Work out the following questions in a simple way! 8.41 times 47 + 8.41 times 52 + 8.41 12.67-（2.67+0.89）

Work out the following questions in a simple way! 8.41 times 47 + 8.41 times 52 + 8.41 12.67-（2.67+0.89）

8.41*47+8.41*52+8.41
=8.41*47+8.41*52+8.41*1
=8.41*（47+52+1）
=8.41*100
=841
12.67-（2.67+0.89）
=12.67-2.67-（1-0.11）
=10-1+0.11
=9.11

It is known that 3N + M can be divisible by 13

It is proved that if 3N + M = 13 а, then 3N = 13 а - M3N + 3 + M = 27 × (3n) + M = 27 (13 а - M) + M = 27 (13 а) - 26m = 13 (27 а - 2m) а3n + 3 + M can also be divisible by 13

8x-3 (3x + 2) = 6 solutions

Calculation: (1 / 50-1) * (1 / 49-1) * (1 / 48-1) *... * (1 / 4-1) * (1 / 3-1)

（1/50-1）*（1/49-1）*（1/48-1）*...*（1/4-1）*（1/3-1）
=（-49/50）*（-48/49）*（-47/48）*…… *（-2/3）
There are 48 negative factors, so the result is positive. The numerator of the former fraction can be reduced to the denominator of the latter fraction
=2/50
=1/25

4 ^ X-2 ^ (x + 1) + M = 0, find the value range of real number M

4^x-2^(x+1)+m=0
Then (2 ^ x) & sup2; - 2 × 2 ^ x + M = 0
Then (2 ^ x) & sup2; - 2 × 2 ^ x + 1 = 1-m
Then (2 ^ x-1) & sup2; = 1-m
Because (2 ^ x-1) & sup2; ≥ 0
So 1-m ≥ 0
So m ≤ 1

Find the remainder of the product 418 × 814 × 1616 divided by 13

418÷13=32… 2，814÷13=62… 8，1616÷13=124… 4，2×8×4=64，64÷13=4… 12. A: the product 418 × 814 × 1616 divided by 13 is 12

9.6 * 1.5 / 2.4 simple calculation 8.1 / 1.8 simple calculation 5.6 / 3.5 simple calculation

9.6*1.5/2.4
=(9.6/2.4)*1.5
=4*1.5
=6
8.1/1.8
=(0.9*9)/(0.9*2)
=9/2
=4.5
5.6/3.5
=(0.7*8)/(0.7*5)
=8/5
=1.6

Let three vertices of the triangle ABC be on the conic, and prove that the angles between AB and AC on both sides of the triangle ABC and a symmetry axis of the conic are equal if and only if the angles between the edge BC and the line L tangent to the conic at point a and a symmetry axis of the conic are equal

Desargues' homology therm (Therem of homologous triangles) there are two triangles △ ABC and △ def on the plane of Desargues' homology therm (Therem of homologous triangles). Let the lines of their corresponding vertices (A and D, B and E, C and F) intersect at one point

If the inequality system X ≤ MX > 11 has no solution, then the range of M is______ ．

Because the system of inequalities x ≤ MX ＞ 11 has no solution, according to the "large and small solutions can not" so m ≤ 11. So the answer is m ≤ 11

6.3 * 9.9 + 0.99 * 37, simple calculation
the sooner the better

= 63*0.99 + 37*0.99
=(63+37)*0.99
=100*0.99
=99