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Đổi 30 phút = 0,5 giờ
Quãng sông từ A đến B dài là:
\(x\) \(\times\) 0,5 + y \(\times\) 1 = 0,5\(x\) + y (km)
Kết luận Quãng đường từ A đên B dài: 0,5\(x\) + y (km)
Lời giải:
Áp dụng tính chất tổng 3 góc trong 1 tam giác bằng $180^0$
Hình 1: Hình không rõ ràng. Bạn xem lại.
Hình 2: $x+x+120^0=180^0$
$2x+120^0=180^0$
$2x=60^0$
$x=60^0:2=30^0$
Hình 3:
$2y+y+90^0=180^0$
$3y=180^0-90^0=90^0$
$y=90^0:3=30^0$
\(5x=3y\Rightarrow x=\dfrac{3y}{5}\)
Thay \(x=\dfrac{3y}{5}\) vào biểu thức \(x^2-y^2=-4\) ta có:
\(\left(\dfrac{3y}{5}\right)^2-y^2=-4\)
\(\dfrac{9y^2}{25}-y^2=-4\)
\(-\dfrac{16}{25}y^2=-4\)
\(y^2=-\dfrac{4}{\dfrac{-16}{25}}\)
\(y^2=\dfrac{25}{4}\)
\(\Rightarrow y=-\dfrac{5}{2};y=\dfrac{5}{2}\)
*) \(y=-\dfrac{5}{2}\Rightarrow x=\dfrac{3.\left(-\dfrac{5}{2}\right)}{5}=-\dfrac{3}{2}\)
*) \(y=\dfrac{5}{2}\Rightarrow x=\dfrac{3.\dfrac{5}{2}}{5}=\dfrac{3}{2}\)
Vậy ta được các cặp giá trị \(\left(x;y\right)\) thỏa mãn:
\(\left(-\dfrac{3}{2};-\dfrac{5}{2}\right);\left(\dfrac{3}{2};\dfrac{5}{2}\right)\)
Lời giải:
Áp dụng tính chất tổng 3 góc trong một tam giác bằng $180^0$
a.
$x=180^0-80^0-45^0=55^0$
b.
$y=180^0-30^0-90^0=60^0$
c.
$z=180^0-30^0-25^0=125^0$
a: \(-1,2+\dfrac{2}{3}+x=5\)
=>\(x=5+1,2-\dfrac{2}{3}=6,2-\dfrac{2}{3}\)
=>\(x=\dfrac{31}{5}-\dfrac{2}{3}=\dfrac{93}{15}-\dfrac{10}{15}=\dfrac{83}{15}\)
b: \(2\dfrac{4}{7}-3x=\dfrac{-4}{5}+\dfrac{2}{3}\)
=>\(\dfrac{18}{7}-3x=\dfrac{-12}{15}+\dfrac{10}{15}=\dfrac{-2}{15}\)
=>\(3x=\dfrac{18}{7}+\dfrac{2}{15}=\dfrac{270}{105}+\dfrac{14}{105}=\dfrac{284}{105}\)
=>\(x=\dfrac{284}{315}\)
c: \(\dfrac{1}{6}-\dfrac{3}{8}+1,75=3\dfrac{4}{3}-x\)
=>\(\dfrac{13}{3}-x=\dfrac{4}{24}-\dfrac{9}{24}+\dfrac{42}{24}=\dfrac{37}{24}\)
=>\(x=\dfrac{13}{3}-\dfrac{37}{24}=\dfrac{108}{24}-\dfrac{37}{24}=\dfrac{71}{24}\)
d: \(\dfrac{1}{6}-\dfrac{4}{9}+0,125=2\dfrac{4}{3}-2x\)
=>\(\dfrac{10}{3}-2x=\dfrac{-11}{72}\)
=>\(2x=\dfrac{10}{3}+\dfrac{11}{72}=\dfrac{240}{72}+\dfrac{11}{72}=\dfrac{251}{72}\)
=>\(x=\dfrac{251}{144}\)
e: \(2\dfrac{2}{3}-4x=\dfrac{-7}{5}+\dfrac{2}{3}\)
=>\(2+\dfrac{2}{3}-4x=\dfrac{-7}{5}+\dfrac{2}{3}\)
=>\(2-4x=-\dfrac{7}{5}\)
=>\(4x=2+\dfrac{7}{5}=\dfrac{17}{5}\)
=>\(x=\dfrac{17}{20}\)
f: \(\dfrac{1}{2}-\left(x+\dfrac{1}{3}\right)=\dfrac{5}{6}\)
=>\(x+\dfrac{1}{3}=\dfrac{1}{2}-\dfrac{5}{6}=\dfrac{3}{6}-\dfrac{5}{6}=\dfrac{-2}{6}=-\dfrac{1}{3}\)
=>\(x=-\dfrac{1}{3}-\dfrac{1}{3}=-\dfrac{2}{3}\)
g: \(\left(\dfrac{3}{5}-\dfrac{4}{3}\right)+\left(\dfrac{5}{8}-x\right)=\dfrac{9}{7}\)
=>\(\dfrac{-11}{15}+\dfrac{5}{8}-x=\dfrac{9}{7}\)
=>\(\dfrac{-13}{120}-x=\dfrac{9}{7}\)
=>\(x=-\dfrac{13}{120}-\dfrac{9}{7}=\dfrac{-1171}{840}\)
a, \(-1,2+\dfrac{2}{3}+x=5\Leftrightarrow x=5+1,2-\dfrac{2}{3}=\dfrac{83}{15}\)
b, \(2\dfrac{4}{7}-3x=-\dfrac{4}{5}+\dfrac{2}{3}\Leftrightarrow\dfrac{18}{7}-3x=-\dfrac{2}{15}\Leftrightarrow3x=\dfrac{284}{105}\Leftrightarrow x=\dfrac{284}{315}\)
c, \(\dfrac{1}{6}-\dfrac{3}{8}+1,75=3\dfrac{4}{3}-x\Leftrightarrow-x+\dfrac{13}{3}=\dfrac{37}{24}\Leftrightarrow x=\dfrac{13}{3}-\dfrac{37}{24}=\dfrac{67}{24}\)
d, \(\dfrac{1}{6}-\dfrac{4}{9}+0,125=2\dfrac{4}{3}-2x\Leftrightarrow-2x+\dfrac{10}{3}=-\dfrac{-11}{72}\Leftrightarrow2x=\dfrac{251}{72}\Leftrightarrow x=\dfrac{251}{144}\)
e, \(2\dfrac{2}{3}-4x=-\dfrac{7}{5}+\dfrac{2}{7}\Leftrightarrow\dfrac{8}{3}-4x=-\dfrac{39}{35}\Leftrightarrow4x=\dfrac{397}{105}\Leftrightarrow x=\dfrac{397}{420}\)
f, \(\dfrac{1}{2}-\left(x+\dfrac{1}{3}\right)=\dfrac{5}{6}\Leftrightarrow x+\dfrac{1}{3}=\dfrac{1}{2}-\dfrac{5}{6}=-\dfrac{1}{3}\Leftrightarrow x=-\dfrac{2}{3}\)
g, \(\left(\dfrac{3}{5}-\dfrac{4}{3}\right)+\left(\dfrac{5}{8}-x\right)=\dfrac{9}{7}\Leftrightarrow\dfrac{-11}{15}+\dfrac{5}{8}-x=\dfrac{9}{7}\Leftrightarrow\left(-\dfrac{13}{120}\right)-x=\dfrac{9}{7}\Leftrightarrow x=-\dfrac{1171}{840}\)