Solving practical problems with equations There are two kinds of alcohol with 75% and 45% concentration. To prepare 300 grams of alcohol with 65% alcohol, how many grams should be taken from each of the two kinds of alcohol? What I want is the process of solving the equation, and write out the equivalent relation and reason of the equation!

If we want to take 75% alcohol x g, we need to take 45% alcohol 300-x g, 75% * x + (300-x) * 45% = 300 * 65% 0.75x + 135-0.45x = 1950.3x = 60 x = 200 300-x = 300-200 = 100. If we want to take 75% alcohol 200 g, we need to take 45% alcohol 100 g

There are 860 students in grade 4, 5 and 6 of Yucai primary school. The ratio of grade 5 to grade 4 is 5 to 4, and the number of grade 6 is 16 / 15 of grade 5

There are 12x in grade 4, 15x in Grade 5 and 16x in Grade 6
So 12x + 15x + 16x = 860
43X=860
X=20
So there are more students in grade six than in grade four, 16x-12x = 4x = 4 * 20 = 80
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What is the square root of 14?

The square root of 14, which means the arithmetic square root of 14, is a positive number
About 3.741657

The ratio of a to B is 3:4, the ratio of B to C is 5:6, so the ratio of a to B to C is 3:4______ ．

Let a be 3x, B be 4x, then C be 4x △ 56 = 245x, so the ratio of a, B and C is 3x: 4x: 245x = 15:20:24, so the answer is: 15:20:24

Factorization (the number after the letter is the exponent of the letter)
1. (2x + 3Y) square - (3x-2y) square
2. 49a4b square - 64c square (x + 2Y) square
3. (2x-y) square - (x + 2Y) square

1、(2x+3y)^2-(3x-2y)^2
=(2x+3y+3x-2y)(2x+3y-3x+2y)
=(5x+y)(5y-x)
2、49a^4b^2-64c^2(x+2y)2
=(7a^2b) ^2-[8c(x+2y)]^2
=[7a^2b+8c(x+2y)][7a^2b-8c(x+2y)]
=(7a^2b+8cx+16cy)(7a^2b-8cx-16cy)
3、(2x-y)^2-(x+2y)^2
=(2x-y+x+2y)(2x-y-x-2y)
=(3x+y)(x-3y)

Five thirds of the number a is equal to seventy-five eighth of the number B. the number B is 120 and the number a is []

120x7/8÷5/3
=105x3/5
=63

A = {2a, the second power of A-A}, the value range of a is?
In addition, if the solution of the inequality about X is {x | 0 ＜ x ＜ 2}, then the value of real number m is {x | 0 ＜ x ＜ 2}?

2a≠a^2-a
a^2-3a≠0
A ≠ 0 and a ≠ 3
(-1/2)x^2+2x>mx
The two endpoint values of the solution set are the roots of the corresponding equation (- 1 / 2) x ^ 2 + 2x = MX, so x = 2 is substituted into the equation to find M = 1

3 / 8 of a equals B. B is 27. What's a

Number a
=27 △ 3 / 8
=27 × 8 / 3
=72
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Let the rank of the coefficient matrix of a system of four variable non-homogeneous linear equations be 3, and we know that η 1, η 2 and η 3 are its three solution vectors, and that η 1 = (2,3,4,5) t (this vector is a column vector, the same after); and that η 2 + 2 and η 3 = (3,4,5,6) t, then we obtain the general solution of the system of equations

Because the rank of coefficient matrix of four variable non-homogeneous linear equations is 3
So the basic solution system of the derived system contains 4-3 = 1 vector
From the properties of solutions of homogeneous linear equations and their derived systems
Both η 1 - η 2 and η 1 - η 3 are solutions of the derived system
So (η 1 - η 2) + 2 (η 1 - η 3)
= 3η1 - (η2+2η3)
= 3(2,3,4,5)^T - (3,4,5,6)^T
= (3,5,7,9)^T
Is the solution of the derived group
So the general solution of the equations is (2,3,4,5) ^ t + C (3,5,7,9) ^ t

To process the same parts, a processes 9 parts in 4 hours, B processes 7 parts in 3 hours, and C processes 11 parts in 5 hours. Whose work efficiency is high and whose work efficiency is low?

Is it right that B is more efficient and C is less efficient?