is 59 yuan.

2.Solution: If volleyball is x, then football is 3x

x-10)/(3x+10)=1/7

Solution x=20

20 for volleyball, 60 for football

1 Suppose the number of small flowers is 3x Xiaohong is 4x, and Xiao Ming should be 3x + 53x + 4x + 3x + 5 = 185 x = 18 Xiao Hong has 54 pieces 2 Suppose you buy 3x footballs, then volleyball is x, 7 * (x-10) = 3x + 10 x = 20 There are 60 footballs and 10 volleyballs.

1.If Xiaoduo has 3x yuan, then Xiaohong has 4x yuan, and Xiaoming has 3x+53x+4x+3x+5=185

x=18 Xiaoduo has 54 yuan, then Xiaohong has 72 yuan, and Xiaoming has 59

2.If volleyball is x, then football is 3x

x-10)/(3x+10)=1/7

x=20 for volleyball is 20 for football and 60 for football

1. Let Xiao Duo x Xiao Hong=(4 3)X, Xiao Ming=x+5 X+(4 3)X+(X+5)=185 ,X=?

2. Let volleyball x football = 3x x-10 = (1 7) * (3x + 10), x = ?

Do you want a process? And you may have a problem with the first question itself.

First, x 2+x+a=0 has two unequal real roots, and secondly, one of the two roots is greater than 0 and less than 0, a system of equations.

1-4a＞0

x1-1）（x2-1）＜0

The first formula is solved as a 1 4

The second equation is followed by Veda's theorem, x1x2-x1-x2+1 0a+1+1 0

a -2 in summarya -2

Happy studying.

Solution: Minutes walk in a circle every 60 minutes, 6 degrees per minute.

The hour hand travels 1 12 times per hour, 30 degrees in the first hour, and 0 points per minute as the reference point.

Morning departure at 7:30

The angle of the hour hand is degrees.

The angle of the minute hand is 6 30 180 degrees.

7:30, the angle between the hour and minute hands 225 180 45 degrees 6:30 when returning to school.

The angle of the hour hand is degrees.

The angle of the minute hand is 6 30 180 degrees.

6:30, the angle between the hour and minute hands 195 180 15 degrees, the angle between the hour and minute hands at departure and return to school, and 45 15 60 degrees.

Minutes walk in a circle every 60 minutes, 6 degrees per minute.

The hour hand travels 1 12 times every 60 minutes, a degree per minute.

The angle at 7 o'clock is 210 degrees, so the angle at 7:30 is 210+ degrees, and the angle at 6 o'clock in the afternoon is 180 degrees, so the angle at 6:30 is 180+ degrees.

I don't really understand what you mean, is it the sum of the angles between the departure and return, or the difference between the departure and return minutes, the difference between the minute hand is the same, the difference in the hour hand is an hour, 30 degrees. If you add it, it's 45 degrees. If you separate it, one is 45 and the other is 15

113 -4 1

Simplify: a 0, b 0, c 0. And c a, b and a+b so, a =a a-c =a-c c =-c b+a-c =a+b-c -c+a =a-c so a - a-c + c =a-(a-c)-c=0 b+a-c - c+a =a+b-c-(a-c)=b

1、a+b=1

2. The value of m can be any positive integer.

The title seems to be expressed as: x 2-m=0 has an integer root, then the value of m can be The result should be .

3. Fill in from left to right, from top to bottom

1、a=-2,b=3;So, a+b=1

or other integers greater than or equal to 0.

1.The set price is 30% x 80% - 50% x 20% = 14%x, so after the sale, the store will make a profit of 14% (this is not particularly certain).

2.Set the original price to x yuan x (1-20%) (1-20%) = 64% x 1-64% = 36% After the second price reduction, this batch of goods was 36% lower than the original price

3.Let basket A have x kg, then basket B has (78-x) kg (1-20%)-1=(78-x)+20%x+1 solution x=50 then 78-x=28

4.Let the length be a, and the width be b (1+20%)b·(1-20%)a=96%ab 1-96%=4%.

5.Let the original x-tons x-40=85%x-16 solution x=160

Let's do these first, there are too many! Huh

A: B = 4:3, let A be 4x, then B is 3x

B: C = 4:5, B is 3x, then C is 15x 4A:

B: C = 4x: 3x:

15x 4, dissolved A:B:C = (16):

B's three and four are multiplied by twelve, A is multiplied by four to be sixteen, and C is multiplied by three to be fifteen.

A:B=4:3 and B:

The connection between C = 4:5 is B, the first B is 3 and the second is 4 To make two Bs equal, multiply them by 4 and 3 respectively A: B = 16:

12 B:C = 12:15 And the result will be out.

n=32×8^n÷16^n=2×8^n÷(2×8)^n=2×8^n×(2×8)^-n=2×8^n×8^-n×2^-n=2^(1-n)=2^(-2)

Supplement 2 n means 2 to the nth power.