) 1. There are two filling pipes of oil tank a and B in an oil depot. It takes 4 hours to fill the oil tank by opening pipe a separately than by opening pipe B separately. After 3 hours of opening both pipes at the same time, pipe a stops filling due to failure, and pipe B continues to fill the oil tank after 9 hours. How many hours does it take for pipe a and pipe B to fill the oil tank separately. 2. In the sales of clothing cabinets in department stores, it is found that an average of 20 pieces of children's clothing of a certain brand can be sold every day, with a profit of 40 yuan per piece. In order to meet the children's day, the department stores decided to take appropriate price reduction measures to expand sales, increase profits and reduce inventory. According to the market survey, if the price of each children's clothing is reduced by 1 yuan, two more children's clothing can be sold every day on average. In order to make an average profit of 1200 yuan, how much should the price be reduced? 3. A fruit wholesale market sells a kind of high-grade fruit. If the profit per kilogram is 10 yuan, 500 kg can be sold every day. According to the market survey, if the price per kilogram is increased by 1 yuan and the daily sales volume is reduced by 20 kg under the condition that the purchase price remains unchanged, now the market wants to make a profit of 6000 yuan every day and at the same time make customers get benefits. How much yuan should the price per kilogram be increased?

1. If a is x hours, B will be x + 4 hours. If B is 12 hours, it will be 3 / x + 12 / (x + 4) = 1. If x = 12, it will be 12 hours for a and 16 hours for B. 2. If the price is reduced by X Yuan, it will be (40-x) yuan for each piece. If the number of pieces sold is 20 + 2x, it will be (40-x) (20 + 2x) = 1200
1. Suppose that a takes x hours and B takes y hours
x=y+4......①
1-【（1/x+1/y）*3】=（1/y）*9......②
Simultaneous solution
One
If a is x hours, B is x + 4 hours. If a is put for 3 hours, B is put for 12 hours
3/x+12/(x+4)=1
The solution is x = 12
It takes 12 hours to fill a and 16 hours to fill B alone
Two
If the price is reduced by X Yuan, the profit of each piece is (40-x) yuan, and the number of pieces sold is 20 + 2x
Then (40-x) (20 + 2x) = 1200
The solution is X1 = 20, X2 = 50
So cut the price by 20 yuan
One
If a is x hours, B is x + 4 hours. If a is put for 3 hours, B is put for 12 hours
3/x+12/(x+4)=1
The solution is x = 12
It takes 12 hours to fill a and 16 hours to fill B alone
Two
If the price is reduced by X Yuan, the profit of each piece is (40-x) yuan, and the number of pieces sold is 20 + 2x
Then (40-x) (20 + 2x) = 1200
The solution is X1 = 20, X2 = 50
So after 20 yuan price reduction, we can make a profit of 1200 yuan per day
3. Same as topic 2
If the price is increased by X Yuan, the profit per kilogram will be 10 + X Yuan, and the sales volume will be 500-20xkg
There are
(10+x)(500-20x)=6000
The solution is X1 = 5, X2 = 10
If you want customers to get benefits, in fact, the price increase is the least. If the price per kilogram is 5 yuan, you can make a profit of 6000 yuan per day
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What about the title?
(1) In the triangle ABC, AC = 9, BC = 6, ask whether there is a point D on the side of AC, so that the triangle ABC is similar to the triangle BDC. If there is, please calculate the length of CD
(2) In the triangle ABC, ad is the height on the side of BC, and the square of AB = BD * BC, then what is the degree of the angle BAC?
