b: \(\dfrac{2x^3-3x^2+6x-9}{2x-3}=x^2+3\)

\(\widehat{bOm}=\widehat{aOm}=\dfrac{30}{2}=15^o\)

\(\widehat{cOn}=\widehat{aOn}=\dfrac{130}{2}=65^o\)

\(\widehat{nOb}=\widehat{aOn}-\widehat{aOb}=65-30=35^o\)

\(\rightarrow\widehat{nOm}=\widehat{nOb}+\widehat{mOb}=35+15=50^o\)

1b)

Song song => (d): x-y +a =0

Vì d đi qua C(2;-2) => 2- (-2)+a=0

<=>a=4

=> d: x-y+4=0

jimmmmmmmmmmmmmmmmmmmmmmmmmmm

he he he he he he

bài 1:

bn lấy giá trị của √(4^2-3,9^2) là dc

bài 2

AB+BC=2√(3^2+4^2)=??

Bài 4:

a: Ta có: DB⊥AE

AC⊥EA

Do đó: DB//AC

Xét ΔEAC có DB//AC

nên \(\frac{EB}{BA}=\frac{ED}{EC}\)

b: Xét ΔCEK có DB//EK

nên \(\frac{DB}{EK}=\frac{CD}{CE}\) (2)

Xét ΔCAE có DB//AE

nên \(\frac{CD}{DE}=\frac{AB}{BE}\)

=>\(\frac{CD}{DE+CD}=\frac{AB}{BE+AB}\)

=>\(\frac{CD}{CE}=\frac{AB}{AE}\) (1)

Xét ΔAEI có DB//EI

nên \(\frac{DB}{EI}=\frac{AB}{AE}\) (3)

Từ (1),(2),(3) suy ra \(\frac{DB}{EK}=\frac{DB}{EI}\)

=>EK=EI

c: Xét ΔHNC và ΔHEK có

\(\hat{HNC}=\hat{HEK}\) (hai góc so le trong, CN//EK)

\(\hat{NHC}=\hat{EHK}\) (hai góc đối đỉnh)

Do đó: ΔHNC~ΔHEK

=>\(\frac{NC}{EK}=\frac{HN}{HE}\left(4\right)\)

Xét ΔHNA và ΔHEI có

\(\hat{HNA}=\hat{HEI}\) (hai góc so le trong, NA//EI)

\(\hat{NHA}=\hat{EHI}\) (hai góc đối đỉnh)

Do đó: ΔHNA~ΔHEI

=>\(\frac{NA}{EI}=\frac{HN}{HE}\left(5\right)\)

Từ (4),(5) suy ra \(\frac{NC}{EK}=\frac{NA}{EI}\)

mà EK=EI

nên NC=NA

Xét ΔQNC và ΔQDB có

\(\hat{QNC}=\hat{QDB}\) (hai góc so le trong, CN//DB)

\(\hat{NQC}=\hat{DQB}\) (hai góc đối đỉnh)

Do đó: ΔQNC~ΔQDB

=>\(\frac{NC}{DB}=\frac{QN}{QD}=\frac{QC}{QB}\) (7)

Xét ΔPAN và ΔPDB có

\(\hat{PAN}=\hat{PDB}\) (hai góc so le trong, AN//BD)

\(\hat{APN}=\hat{DPB}\) (hai góc đối đỉnh)

Do đó: ΔPAN~ΔPDB

=>\(\frac{AN}{DB}=\frac{PA}{PD}=\frac{PN}{PB}\)

mà NC=NA

nên \(\frac{NC}{DB}=\frac{PA}{PD}=\frac{PN}{PB}\) (6)

Từ (6),(7) suy ra \(\frac{PA}{PD}=\frac{PN}{PB}=\frac{QN}{QD}=\frac{QC}{QB}\)

Xét ΔNDB có \(\frac{NQ}{QD}=\frac{NP}{PB}\)

nên QP//BD

\(\dfrac{9^{15}.8^{11}}{3^{29}.16^8}=\dfrac{\left(3^2\right)^{15}.\left(2^3\right)^{11}}{3^{29}.\left(2^4\right)^8}=\dfrac{3^{30}.2^{33}}{3^{29}.2^{32}}\)

Ta lấy vễ trên chia vế dưới

\(=3.2=6\)

\(\dfrac{2^{11}.9^3}{3^5.16^2}=\dfrac{2^{11}.\left(3^2\right)^3}{3^5.\left(2^4\right)^2}=\dfrac{2^{11}.3^6}{3^5.2^8}\)

Ta lấy vế trên chia vế dưới

\(=2^3.3=24\)

\(\dfrac{9^{15}.8^{11}}{3^{29}.16^8}=\dfrac{\left(3^2\right)^{15}.\left(2^3\right)^{11}}{3^{29}.\left(2^4\right)^8}=\dfrac{3^{30}.2^{33}}{3^{29}.3^{32}}=3.2=6\)
\(\dfrac{2^{11}.9^3}{3^5.16^2}=\dfrac{2^{11}.\left(3^2\right)^3}{3^5.\left(2^4\right)^2}=\dfrac{2^{11}.3^6}{3^5.2^8}=2^3.3=8.3=24\)

\(\dfrac{9^{15}.8^{11}}{3^{29}.16^8}=\dfrac{3^{30}.2^{33}}{3^{29}.2^{32}}=3.2=6\)

\(\dfrac{2^{11}.9^3}{3^5.16^2}=\dfrac{2^{11}.3^6}{3^5.2^8}=2^3.3=8.3=24\)