\(10+20+30+40+50+60+70+80+90\)

\(=\left(10+90\right)+\left(20+80\right)+\left(30+70\right)+\left(40+60\right)+50\)

\(=100+100+100+100+50\)

\(=400+50\)

\(=450\)

The average of 6, 8 and 16 is:

\(\dfrac{6+8+16}{3}=\dfrac{30}{3}=10\)

Answer: 10

We have: \(\dfrac{10+10+10}{3}=\dfrac{30}{3}=10\)

So the average of 10 + 10 + 10 is 10.

\(M=\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)\)

\(M=\dfrac{5}{7}.\dfrac{-7}{11}\)

\(M=\dfrac{-5}{11}\)

Welcome!

\(3^2+3^3+3^4=9+27+81=117\)

Don't you ask and answer by yourself?

You left: 130 - 100 = 30 (apples)

20 + 80 + 40 + 50 + 20 + 60

= (20 + 80) + (40 + 60) + 50 + 20

= 100 + 100 + 50 + 20

= 270

The age of the younger sister in this year is: (43 - 7) : 2 = 18 (years old)

The age of the younger sister in 7 years later is: 18 + 7 = 25 (years old)

We have:

\(4=2^2\)

\(8=2^3\)

\(10=2.5\)

\(\Rightarrow LCM\left(4;8;10\right)=2^3.5=40\)

What do you mean? I just rewrite the question! The one who asked is Lula Nguyễn, not me!

\(A=\dfrac{2}{4.5}+\dfrac{2}{5.6}+\dfrac{2}{6.7}+...+\dfrac{2}{15.16}\)

\(A=2\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{15.16}\right)\)

\(A=2\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)\)

\(A=2\left(\dfrac{1}{4}-\dfrac{1}{16}\right)\)

\(A=2.\dfrac{3}{16}\)

\(A=\dfrac{6}{16}=\dfrac{3}{8}\)

\(A=\dfrac{\left(1+50\right).50}{2}\)

\(A=\dfrac{51.50}{2}\)

\(A=\dfrac{2550}{2}\)

\(A=1275\)

Faded and Fake! This topic isn't a question, you shouldn't post it anymore.

\(A=2^2.2^3.2^4.2^5\)

\(A=2^{2+3+4+5}\)

\(A=2^{14}\)

a) 46 + 17 + 54

= (46 + 54) + 17

= 100 + 17

= 117

b) 4 . 35 . 25

= (4 . 25) . 35

= 100 . 35

= 3500

\(x-10+2=20+10\)

\(\Leftrightarrow x-8=30\)

\(\Leftrightarrow x=30+8\)

\(\Leftrightarrow x=38\)

Check my answer, it's shorter than the others people's answer.

We have:

\(10=2.5\)

\(20=2^2.5\)

\(30=2.3.5\)

\(\Rightarrow GCD\left(10;20;30\right)=2.5=10\)

We have:SCM

\(4=2^2\)

\(6=2.3\)

\(8=2^3\)

\(\Rightarrow SCM\left(4;6;8\right)=2^3.3=24\)

You can see them on the last pages of the dictionary.

\(\dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{4}+\dfrac{1}{3}\)

\(=\left(\dfrac{1}{2}+\dfrac{3}{4}\right)+\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\)

\(=\left(\dfrac{2}{4}+\dfrac{3}{4}\right)+1\)

\(=\dfrac{5}{4}+1\)

\(=\dfrac{9}{4}\)

"First month", not "month 1". We can also call it is "January". There are 31 days in January.

\(S=1+3+3^2+...+3^{50}\)

\(\Rightarrow3S=3+3^2+3^3+...+3^{51}\)

\(\Rightarrow3S-S=2S=3^{51}-1\)

So \(S=\dfrac{3^{51}-1}{2}\)

\(A=\dfrac{3\left|x\right|+2}{4\left|x\right|-5}\)

\(\Leftrightarrow4A=\dfrac{12\left|x\right|+8}{4\left|x\right|-5}\)

\(\Leftrightarrow4A=\dfrac{3\left(4\left|x\right|-5\right)+23}{4\left|x\right|-5}\)

\(\Leftrightarrow4A=\dfrac{3\left(4\left|x\right|-5\right)}{4\left|x\right|-5}+\dfrac{23}{4\left|x\right|-5}\)

\(\Leftrightarrow4A=3+\dfrac{23}{4\left|x\right|-5}\)

We have \(\left|x\right|\ge0\Rightarrow4\left|x\right|\ge0\Rightarrow4\left|x\right|-5\ge-5\)

\(\Rightarrow\dfrac{1}{4\left|x\right|-5}\le-\dfrac{1}{5}\)

\(\Rightarrow\dfrac{23}{4\left|x\right|-5}\le-\dfrac{23}{5}\)

\(\Rightarrow3+\dfrac{23}{4\left|x\right|-5}\le3+\left(-\dfrac{23}{5}\right)\)

\(\Rightarrow4A\le-\dfrac{8}{5}\)

\(\Rightarrow A\le-\dfrac{2}{5}\)

\(\Rightarrow MaxA=-\dfrac{2}{5}\) when \(x=0\)