(3) ABCD is a general quadrilateral. Points e, F, G and G are the key points of AB, BC, CD and ad respectively. Connect e, F, G and h in turn. Prove that efgh is a parallelogram
1. To make the two triangles similar, only AC / BC = BC / DC is needed, so DC= BC.BC/AC The solution is CD = 36 / 9 = 4.2, because the square of AB = BD * BC, so AB / BD = BC / AB, and because ﹥ abd = ﹥ CBA, so the triangle abd knows the expected triangle CBA, so ﹥ BAC = ﹥ BDA = 90 degrees
Two elementary 3 mathematics solution 1 yuan quadratic equation problem trouble you prawns~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`
(1) The square of (x + 1) = 2 (2) the square of 3 (X-5) = 2 (5-x)
It's going to be a lot of trouble
(1)
(x+1)^2=2
X + 1 = sqrt (2) or x + 1 = - sqrt (2)
X = - 1 + sqrt (2) or x = - 1-sqrt (2)
(2)
3(x-5)^2=2(5-x)
3(x-5)^2-2(5-x)=0
3(x-5)^2+2(x-5)=0
(x-5)[3(x-5)+2]=0
(x-5)(3x-13)=0
X = 5 or x = 13 / 3
(1)x+1=±√2
X1=√2-1 X2=-√2-1
The cubic power of x plus (or minus) the cubic power of Y is equal to?
x^3+y^3=(x+y)(x^2-xy+y^2)
x^3-y^3=(x-y)(x^2+xy+y^2)
x^3+y^3
=[x+y][x^2+y^2-xy]
=[x+y][(x+y)^2-3xy]
If a is the equation about X, the square of X + BX + a = 0, and a is not equal to 0
First, choose the appropriate option from 1.2.3.4 in brackets after each sub question and fill it in the horizontal line,
(1) If a is the root of the equation x + BX + a = 0, and a is not equal to 0, find the value of ()
(1. AB 2. B, a 3. A + B 4. A-B}
(2) We know that the square of 7x + the square of 5Y = 12xy, and XY is not equal to 0
(1. XY 2. X: y 3. X + y 3. X-Y)
(1) All four can be solved. Using the relationship between and coefficient. A * x = - A, so the other root is - 1, which is substituted into the equation, A-B = - 1
(2)7x^2+5y^2=12xy
Factorization factor: (7x-5y) (X-Y) = 0
So you can choose X-Y
Three
Two
Find all positive integer solutions of Diophantine equation 3 to the power of X + 4 to the power of y = 5 to the power of Z
The indefinite equation has only unique integer solution x = y = z = 2. It is proved by the counter proof method that: according to the meaning of the question: 3 & # 178; + 4 & # 178; = 5 & # 178; that is: 9 + 16 = 25. Suppose there are other solutions, let it have the same increment t on the basis of 2 (t is not equal to 0), then there are: 3 ^ (2 + T) + 4 ^ (2 + T) = 5 ^ (2 + T), that is, 9 × (3 ^ t) + 16 × (4 ^ t) = 2
Given the equation (K's square-4) x's square + (K-2) x + (K-8) y = k-7, when k=___ When k, the equation is of degree 1=___ The equation is a quadratic equation with two variables
The original equation has two unknowns, X and Y. when all coefficients of one of them are 0, and the other is not 0, the equation is a univariate equation. If the coefficient of quadratic term is 0, it is a first-order equation
When k = 2, it is a linear equation of one variable. When k = - 2, it is a quadratic equation of two variables.
How to write the expression of Z = x to the power of Y for y equal to Z and X?
Find the exponent, use logarithm:
Y=㏒X(Z).
z=x^y
Generally, natural logarithm is used, but x > 0, z > 0
Take natural logarithm on both sides
lnz=y*lnx
y=lnz/lnx
If (m-1) xsquare + X-1 is a quadratic equation with one variable and has a real root, we can find the value of M
If M-1 is a quadratic equation of one variable, then M-1 is not equal to 0
b2-4ac>=0
1+4(m-1)>=0
m> = 3 / 4 and M is not equal to 1
M-1 is not equal to 0
1+4(m-1)>=0
Ψ m > = 3 / 4 and M is not equal to 1
M is not equal to 1, and then solved by Δ
If there are real roots, then B ^ 2-4ac > = 0, that is, 1-4 (m-1) (- 1) > = 0
1+4m-4>=0
4m>=3
m>=3/4
X2 power + 2x-99 = 0 of quadratic equation with one variable
X = 9 or - 11
（x-9)(x+11)=0
X = 9 or - 11
(x + 1) ^ 2 = 100, so x + 1 = 10 or - 10, that is, x = 9 or - 11.

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