câu 3 5c mn giúp em cần gấp lắm ạ
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a: Xét ΔABM và ΔACM có
AB=AC
AM chung
BM=CM
Do đó:ΔABM=ΔACM
b: ta có: ΔABC cân tại A
mà AM là đường trung tuyến
nên AM là đường cao
c: BC=6cm
nên BM=3cm
=>AM=4cm
d: Xét ΔABC cân tại A có AM là đường cao
nên AM là phân giác của góc BAC
Xét ΔABC có
AM là đường phân giác
BI là đường phân giác
AM cắt BI tại I
Do đó: CI là tia phân giác của góc ACB
\(11,\\ a,M=\dfrac{1+\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\dfrac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}=\dfrac{\sqrt{a}-1}{\sqrt{a}}\\ b,M=\dfrac{\sqrt{a}-1}{\sqrt{a}}=1-\dfrac{1}{\sqrt{a}}< 1\left(\dfrac{1}{\sqrt{a}}>0\right)\)
\(9,\\ a,=\left|2-\sqrt{7}\right|=\sqrt{7}-2\\ b,=5\sqrt{3}+4\sqrt{3}-10\sqrt{3}=-\sqrt{3}\\ c,=3-4+2=1\\ d,=6\sqrt{3a}-4\sqrt{3a}=2\sqrt{3a}\\ 10,\)
a, Áp dụng HTL: \(x=\sqrt{9\cdot25}=15\)
b, Áp dụng HTL: \(\left\{{}\begin{matrix}8^2=10x\\y^2=x\left(x+10\right)\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=6,4\\y=\sqrt{6,4\cdot16,4}\approx10,245\end{matrix}\right.\)
Bài 6:
\(\Leftrightarrow6n+4⋮2n-1\)
\(\Leftrightarrow2n-1\in\left\{1;-1;7;-7\right\}\)
hay \(n\in\left\{1;0;4;-3\right\}\)
Refer
1 my sister is old. she can driver a car
=> My sister is old enough to drive a car
2 the ladder wasn't verry long .it didn't reach the ceiling
=> The ladder wasn't long enough to reach the ceiling
3 the fire isn't very hot. it won't boil a kettle
=> The fire isn't hot enough to boil a kettle
4 he is strong. he can carry that suicase
=> He is strong enough to carry that suitcase
5 Lan isn't strong . she can't swim across the rive
=> Lan isn't strong enough to swim across the river
6 she is beautiful and intelligent . she can become Miss World
=> She is beautiful and intelligent enough to become Miss World
7 MrRobert isn't rich he can't buy a house
=> Mr Robert isn't rich enough to buy a house
8 the worker in very clever . he can make nice things from wood
=> The worker is clever enough to make nice things from wood
9 our team is very good . we win the foodball match very often
=> Our team is good enough to win the football match very often
10 the radio isn't small . it can't be put it in your pocket
=> The radio isn't small enough to put in your pocket
Qua D kẻ đường thẳng song song AC cắt BA kéo dài tại E
\(\Rightarrow BE=2BA=2a\)
\(AC||DE\Rightarrow AC||\left(SDE\right)\Rightarrow d\left(AC;SD\right)=d\left(AC;\left(SDE\right)\right)=d\left(A;\left(SDE\right)\right)\)
\(AE=AD=a\Rightarrow\Delta ADE\) vuông cân tại A
Gọi I là trung điểm DE \(\Rightarrow AI\perp DE\Rightarrow DE\perp\left(SAI\right)\)
Trong mp (SAI), kẻ \(AJ\perp SI\Rightarrow AJ\perp\left(SDE\right)\Rightarrow AJ=d\left(A;\left(SDE\right)\right)\)
\(AI=\dfrac{AD}{2}=\dfrac{\sqrt{AE^2+AD^2}}{2}=\dfrac{a\sqrt{2}}{2}\)
\(\dfrac{1}{AJ^2}=\dfrac{1}{AI^2}+\dfrac{1}{SA^2}\Rightarrow AJ=\dfrac{AI.SA}{\sqrt{AI^2+SA^2}}=\dfrac{a\sqrt{3}}{3}\)