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Câu 1: A
Câu 2: D
Câu 3: C
Câu 4: A
Câu 5: A
Câu 6: B
Câu 7: C
Câu 8: D
Bài 5:
a) \(0,24\cdot-\dfrac{15}{4}=\dfrac{6}{25}\cdot-\dfrac{15}{4}=\dfrac{6\cdot-15}{25\cdot4}=-\dfrac{90}{100}=-\dfrac{9}{10}\)
b) \(4,5\cdot\dfrac{-4}{9}=\dfrac{9}{2}\cdot\dfrac{-4}{9}=\dfrac{9\cdot-4}{2\cdot9}=-\dfrac{4}{2}=-2\)
c) \(3,5\cdot-1\dfrac{2}{5}=\dfrac{7}{2}\cdot\dfrac{-7}{5}=\dfrac{7\cdot-7}{2\cdot5}=-\dfrac{49}{10}\)
Bài 6:
a) \(1\dfrac{1}{17}\cdot\left(-2\dfrac{1}{8}\right)=\dfrac{18}{17}\cdot\dfrac{-17}{8}=\dfrac{18\cdot-17}{17\cdot8}=\dfrac{-18}{8}=-\dfrac{9}{4}\)
b) \(\left(-2\dfrac{1}{3}\right)\cdot1\dfrac{1}{14}=-\dfrac{7}{3}\cdot\dfrac{15}{14}=\dfrac{-7\cdot15}{3\cdot14}=-\dfrac{5}{2}\)
c) \(1,25\cdot\left(-3\dfrac{3}{8}\right)=\dfrac{5}{4}\cdot-\dfrac{27}{8}=\dfrac{5\cdot-27}{4\cdot8}=-\dfrac{135}{32}\)
a. f(\(\dfrac{-1}{2}\)) = \(4.\left(\dfrac{-1}{2}\right)^2+3.\left(\dfrac{-1}{2}\right)-2\)
= \(4.\dfrac{1}{4}-\left(\dfrac{-3}{2}\right)-\dfrac{4}{2}\)
= \(\dfrac{2}{2}+\dfrac{3}{2}-\dfrac{4}{2}\)
= \(\dfrac{1}{2}\)
Bài 3:
a) \(\left(-\dfrac{2}{3}\right)^2\cdot\left(\dfrac{2}{3}\right)^5\)
\(=\left(\dfrac{2}{3}\right)^2\cdot\left(\dfrac{2}{3}\right)^5\)
\(=\left(\dfrac{2}{3}\right)^{2+5}\)
\(=\left(\dfrac{2}{3}\right)^7\)
b) \(\left(-\dfrac{1}{2}\right)^5\cdot\left(-\dfrac{1}{2}\right)^3\)
\(=\left(-\dfrac{1}{2}\right)^{5+3}\)
\(=\left(-\dfrac{1}{2}\right)^8\)
\(=\left(\dfrac{1}{2}\right)^8\)
c) \(\left(\dfrac{6}{5}\right)^7\cdot\left(-\dfrac{6}{5}\right)^4\)
\(=\left(\dfrac{6}{5}\right)^7\cdot\left(\dfrac{6}{5}\right)^4\)
\(=\left(\dfrac{6}{5}\right)^{7+4}\)
\(=\left(\dfrac{6}{5}\right)^{11}\)
Bài 4:
a) \(\left(\dfrac{3}{7}\right)^4:\left(-\dfrac{3}{7}\right)^2\)
\(=\left(\dfrac{3}{7}\right)^4\cdot\left(\dfrac{3}{7}\right)^2\)
\(=\left(\dfrac{3}{7}\right)^{4+2}\)
\(=\left(\dfrac{3}{7}\right)^6\)
b) \(\left(\dfrac{5}{9}\right)^{11}:\left(\dfrac{5}{9}\right)^7\)
\(=\left(\dfrac{5}{9}\right)^{11-7}\)
\(=\left(\dfrac{5}{9}\right)^4\)
c) \(\left(\dfrac{2}{13}\right)^7:\left(\dfrac{2}{13}\right)^5\)
\(=\left(\dfrac{2}{13}\right)^{7-5}\)
\(=\left(\dfrac{2}{13}\right)^2\)
Bài 2:
a: Ta có: ΔABC cân tại A
mà AH là đường cao
nên AH là tia phân giác của góc BAC
b: Xét ΔAMH vuông tại M và ΔANH vuông tại N có
AH chung
\(\widehat{MAH}=\widehat{NAH}\)
Do đó: ΔAMH=ΔANH
Suy ra: AM=AN
hay ΔAMN cân tại A
c: Xét ΔABC có AM/AB=AN/AC
nên MN//BC
d: \(AH^2-AN^2=HN^2\)
\(BH^2-BM^2=MH^2\)
mà HN=MH
nên \(AH^2-AN^2=BH^2-BM^2\)
hay \(AH^2+BM^2=BH^2+AN^2\)
TL:
10. A(1;-2) (hoặc bn có thể chọn điểm khác vs tạo độ khác cx đc)
11. y tỉ lệ thuận với x
\(\dfrac{11}{15}-\dfrac{9}{10}< x< \dfrac{11}{5}:\dfrac{9}{10}\)
\(\Leftrightarrow\dfrac{22-27}{30}< x< \dfrac{11}{5}\cdot\dfrac{10}{9}\)
\(\Leftrightarrow\dfrac{-1}{6}< x< \dfrac{22}{9}\)
\(\Leftrightarrow x\in\left\{0;1;2\right\}\)
c) Ta có: \(-16x^{3-n}\cdot\left(\dfrac{-5}{8}ax^{3+n}\right)\cdot\left(-2017x^n\right)^0\)
\(=-16x^{3-n}\cdot\dfrac{-5}{8}a\cdot x^{3+n}\)
\(=10ax^{9-n^2}\)