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4:
a: =>2/5x+7/20-2/20=1/10
=>2/5x+5/20=1/10
=>2/5x=1/10-1/4=4/40-10/40=-6/40=-3/20
=>x=-3/20:2/5=-3/20*5/2=-15/40=-3/8
b: 3/2-1/2x=-1/3+3=8/3
=>1/2x=3/2-8/3=9/6-16/6=-7/6
=>x=-7/6*2=-7/3
c: 15/8-1/8:(1/4x-0,5)=5/4
=>1/8:(1/4x-1/2)=15/8-5/4=15/8-10/8=5/8
=>1/4x-1/2=1/8:5/8=1/5
=>1/4x=1/5+1/2=7/10
=>x=7/10*4=28/10=2,8
d: \(\Leftrightarrow\left[\left(x+\dfrac{1}{2}\right)^3-\dfrac{5}{4}\right]=\dfrac{11}{4}-\dfrac{5}{8}=\dfrac{22-5}{8}=\dfrac{17}{8}\)
=>\(\left(x+\dfrac{1}{2}\right)^3=\dfrac{17}{8}+\dfrac{5}{4}=\dfrac{27}{8}\)
=>x+1/2=3/2
=>x=1
a:
C1: =3/4*2*1/2=3/2*1/2=3/4
C2: =1/2*2*3/4=1*3/4=3/4
b:
C1: =5/4*5/7=25/28
C2: =3/4*5/7+1/2*5/7=15/28+5/14=25/28
c:
C1: =13/21(5/7+2/7)=13/21
C2: =65/147+26/147=91/147=13/21
1 It was such a difficult climb that we stopped to rest several times
2 She didn't ran fast enough to win the race
3 It was such a heavy bag that I had to ask for help
4 The house is too small for us to live in
5 Jack's suit was so elegant that everyone complimented him
6 My sister is not old enough to watch horror films
7 My mother is such a wise person that people often aske her for advice
8 The package is not light enough for you to lift by yourself
9 This book is too old for the children to eat
10 It was such an interesting book that I couldn't put it down
11 It is such a weak bird that it can't fly
12 These boyss aren't old enough to watch that film
13 They are such small sandals that they don't fit me
Bài 1
Do BO là tia phân giác của ∠ABC (gt)
⇒ ∠OBE = ∠OBI
Do AO là tia phân giác của ∠BAC (gt)
⇒ ∠OAE = ∠OAF
Xét hai tam giác vuông: ∆OAE và ∆OAF có:
OA chung
∠OAE = ∠OAF (cmt)
⇒ ∆OAE = ∆OAF (cạnh huyền - góc nhọn)
⇒ OE = OF (hai cạnh tương ứng) (1)
Xét hai tam giác vuông: ∆OBE và ∆OBI có:
OB chung
∠OBE = ∠OBI (cmt)
⇒ ∆OBE = ∆OBI (cạnh huyền - góc nhọn)
⇒ OE = OI (hai cạnh tương ứng) (2)
Từ (1) và (2) ⇒ OE = OF = OI
Bài 2
a) Xét hai tam giác vuông: ∆BMI và ∆CMK có:
BM = CM (gt)
∠BMI = ∠CMK (đối đỉnh)
⇒ ∆BMI = ∆CMK (cạnh huyền - góc nhọn)
⇒ BI = CK (hai canhk tương ứn
b) Do ∆BMI = ∆CMK (cmt)
⇒ MI = MK (hai cạnh tương ứng)
Xét ∆BMK và ∆CMI có:
MK = MI (cmt)
∠BMK = ∠CMI (đối đỉnh)
BM = CM (gt)
⇒ ∆BMK = ∆CMI (c-g-c)
⇒ ∠MBK = ∠MCI (hai góc tương ứng)
Mà ∠MBK và ∠MCI là hai góc so le trong)
⇒ BK // CI
1 He is told to take a long rest
2 This plant isn't watered everyday
3 Beer is drunk all over the world
4 Uniform is worn to school by students
5 Reports are sent to the manager by the secretary in the afternoon
6 How many languages are spoken in Canada?
Bài 2
1 I was brought this dish by the waiter
2 I wasn't showed the special cameras
3 Her ticket was showed to her friends
4 The broken cup was hidden in the drawer by Tom
5 The fridge wasmoved into the living room by his uncle
1 that players understand
2 that you be
3 that young people have
4 that I speak
5 that the team get
6 that he pass
7 that we speak
8 that he meet
9 that he find
10 that he tell
Ta có: \(\dfrac{AB}{AC}=\dfrac{2}{3}\). Gọi \(AB=2x\left(cm\right),AC=3x\left(cm\right)\)
Áp dụng định lý Pytago trong tam giác vuông ABC:
\(BC^2=AB^2+AC^2=4x^2+9x^2=13x^2\)
\(\Rightarrow BC=\sqrt{13}x\)
Xét tam giác ABC vuông tại A có đường cao AH:
\(AH.BC=AB.AC\)(hệ thức lượng trong tam giác vuông)
\(\Rightarrow6\sqrt{13}x=6x^2\)
\(\Rightarrow x^2-\sqrt{13}x=0\)
Vì x > 0
\(\Rightarrow x=\sqrt{13}\left(cm\right)\)
\(\Rightarrow\left\{{}\begin{matrix}AB=2x=2\sqrt{13}\left(cm\right)\\AC=3x=3\sqrt{13}\left(cm\right)\\BC=\sqrt{13}x=13\left(cm\right)\end{matrix}\right.\)
Ta có: \(\dfrac{AB}{AC}=\dfrac{2}{3}\)
nên \(\dfrac{HB}{HC}=\dfrac{4}{9}\)
\(\Leftrightarrow HB=\dfrac{4}{9}HC\)
Ta có: \(AH^2=HB\cdot HC\)
\(\Leftrightarrow HC^2\cdot\dfrac{4}{9}=36\)
\(\Leftrightarrow HC^2=16\)
\(\Leftrightarrow HC=4\left(cm\right)\)
\(\Leftrightarrow HB=9\left(cm\right)\)
Ta có: BH+HC=BC
nên BC=4+9=13(cm)
Áp dụng hệ thức lượng trong tam giác vuông vào ΔABC vuông tại A có AH là đường cao ứng với cạnh huyền BC, ta được:
\(\left\{{}\begin{matrix}AB^2=BH\cdot BC\\AC^2=CH\cdot BC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}AB=2\sqrt{13}\left(cm\right)\\AC=3\sqrt{13}\left(cm\right)\end{matrix}\right.\)