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Explore the innovation problem The fourth grade students of Wangcun Central Primary School form a square array, and there are still 10 more students. If Hengjian adds a row to form a bigger square array, there are 9 less students,
There are x people, and the other square array is y and y + 1
Equations. Y2 = X-10
（y+1）2=x+9
We get x = 91
A piece of wood is five meters long. It takes five minutes to cut it into five sections. It takes five minutes to finish sawing this piece of wood______ Minutes
5 × (5-1) = 5 × 4 = 20 (minutes) a: it takes 20 minutes to finish sawing this piece of wood
Page 7
If the land area is x billion square kilometers, the sea area is 240 million square kilometers
x+2.4x=5.1
3.4x=5.1
x=1.5
The sea area is 2.4x = 2.4x 1.5 = 360 million square kilometers
A: the land area is 150 million square kilometers, and the sea area is 360 million square kilometers
The answer to question 3 on page 6 of the summer homework of mathematics published by people's Education Press
67*14=938
61*307=18727
969*19=51
What does enlightenment mean? Please write a sentence with the word enlightenment
Urgent!
Enlightenment is to give you inspiration, let you have new feelings, new understanding
This film is very meaningful and gives me profound enlightenment in life
Square within 15, cube within 10, prime number column, composite number column,
Squares within 15: = 4, = 9, = 16, = 25, = 36, = 49, = 64, = 81,10 ~ = 100,11 ~ = 121,12 ~ = 144,13 ~ = 169,14 ~ = 188,15 ~ = 22510 cubes within 10: = 1, = 8, = 27, = 64, = 125, = 216, = 343, = 512, = 7291000 prime numbers within 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53
7-2 △ x = 3 to solve the equation
7-2÷x=3
2÷x=7-3
2÷x=4
x=2÷4
x=1/2
The characteristics of rectangle, square, circle, parallelogram, trapezoid, triangle and various formulas
There are also three-dimensional graphics, cuboids, cubes, cylinders, cones
It's better to make it clear one by one. The format is as follows:
Rectangle: (characteristic), (formula)
Square: (characteristic), (formula)
……
Formula to the whole, area, perimeter, volume of solid graphics, edge length sum (cuboid, cube) surface area
Three grams of oil,
(1) Parallelogram
Two groups of parallelograms whose opposite sides are parallel are called parallelograms
Properties: the opposite sides of a parallelogram are parallel and equal; the opposite angles are equal; the two adjacent angles complement each other; the diagonal lines are equally divided
C (perimeter) = 2 (a + b)
S (area) = a × H (H is the height of side a) or S = ab × sin ф (ф is the angle of AB)
(2) Rectangle (rectangle)
A parallelogram with a right angle is called a rectangle
Properties: a rectangle has all the properties of a parallelogram. In addition, it also has the following properties: the four corners of a rectangle are right angles; the diagonals are equal
C=2(a+b)
S=ab
(3) Rhombus
A group of parallelograms with equal adjacent sides is called rhombus
Properties: a diamond has all the properties of a parallelogram. In addition, it has the following special properties: the four sides of a diamond are equal; the diagonals are perpendicular to each other, and each diagonal bisects a group of diagonals
(4) Square
A set of parallelograms with equal adjacent sides and a right angle is called a square
A square is not only a group of rectangles with equal adjacent sides, but also a diamond with right angles
C= 4a
S= a²
(5) Trapezoid
The paralleled two sides are called the bottom of the trapezoid. The shorter one is called the upper one, and the longer one is called the lower one. The nonparallel two sides are called the waist of the trapezoid. The vertical line between the two bottoms is called the height of the trapezoid. The line connecting the middle points of the two waists of the trapezoid is called the median line of the trapezoid
① A trapezoid with two equal waists is called an isosceles trapezoid. A trapezoid with one waist perpendicular to the bottom is called a right angle trapezoid
② Two internal angles on the same base of an isosceles trapezoid are equal; the diagonals are equal
③ The median line of the trapezoid is parallel to the two bases and equal to half of the sum of the two bases
④ Two trapezoids with equal inner angles on the same base are called isosceles trapezoids
Trapezoid is usually divided into parallelogram (rectangle) and triangle to explore
