image imagewidth (px) 28 3.57k | label stringlengths 3 469 | image_path stringlengths 32 36 |
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( x - 2 ) ( x + 1 ) = 0 | ./MLHME\train_images\train_0.jpg | |
6 H C l + F e _ { 2 } O _ { 3 } = 2 F e C l _ { 3 } + 3 H _ { 2 } O . | ./MLHME\train_images\train_1.jpg | |
\frac { 2 ( 1 + b ) x + 2 b c x } { b ( 1 + a c + c ) } = 1 \Rightarrow \frac { 2 \times ( a c + 1 + c ) } { 1 + a c + c } = 1 | ./MLHME\train_images\train_2.jpg | |
x = - \sqrt { 7 } | ./MLHME\train_images\train_3.jpg | |
3 0 0 \times 1 = 3 0 0 1 0 0 \times 3 = 3 0 0 | ./MLHME\train_images\train_4.jpg | |
I _ { 3 } = \frac { U _ { 3 } } { R _ { 3 } } = \frac { 4 V } { 8 \Omega } = 0 . 5 A | ./MLHME\train_images\train_5.jpg | |
\vert a - 2 \vert + 1 = - ( a - 2 ) + 1 = - a + 3 | ./MLHME\train_images\train_6.jpg | |
\frac { 7 } { 1 8 } = \frac { 7 \times 2 } { 1 8 \times 2 } - \frac { 1 4 } { 3 6 } | ./MLHME\train_images\train_8.jpg | |
A E = B F = \angle G = D H | ./MLHME\train_images\train_10.jpg | |
( 3 x - \frac { 8 } { 3 } ) ^ { 2 } = \frac { 1 0 0 } { 9 } | ./MLHME\train_images\train_11.jpg | |
. \angle B D E = \angle B E D = \frac { 1 } { 2 } ( 1 8 0 - 3 0 ) = 7 5 ^ { \circ } | ./MLHME\train_images\train_12.jpg | |
\frac { 1 } { 2 } [ 2 2 - ( 2 2 k - 1 ) ] = \frac { 2 } { 3 } ( 2 2 - k ) | ./MLHME\train_images\train_13.jpg | |
( 3 + 5 ) \times 5 = O H \times \sqrt { 8 ^ { 2 } + 5 ^ { 2 } } | ./MLHME\train_images\train_14.jpg | |
\frac { 1 } { a } = \frac { 1 } { 2 } | ./MLHME\train_images\train_15.jpg | |
\lambda _ { 1 } = \frac { h } { P _ { 1 } } . \lambda _ { 2 } = \frac { h } { P _ { 2 } } | ./MLHME\train_images\train_16.jpg | |
[ ( 5 6 + 4 4 ) \div 2 ] \times ( 5 6 - 4 4 ) = 6 0 0 | ./MLHME\train_images\train_18.jpg | |
v = \frac { m } { p g } = \frac { 0 . 8 k g } { 1 . 0 \times 1 0 ^ { 3 } k g / m ^ { 2 } } = 0 . 8 \times 1 0 ^ { - 3 } m ^ { 3 } | ./MLHME\train_images\train_19.jpg | |
\frac { 1 } { a ^ { 3 } } + \frac { 1 } { b ^ { 3 } } + \frac { 1 } { c ^ { 3 } } \geq \frac { 3 } { a b c } | ./MLHME\train_images\train_20.jpg | |
\frac { 1 } { \sqrt { c } } = t | ./MLHME\train_images\train_21.jpg | |
1 0 0 \times \frac { 2 } { 1 0 } = 2 0 ( g ) | ./MLHME\train_images\train_22.jpg | |
( a _ { 1 } + 4 a + 1 ) ^ { 2 } = a _ { 1 } ( a _ { 1 } + 2 2 d + 1 ) | ./MLHME\train_images\train_23.jpg | |
a _ { n } = n ( a _ { n + 1 } - a _ { n } ) ( n \in N ^ { + } ) . | ./MLHME\train_images\train_24.jpg | |
\angle A O D = 9 0 ^ { \circ } - a | ./MLHME\train_images\train_25.jpg | |
5 \times 3 \times 4 = 6 0 ( d m ) ^ { 3 } | ./MLHME\train_images\train_27.jpg | |
\cdot ( 2 ^ { 6 } ) ^ { 2 x } \div ( 2 ^ { 3 } ) ^ { 2 x } \div 2 ^ { 2 } = 2 ^ { 6 } | ./MLHME\train_images\train_28.jpg | |
5 9 . 0 2 > 5 8 . 5 2 > 5 8 . 1 7 > 5 8 . 0 9 | ./MLHME\train_images\train_30.jpg | |
x _ { 1 } = \frac { \sqrt { 6 } } { 3 } | ./MLHME\train_images\train_38.jpg | |
2 \times 7 = 1 4 ( m ^ { 2 } ) | ./MLHME\train_images\train_39.jpg | |
