mn giup mik nhanh lên nhé! mik đang vội, ai làm nhanh mik tim cho:D
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\(f,=\left(5^2+3\right):7=28:7=4\\ g,=7^2-9+8\cdot25=49-9+200=240\\ h,=600+72+18=690\\ i,=5^2+5-20=10\\ j,=45-28+83=100\)
\(2A=\frac{4}{1.5}+\frac{6}{5.11}+\frac{8}{11.19}+\frac{10}{19.29}+\frac{12}{29.41}\)
\(=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{11}+\frac{1}{11}-\frac{1}{19}+...+\frac{1}{29}-\frac{1}{41}=1-\frac{1}{41}=\frac{40}{41}\)
\(\Rightarrow A=\frac{20}{21}\)
\(3B=\frac{3}{1.4}+\frac{6}{4.10}+\frac{9}{10.19}+\frac{12}{19.31}=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{10}+\frac{1}{10}-\frac{1}{19}+\frac{1}{19}-\frac{1}{31}\)
\(=1-\frac{1}{31}=\frac{30}{31}\)
\(\Rightarrow B=\frac{10}{31}=\frac{20}{62}<\frac{20}{41}\)
Do đó $A>B$
Ta có: \(A=\dfrac{2}{1.5}+\dfrac{3}{5.11}+\dfrac{4}{11.19}+\dfrac{5}{19.29}+\dfrac{6}{29.41}\)
\(2A=1-\dfrac{1}{5}+\dfrac{1}{5}+...+\dfrac{1}{29}-\dfrac{1}{41}\)
\(2A=1-\dfrac{1}{41}=\dfrac{40}{41}\)
\(A=\dfrac{20}{41}\)
Lại có: \(B=\dfrac{1}{1.4}+\dfrac{2}{4.10}+\dfrac{3}{10.19}+\dfrac{4}{19.31}\)
\(3B=\dfrac{3}{1.4}+\dfrac{6}{4.10}+\dfrac{9}{10.19}+\dfrac{12}{19.31}\)
\(3B=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{10}+...+\dfrac{1}{19}-\dfrac{1}{31}\)
\(3B=1-\dfrac{1}{31}=\dfrac{30}{31}\)
\(B=\dfrac{10}{31}\)
Vì \(\dfrac{20}{41}>\dfrac{10}{31}\) nên...
gọi d là ƯCLN(18n+3,21n+7)
ta có 18n+3chia hết cho d
21n+7 chia hết cho d
⇔21n+7-18n-3 chia hết cho d
⇔126n+42-126n-21 chia hết cho d
21 chia hết cho d
⇒d∈Ư(21)=1;3;7;21
n ≠ 3k-1;3k-3;3k-7;3k-21
Bài 4:
a) Ta có: \(\widehat{yOz}+\widehat{xOy}=180^0\)(2 góc kề bù)
\(\Rightarrow\widehat{yOz}=180^0-\widehat{xOy}=180^0-50^0=130^0\)
b) Ta có: \(\widehat{zOt}=\widehat{yOt}=\dfrac{1}{2}\widehat{yOz}=\dfrac{1}{2}.130^0=65^0\)(do Ot là tia phân giác \(\widehat{yOz}\))
c) Ta có: \(\widehat{xOt}=\widehat{yOt}+\widehat{xOy}=65^0+50^0=115^0\)
Bài 5:
a) Ta có: \(\widehat{xOz}+\widehat{xOy}=180^0\)(2 góc kề bù)
\(\Rightarrow\widehat{xOz}=180^0-\widehat{xOy}=180^0-110^0=70^0\)
b) Ta có: \(\widehat{zOt}=\dfrac{1}{2}\widehat{xOz}=\dfrac{1}{2}.70^0=35^0\)( Ot là tia phân giác \(\widehat{xOz}\))
c) Ta có: \(\widehat{xOt}=\widehat{zOt}=35^0\)( Ot là tia phân giác \(\widehat{xOz}\))
Bài 4:
a: Ta có: \(\widehat{xOy}+\widehat{yOz}=180^0\)
\(\Leftrightarrow\widehat{yOz}=180^0-50^0\)
\(\Leftrightarrow\widehat{yOz}=130^0\)
b: \(\widehat{zOt}=\dfrac{\widehat{yOz}}{2}=65^0\)
\(3n-2\inƯ\left(15\right)\) \(=\left\{1;-1;3;-3;5;-5;15;-15\right\}.\)
\(\Leftrightarrow n\in\left\{1;\dfrac{1}{3};\dfrac{5}{3};\dfrac{-1}{3};\dfrac{7}{3};-1;\dfrac{17}{3};\dfrac{-13}{3}\right\}.\)
Mà \(n\ne\dfrac{2}{3};n\in Z.\)
\(\Rightarrow n\in\left\{1;-1\right\}.\)
Bài 1:
c: Đặt \(\dfrac{x}{3}=\dfrac{y}{4}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=3k\\y=4k\end{matrix}\right.\)
Ta có: xy=48
\(\Leftrightarrow12k^2=48\)
\(\Leftrightarrow k^2=4\)
Trường hợp 1: k=2
\(\Leftrightarrow\left\{{}\begin{matrix}y=3k=3\cdot2=6\\y=4k=4\cdot2=8\end{matrix}\right.\)
Trường hợp 2: k=-2
\(\Leftrightarrow\left\{{}\begin{matrix}y=3k=3\cdot\left(-2\right)=-6\\y=4k=4\cdot\left(-2\right)=-8\end{matrix}\right.\)