C = a + B + C + D (a, B, C and D are upper, lower, left and right lumbar, respectively)
S = 1 / 2 (a + b) H (H is the high of B)
(6) Triangle
A plane figure composed of three line segments which are not on the same line are called a triangle
Classification of triangles
① Classification by angle: acute triangle [its angle is (0, 90)]; right triangle (its teaching is right angle); obtuse triangle [its teaching is (90, 180)]
② According to the side classification: unequal triangle, isosceles triangle (especially, when three sides are equal, called equilateral triangle or regular triangle)
(2) Properties of general triangle
① Angle: the sum of the inner angles of a triangle is equal to 180 degrees; the sum of the outer angles of a triangle is equal to 360 degrees; an outer angle is equal to the sum of two inner angles not adjacent to it, and greater than any inner angle not adjacent to it
② Side: the sum of any two sides of a triangle is greater than the third side; the difference between any two sides of a triangle is less than the third side;
③ Sides and angles: in a triangle, equal sides are equal angles, and equal angles are equal sides
(3) The properties of special triangles are as follows
① Isosceles triangle: the two base angles are equal; the bisector of vertex angle, the middle line on the bottom and the height on the bottom are coincident with each other (three lines in one), and the line where the line segment is located is the symmetry axis of isosceles triangle
② Equilateral triangle: three equal angles, all 60 degrees
③ Right triangle: two acute angles complement each other; the median line on the hypotenuse is equal to half of the hypotenuse; the square of the hypotenuse is equal to the sum of the squares of the two right angles (Pythagorean theorem: A & sup2; + B & sup2; = C & sup2;); the right side opposite an angle of 30 degrees is equal to half of the hypotenuse
(4) Area of triangle
① General triangle: s △ = 1 / 2ah (H is the height on side a)
② Right triangle: s △ = 1 / 2Ab = 1 / 2CH (a, B are right angles, C is hypotenuse, h is height on hypotenuse)
③ Equilateral triangle: s △ = (radical 3) / 4A & sup2; (a is the side length)
(5) Circle
A set whose distance from a fixed point in a plane is equal to a fixed length is called a circle
① Symmetry of circle
A circle is a rotationally symmetric figure, and the center of symmetry is the center of the circle
② Chord, arc and diameter
The diameter perpendicular to the chord must bisect the chord and the arc it faces
③ Chord, arc and center angle
In the same circle or equal circle, the center angle of the circle is equal ← → the arc is equal ← → the chord is equal ← → the chord center distance is equal
④ Center angle and circumference angle
A semicircle or diameter is a right angle to a circle; conversely, a 90 degree angle is a diameter to a chord
In the same circle or equal circle, the equal circle angle of the same arc or equal arc is equal to half of the center angle of the circle, and the equal circle angle is equal to the arc
⑤ Calculation in circle
Let R be the radius of the circle, l be the length of the arc, and n be the degree of the central angle of the arc,
C (circumference of circle) = 2 π R
S (area of circle) = π R & sup2;
Arc length L = n π R / 180 degrees
Sector area s = n π R & sup2 / 360 degree = 1 / 2 LR
(three dimensional graphics, I'll make it easier. If you want to be more detailed, please come to me again!)
Cuboid v = ABC C = 4 (a + B + C) s (surface area) = 2 (AB + AC + BC)
Cube v = a, cubic C = 12a
S (surface area) = 6 × A & sup2;
Cylinder C = 4 π R + L S (surface area) = 2 π R (R + L)
V = sh = π R & sup2; H (s is the bottom area, h is the height of the cylinder)
Cone C = 2 (L + π R)
S (surface area) = π (R '& sup2; + R & sup2; + r'l + RL)
(R is the radius of the upper bottom, R 'is the radius of the lower bottom, l is the generatrix length of the cone)
V=1/3 sh = 1/3 πR ²h
This sin2a + sin2b = sin2c, how to get 2Sin (a + b) cos (a-b) = 2sinccosc?
The left side uses: (a + b) + (a-b) = 2A
After (a + b) - (a-b) = 2B, the sum angle (difference angle) formula is used
Double angle formula on the right
Write the value of X directly: 80-0.5x = 2538 + 2x = 601.9 + x = 6.32-10.1x = 29 + 0.3x = 12
80-0.5X=25
0.5x=55
x=110
38+2X=60
x=11
1.9+X=6.3
x=4.4
2-10.1X=2
x=0
9+0.3X=12
x=10
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