A village plans to build an isosceles trapezoid channel in the east of the village. The cross-section area is 1.6. The width of the upper entrance is 1.6m more than the width of the channel bottom, and the depth of the channel is 0.4m less than the width of the channel bottom

A village plans to build an isosceles trapezoid channel in the east of the village. The cross-section area is 1.6. The width of the upper entrance is 1.6m more than the width of the channel bottom, and the depth of the channel is 0.4m less than the width of the channel bottom

The width of canal bottom is assumed to be x M
（x+1.6+x）(x-0.4)÷2=1.6
x=1.2
X = - 1.6 (rounding off)
Channel depth 1.2-0.4 = 0.8m

It is known that the height of the trapezoid is 4m, the area is 18m, and the upper bottom of the trapezoid is 1cm more than one third of the lower bottom
Solving the first order equation with two variables

Let the upper bottom be x m, then the lower bottom be YM
｛（x+y）*2=18
1/3*y+1=x
x=3 y=6

An isosceles trapezoid is formed by a 12.4 decimeter long iron wire. It is known that the two sides of the trapezoid are 6.4 decimeters long and the area is 9 square decimeters. What is the height of the trapezoid?

9 × 2 △ 12.4-6.4 = 18 △ 6 = 3 (decimeter) a: the height of trapezoid is 3 decimeter

Given that a = 2x-4xy-2x-3, B = - x + XY + 2, and the value of 3A + 2B has nothing to do with the first term of X, can you find the value of the letter Y?

3A+2B
=3(2x^2-4xy-2x-3)+2(-x^2+xy+2)
=6x^2-12xy-6x-9-2x^2+2xy+4
=4x^2-10xy-6x-5
=4X ^ 2 - (10y-6) X-5 (treat y as a constant)
Because it has nothing to do with the first term of X
So 10y-6 = 0
10y=6
y=0.6
Is that ok?

Find the maximum value g (a) of function f (x) = (3a-2) x ^ 2 + 2x + 1 on [- 3,2]

First of all, when a = 2 / 3, f (x) = 2x + 1, take the maximum value of 5 at x = 2, so g (2 / 3) = 5
When a > 2 / 3, the opening of F (x) is upward, and the maximum value is taken at both ends, f (- 3) = 27a-23, f (2) = 12a-3
F (- 3) > F (2) is equivalent to a > 4 / 3
f(-3)

The maximum value of function f (x) = - x2 + 2x + 1 on interval [- 2,3]

This is a quadratic function, you use the image to help solve
It is a parabola with an opening downward, because the coefficient of quadratic term is - 1, less than zero
Its axis of symmetry is: x = - B / 2A = 1
When x = - 2, y is the minimum, and y = - 7 because it is farther from the axis of symmetry than 3
When x = 1, y is the maximum, and y = 2

Factorization to the fourth power of x-29x & #178; + 100
-2x²z+24xyz-70y²z
（x+y）²-4（x+y）-12
x²+（k+2）x+（k+1）
4a²b²-（a²+b²）²

X quartic power - 29x & # 178; + 100
=（x²-4)(x²-25)
=(x+2)(x-2)(x+5)(x-5)
-2x²z+24xyz-70y²z
=-2z(x²-12xy+35y²)
=-2z(x-5y)(x-7y)
（x+y）²-4（x+y）-12
=(x+y-6)(x+y+2)
x²+（k+2）x+（k+1）=(x+1)(x+k+1)
4a²b²-（a²+b²）²
=[2ab+(a²+b²)][2ab-(a²+b²)]
=-(a+b)²(a-b)²

It is known that the order of monomial − 23xy2m − 1 is the same as that of - 22x2y2. (1) find the value of M; (2) find the value of monomial − 23xy2m − 1 when x = - 9 and y = - 2

(1) According to the meaning of the question: 1 + 2m-1 = 2 + 2, the solution is: M = 2; (2) − 23xy2m − 1 = - 23xy3, then when x = - 9, y = - 2, the original formula = - 23 × (- 9) × (- 8) = - 48

1. When a = 1 / 2, find the value of 10 - (1-A) - (1-a-a & # 178;) + (1 + A-A & # 178; - A & # 179;)
2. When x = - 2, y = - 1, z = 1 / 3, find the value of 3yZ - {2x & # 178; Y - [3xyz - (2XY & # 178; - X & # 178; y)]}

10-（1-a）-（1-a-a²）+（1+a-a²-a³）=10-（1-1/2）-（1-1/2-1/4）+（1+1/2-1/4-1/8）=10-1/2-1/4+9/8=83/83yz-{2x²y-【3xyz-（2xy²-x²y）】}=3*（-1）*（1/3）- {2*(-2)²*(-1)-...

Given (a + b) &# 178; = 16, (a-b) &# 178; = 4, find (1) a & # 178; + B & # 178;; (2) (AB) &# 179;

∵(a+b)²=16∴a²+2ab+b²=16………… ①∵(a-b)²=4∴a²-2ab+b²=4………… ② 1 + 2 get 2 (A & # - 178; + B & # - 178;) = 20A & # - 178; + B & # - 178; = 10 1 - 2 get 4AB = 12ab = 3 (AB) &# - 179; = 3 & # - 179; = 27 # - A & # - 178; + B & # - 178