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- \(0 , 6 - 75 \% = \frac{3}{5} - \frac{3}{4} = - \frac{3}{20}\).
- \(\frac{1}{5} - 1 \frac{3}{4} = \frac{1}{5} - \frac{7}{4} = - \frac{31}{20}\).
- \(\left(\right. - 3 / 20 \left.\right) : \left(\right. - 31 / 20 \left.\right) = 3 / 31\)=0,0968
theo minh thấy bạn nên hỏi từng câu thì sẽ dễ giải hơn ý
Ta có: \(\dfrac{a}{b}< \dfrac{c}{d}\Rightarrow ad< bc\)
\(\Rightarrow ad+cd< bc+dc\)
\(\Rightarrow d\left(a+c\right)< c\left(b+d\right)\)
\(\Rightarrow\dfrac{a+c}{b+d}< \dfrac{c}{d}\) (1)
\(ad< bc\)
\(\Rightarrow ad+ab< bc+ab\)
\(\Rightarrow a\left(b+d\right)< b\left(a+c\right)\)
\(\Rightarrow\dfrac{a}{b}< \dfrac{a+c}{b+d}\) (2)
Từ (1), (2) \(\Rightarrow\dfrac{a}{b}< \dfrac{a+c}{b+d}< \dfrac{c}{d}\left(đpcm\right)\)
Ta có :
\(\dfrac{a}{b}< \dfrac{c}{d}\Rightarrow ad< bc\)
\(\Rightarrow ad+ab< bc+ab\Rightarrow a\left(d+b\right)< b\left(c+a\right)\)
\(\Rightarrow\dfrac{a}{b}< \dfrac{a+c}{b+d}\left(1\right)\)
Lại có :
\(ad< bc\Rightarrow ad+cd< bc+cd\Rightarrow d\left(a+c\right)< c\left(b+d\right)\)
\(\Rightarrow\dfrac{a+c}{b+d}< \dfrac{c}{d}\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\Leftrightarrow\dfrac{a}{b}< \dfrac{a+c}{b+d}< \dfrac{c}{d}\rightarrowđpcm\)
a) Ta có : (3x - 0.5) ( 2x + 2.5) = 0
\(\Leftrightarrow\orbr{\begin{cases}3x-0,5=0\\2x+2,5=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}3x=0,5\\2x=-2,5\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{0,5}{3}=\frac{1}{6}\\x=-\frac{2,5}{2}=\frac{5}{4}\end{cases}}\)
1) x = 2017
2) Ta có: \(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\Rightarrow\frac{5z-25}{30}=\frac{3x-3}{6}=\frac{4y+12}{16}\)
\(\Rightarrow\frac{5z-25-3x+3-4y-12}{30-6-16}=\frac{\left(5z-3x-4y\right)-25+3-12}{8}=\frac{50-34}{8}=\frac{16}{8}=2\)
\(\Rightarrow x=2.2+1=5\)
\(\Rightarrow y=2.4-3=5\)
\(\Rightarrow z=2.6+5=17\)
Vậy x=5; y=5; z=17
\(x:\left(3-2\right)^2=\left(3-2\right)^3\)
\(x=\left(3-2\right)^3\cdot\left(3-2\right)^2\)
\(x=\left(3-2\right)^5=1^5\)
⇒ x = 1
vậy x = 1
a có:
\(\frac{15}{x - 9} = \frac{20}{y - 12}\)Nhân chéo:
\(15\left(y-12\left.\right)=20\left(x-9\left.\right)\Rightarrow15y-180=20x-180\Rightarrow15y=20x\Rightarrow3y=4x\Rightarrow y=\frac{4 x}{3}\right.\right.(\text{1})\)Lại có:
\(xy=1200(\text{2})\)Thay (1) vào (2), ta được:
\(x \cdot \frac{4 x}{3} = 1200 \Rightarrow \frac{4 x^{2}}{3} = 1200 \Rightarrow 4 x^{2} = 3600 \Rightarrow x^{2} = 900 \Rightarrow x = \pm 30\)Xét từng trường hợp:
Trường hợp 1: \(x = 30 \Rightarrow y = \frac{4 \cdot 30}{3} = 40\)
Ta có:
\(\frac{15}{x - 9} = \frac{15}{21} = \frac{5}{7} \Rightarrow \frac{40}{z - 24} = \frac{5}{7} \Rightarrow 5 \left(\right. z - 24 \left.\right) = 280 \Rightarrow z = 80 > 0 \&\text{nbsp}; \left(\right. \text{th}ỏ\text{a}\&\text{nbsp};\text{m} \overset{\sim}{\text{a}} \text{n} \left.\right)\)Trường hợp 2: \(x = - 30 \Rightarrow y = \frac{4 \cdot \left(\right. - 30 \left.\right)}{3} = - 40\)
Khi đó:
\(\frac{15}{x - 9}=\frac{15}{- 39}=-\frac{5}{13}\Rightarrow\frac{40}{z - 24}=-\frac{5}{13}\Rightarrow-5\left(\right.z-24\left.\right)=520\Rightarrow z=-80+24=-56<0;\left(\right.loại\left.\right)\)Vậy nghiệm của bài toán là:
\(\boxed{x = 30 , y = 40 , z = 80}\)