Give a box of apples to several children. If each child is given 5 apples, there are 12 apples left. If each child is given 8 apples, the last child gets 8 apples, but there are less than 8 apples. Find the number of children and the number of apples in this box

Give a box of apples to several children. If each child is given 5 apples, there are 12 apples left. If each child is given 8 apples, the last child gets 8 apples, but there are less than 8 apples. Find the number of children and the number of apples in this box

If there are x children, then the number of apples is (5x + 12). According to the meaning of the question, we get: 0 ＜ 8x - (5x + 12) ＜ 8, which can be changed into: 3x − 12 ＞ 03x − 12 ＜ 8. The solution is: 4 ＜ x ＜ 203, ∵ x is a positive integer, ∵ x takes 5 or 6, when x = 5, 5x + 12 = 37; when x = 6, 5x + 12 = 42, ∵ there are two situations to meet the meaning of the question: ① there are 37 apples in this box, children have 5 digits; ② there are 42 apples in this box, children have 5 digits There are six friends

To solve the problem about the system of linear inequalities of one variable
If the solution set of inequality (2a-b) x + a-5b > 0 is x < 10 / 7, then the solution set of AX + b > 0 (a > 0) is ()
A.x>-3/5 B.x3/5 D.x
The correct answer in the book is a. in the last question, I mistakenly wrote x ＜ 10 / 7 as X ＞ 10 / 7. Why?

Note that the direction of the inequality sign does not change, indicating that 2a-b > 0
So the solution set of inequality is x > (- A + 5b) / (2a-b)
That is (- A + 5b) / (2a-b) = 10 / 7
So a = 5B / 3
So ax + B = (5b / 3) x + b > 0
Note that a > 0, so B is also greater than 0
Divide B into two parts
x>-3/5
So the answer is a

Solving a mathematical problem of grade one in junior high school
The solutions of the equations {x + y = 1 are x, y, and x > 0, y
Is the system of equations x + y = 1
{
x-y=2a

The solution is x = a + 0.5 > 0 a > - 0.5
y=0.5-a0.5
So a > 0.5

In △ ABC, ∠ C = 90 °, AC = 2.1cm, BC = 2.8cm. (1) find the area of △ ABC; (2) find the length of hypotenuse AB; (3) find the length of height CD

As shown in the figure: (1) s △ ABC = 12ac × BC = 2.94; (2) AB = ac2 + BC2 = 3.5; (3) 12bc × AC = 12ab × CD, the solution is: CD = 1.68

The greatest common factor of two numbers is 14, and the least common multiple is 84. How many groups are there?
Step?

84÷14＝6
6＝1×6＝2×3
There are two groups of such numbers
（1）
1×14＝14
6×14＝84
（2）
2×14＝28
3×14＝42

If the ratio of the corresponding sides of two similar triangles is 2:3 and the sum of their girths is 20, then the girths of the two triangles are ()
A. 8 and 12b. 9 and 11C. 7 and 13D. 8 and 15

∵ the ratio of the corresponding sides of two similar triangles is 2:3, the perimeter ratio of the two triangles is 2:3, the sum of the perimeter of the two triangles is 20, and the perimeter of the two triangles are 20 × 25 = 8 and 20 × 35 = 12 respectively

What are the greatest common divisor and the least common multiple of 15, 36 and 90?

Greatest common divisor 3
Least common multiple 180

Given that the line L1: y = 2x + 3, the line L2 and L1 are symmetric with respect to the line y = - x, then the equation of L2 is?

It is easy to find that the intersection of L1 and y = - x is (- 1,1), and it is obvious that L2 also passes through this point
Take any point (0,3) in L1, the symmetric point of this point about the line y = - x is (- 3,0), and this point is also on L2
Now we know two points (- 1,1) and (- 3,0) on L2
It is easy to get the slope k = 1 / 2, then the equation of L2 written in the oblique form is y-0 = (x + 3) / 2
That is: y = x / 2 + 3 / 2
The equation of L2 is y = x / 2 + 3 / 2

Is there any difference between one and a half sth and one sth and a half

Semantically, there is no difference, but if you add another sth after the latter, it is a and half B

The parabola y = - x2-2x + m, if its vertex is on the X axis, then M=______ ．

∵ parabola y = - x2-2x + m, if its vertex is on the X axis, ∵ 4 × (− 1) × m − (− 2) 24 × (− 1) = 0, the solution is m = - 1. So the answer is: - 1