40 = () ten () = () ten () prime

40 = () ten () = () ten () prime

23+17 3+37

In all factors of 10-21, there are always () pairs of Coprime numbers

Relative prime, also called coprime, refers to two natural numbers whose greatest common divisor is 1
There are 11,13,17,19,21 -- 5 pairs of Coprime with 10
There are 12,13,14,15,16,17,18,19,20,21 -- 10 pairs of Coprime with 11
There are 13,17,19 -- 3 pairs of Coprime with 12
There are 14 ~ 21 -- 8 pairs with 13 prime
There are 15,17,19 -- 3 pairs of Coprime with 14
There are 16,17,19 -- 3 pairs of Coprime with 15
There are 17,19,21 -- 3 pairs of Coprime with 16
There are 18,19,20,21 -- 4 pairs of Coprime with 17
There are 19 -- 1 pairs with 18 prime
There are 20,21 -- 2 pairs of Coprime with 19
There are 21 -- 1 pairs with 20 prime
So all of them add up to 43 pairs

1. In 4,9,10 and 16, there are two pairs of Coprime. 2. In all factors of 21, there are two pairs of Coprime
3. When a number is divided by 3, 5 and 7, there is 1 left. The minimum number is ()
4. The greatest common factor of a two digit number and 48 is 24, which may be ()

Don't grind the knot
Question 1, answers 4 and 9, 9 and 10, 9 and 16
There are four pairs of answers to question 2. The factors of 21 are 1, 3, 7 and 21, and the reciprocal ones are 1 and 3, 1 and 7, 1 and 21, 3 and 7
The least common multiple of 3, 5 and 7 is 105. Of course, the number is 106
In question 4, the answers are 24 and 72.48 = 24 × 2, which means that in addition to 24, the other divisor of this number can not be even but odd, otherwise the greatest common divisor of the two numbers is 48. Both 24 × 1 and 24 × 3 satisfy the condition

How to divide a right angled trapezoid into four equal parts of the same shape and size

The vertical line between figure 1 and Figure 2 is the line passing through the middle point of the upper bottom, the vertical line between figure 3 and Figure 4 is the line passing through the middle point of the lower bottom, the horizontal line between figure 2 and Figure 4 is the middle line of the trapezoid, and the diagonal line on the left side of Figure 3 is symmetrical with the diagonal line on the right side of Figure 4

There are translation, rotation and so on

Symmetry

Given the points a (1,2), B (2,3) and C (- 2,5), what is the relationship between the vector ab → and AC

Points a (1,2), B (2,3), C (- 2,5)
Then the vector ab → = (2-1,3-2) = (1,1)
Vector AC → = (- 2-1,5-2) = (- 3,3)
Then vector ab →. Vector AC → = 1 * (- 3) + 1 * 3 = 0
The relationship between vectors ab → and AC → is perpendicular to each other

As shown in the figure, in the equilateral triangle ABC, the bisectors of ∠ B and ∠ C intersect at O, and the vertical bisectors of OB and OC intersect BC at e and F. try to explore the size relationship of be, EF and FC, and explain the reasons

Conclusion: be = EF = FC (1 point) the reason is: be = EF = FC (1 point) the reason is: ∵ ABC is an equilateral triangle, ∵ ABC = ∠ ACB = 60 ° (2 points), ∵ OC, OB bisection ∵ ACB, ∵ ABC, ∵ OBE = ∠ OCF = 30 ° (3 points), ∵ eg, HF vertical bisection ob, OC, ∵ OE = be, of = FC (5 points), ∵ BOE = ∠ OBE = 30 °, ∵ COF = ∠ OCF = 30 °, ∵ OEF = ∠ ofe = 60 °, ∵ triangle OEF is an equilateral triangle (8 points) Of = OE = EF, be = EF = FC (10 points)

Two problems of mathematics compulsory course in Senior High School
It is known that the circle C: X & sup2; + (Y-1) & sup2; = 5 and the line L: mx-y + 1-m = 0
(1) Verification: the straight line L passes through the fixed point
(2) Let L and circle intersect at two points a and B, if / AB / = root 17, the equation of line L is obtained
Please help me! Thank you!

The first question is about linear system
If M is of this type, m (x-1) - y + 1 = 0
Therefore, it is necessary to pass the fixed point (1,1)
Second question
The formula of distance from point to line is as follows
The distance from the center of the circle (0,1) to the straight line d = | - 1 + 1-m | / √ (1 + m ^ 2) = | / √ (1 + m ^ 2)
Half of chord length = √ 17 / 2
According to Pythagorean theorem, it is concluded that
d^2+17/4=5
The solution is m = ± √ 3
So the equation of straight line is y = ± √ 3 (x-1) + 1

It is known that point e of AB / / CD is a point not on AB, CD, ∠ Abe = 110 °∠ CDE = 120 ° (1) as shown in Figure 1, find the degree of ∠ bed

Let the intersection of AD and be be be f
Angle ADC = angle e + angle DFE (outer angle of triangle)
Angle DFE = 65 degrees - 15 degrees = 50 degrees
Angle a = 180 degrees - (angle ABF + angle AFB) = 180 degrees - (angle ABF + angle DFE) = 180 degrees - (110 degrees + 50 degrees) = 20 degrees

If vector a = (3,0,2), B = (1, - 2,1), then 2a-3b=____ .

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