Lời giải:

Theo đề ta có:

\(\text{sđc(AD)}=\frac{1}{3}\text{sđc(AB)}=\frac{1}{9}[\text{sđc(AB)+sđc(BC)+sđc(CD)}]\)

\(=\frac{1}{9}(360^0-\text{sđc(AD)})\)

\(\Rightarrow \text{sđc(AD)}=36^0\)

\(\widehat{BEC}=\frac{\text{sđc(BC)-sđc(AD)}}{2}=\frac{3\text{sđc(AD)}-\text{sđc(AD)}}{2}=\text{sđc(AD)}=36^0\)

ĐKXĐ: \(\left\{{}\begin{matrix}-3x\ge0\\x^2-1\ne0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\le0\\x^2\ne1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\le0\\x\ne\pm1\end{matrix}\right.\)

Gọi \(J=CE\cap AB\), \(F=BD\cap AC\) , \(H=CE\cap BD\)

Có \(\widehat{EAB}=\widehat{ECB}=\dfrac{1}{2}sđ\stackrel\frown{EB}\)

\(\widehat{CAD}=\widehat{DBC}=\dfrac{1}{2}sđ\stackrel\frown{DC}\)

\(\Rightarrow\widehat{EAB}+\widehat{CAD}=\widehat{ECB}+\widehat{DBC}=180^0-\widehat{BHC}\)  (*)

Lại có \(\widehat{AJC}+\widehat{AFB}=180^0\) => Tứ giác AJHF nội tiếp đường tròn

\(\Rightarrow180^0=\widehat{BAC}+\widehat{JHF}=\widehat{BAC}+\widehat{BHC}\)

\(\Rightarrow180^0-\widehat{BHC}=\widehat{BAC}\) (2*)

Từ (*); (2*) => \(\widehat{EAB}+\widehat{CAD}=\widehat{BAC}\)

\(\Leftrightarrow\widehat{EAB}+\widehat{BAC}+\widehat{CAD}=2\widehat{BAC}\)

\(\Leftrightarrow\widehat{EAD}=2\alpha\)

Ý C

Lời giải:

HPT \(\Leftrightarrow \left\{\begin{matrix} xy+4x-5y-20=xy+x-4y-4\\ xy-3x+y-3=xy-2x-y+2\end{matrix}\right.\)

\( \Leftrightarrow \left\{\begin{matrix} 3x-y=16\\ -x+2y=5\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x=\frac{37}{5}\\ y=\frac{31}{5}\end{matrix}\right.\)

Khi đó: \(m+2n=\frac{37}{5}+2.\frac{31}{5}=\frac{99}{5}\)

Do AB bằng cạnh lục giác đều nội tiếp \(\Rightarrow\widehat{AOB}=\dfrac{1}{6}.360^0=60^0\)

\(\Rightarrow\Delta ABC\) đều \(\Rightarrow\left\{{}\begin{matrix}AB=OA=R\\OH=\dfrac{AB\sqrt{3}}{2}=\dfrac{R\sqrt{3}}{2}\end{matrix}\right.\)

Dây CD bằng cạnh tam giác đều nội tiếp \(\Rightarrow\widehat{COD}=\dfrac{1}{3}.360^0=120^0\Rightarrow\widehat{COK}=60^0\)

\(\Rightarrow\left\{{}\begin{matrix}CD=2CK=2OC.sin\widehat{COK}=R\sqrt{3}\\OK=OC.cos\widehat{COK}=\dfrac{R}{2}\end{matrix}\right.\)

\(\Rightarrow HK=OH-OK=\dfrac{R}{2}\left(\sqrt{3}-1\right)\)

\(S=\dfrac{1}{2}\left(AB+CD\right).HK=\dfrac{R^2}{2}\) (chắc có sự nhầm lẫn trong đáp án, không có hằng số \(\pi\) nào ở đây)

\(\sqrt{2x+5}\) xác định khi \(2x+5\ge0\Rightarrow2x\ge-5\Rightarrow x\ge-\dfrac{5}{2}\)

\(\sqrt{2x+5}\le0\Leftrightarrow2x+5\le0\Leftrightarrow2x\le-5\Leftrightarrow x\ge\dfrac{-5}{2}\)

\(\Rightarrow\) Đáp án:   A

Chọn A

ĐKXĐ: \(2x-3\ge0\\ \Rightarrow2x\ge0+3\\ \Rightarrow2x\ge3\\ \Rightarrow x\ge\dfrac{3}{2}\left(A\right)\)

Chọn A

\(\sqrt{3-2x}\) xác định khi \(3-2x\ge0\Rightarrow2x\le3-0\Rightarrow2x\le3\Rightarrow x\le\dfrac{3}{2}\left(D\right)\)

câu d

\(\sqrt{3-2x}\) xác định khi: \(3-2x\ge0\)

Ta giải BPT:

\(3-2x\ge0\)

<=> \(-2x\ge-3\)

<=> \(-2x:\left(-2\right)\le-3:\left(-2\right)\)

<=> \(x\le\dfrac{3}{2}\)