2 x \frac { 1 } { \cdot \rho } \times \cos \theta + 4 \times \frac { 1 } { \rho } \sin \theta - 1 = 0 | ./MLHME\train_images\train_42.jpg | |
y ^ { 2 } - 2 0 y + 1 0 0 = 4 ( y + 5 ) | ./MLHME\train_images\train_44.jpg | |
x = \sqrt { 3 } - \frac { 1 } { 2 } | ./MLHME\train_images\train_46.jpg | |
x = \frac { 1 } { 3 } + \frac { 1 } { 6 } | ./MLHME\train_images\train_48.jpg | |
\cdot a ^ { 2 } - 4 a + 5 + a ^ { 2 } - 2 a + 1 0 = 1 7 | ./MLHME\train_images\train_49.jpg | |
\sin 1 8 ^ { \circ } = \frac { \pm \sqrt { 5 } - 1 } { 4 } | ./MLHME\train_images\train_50.jpg | |
S O _ { 4 } + B a C l _ { 2 } = 2 N a C C + B a S O _ { 4 } \downarrow | ./MLHME\train_images\train_52.jpg | |
\frac { P } { 2 n - 5 } \leq \frac { 2 p + 1 6 } { 2 ^ { n } } | ./MLHME\train_images\train_53.jpg | |
\frac { 2 7 } { 6 3 } > \frac { 1 8 } { 6 3 } > \frac { 1 4 } { 6 3 } | ./MLHME\train_images\train_54.jpg | |
y ^ { 2 } = \frac { 5 } { 2 } | ./MLHME\train_images\train_56.jpg | |
\therefore \cos \angle B A P = \frac { 8 + 9 - 5 } { 2 \times 2 \sqrt { 2 } \times 3 } = \frac { 1 2 } { 1 2 \sqrt { 2 } } = \frac { \sqrt { 2 } } { 2 } | ./MLHME\train_images\train_57.jpg | |
\frac { 1 } { x - y } = 2 | ./MLHME\train_images\train_58.jpg | |
0 . 5 \times 3 0 0 0 = 1 5 0 0 ( c m ) | ./MLHME\train_images\train_59.jpg | |
\angle D E O = \angle B E D - \angle B E A = 7 5 ^ { \circ } - 4 5 ^ { \circ } = 3 0 ^ { \circ } = \angle D B E | ./MLHME\train_images\train_60.jpg | |
\frac { 2 4 0 } { 4 } = \frac { 3 0 0 } { 5 } = \frac { 3 0 0 } { 6 } = \frac { 4 8 6 } { 8 } = \frac { 5 6 0 } { 9 } = 6 0 | ./MLHME\train_images\train_61.jpg | |
b _ { n + 1 } = \frac { 6 } { 3 } | ./MLHME\train_images\train_63.jpg | |
0 . 5 < 0 . 5 0 1 < 0 . 5 1 < 0 . 5 1 1 | ./MLHME\train_images\train_64.jpg | |
x = \frac { 7 } { 1 0 } | ./MLHME\train_images\train_65.jpg | |
= A B + B C + C D + A D = 1 0 + 1 5 + 6 + 1 0 = 4 1 | ./MLHME\train_images\train_67.jpg | |
a c = b c | ./MLHME\train_images\train_68.jpg | |
( 3 - x ) ^ { 2 } = \overline { ( 2 x - 3 ) } ^ { 2 } | ./MLHME\train_images\train_69.jpg | |
\cos \alpha = \frac { 1 } { s e c \alpha } = - \frac { 3 } { 5 } | ./MLHME\train_images\train_70.jpg | |
\angle C = 9 0 ^ { \circ } , \angle A = 6 0 ^ { \circ } , \therefore \angle B = 9 0 ^ { \circ } - \angle A = 3 0 ^ { \circ } , | ./MLHME\train_images\train_71.jpg | |
y = - \frac { 1 } { 1 0 } x + 1 0 | ./MLHME\train_images\train_74.jpg | |
_ { 。 } \angle C P Q = \angle B = 9 0 ^ { \circ } | ./MLHME\train_images\train_75.jpg | |
: P ( A ) = \frac { C _ { 2 } ^ { 2 } C _ { 3 } ^ { 2 } + C _ { 3 } ^ { 2 } C _ { 3 } ^ { 2 } } { C _ { 8 } ^ { 4 } } = \frac { 6 } { 3 5 } | ./MLHME\train_images\train_76.jpg | |
P = \frac { F } { S } = \frac { 4 9 N } { 1 \times 1 0 ^ { - 2 } m ^ { 2 } } = 4 9 0 0 P a | ./MLHME\train_images\train_77.jpg | |
\angle A C D = 9 0 ^ { \circ } + 4 5 ^ { \circ } = 1 3 5 ^ { \circ } | ./MLHME\train_images\train_79.jpg | |
\sin C = \frac { \sqrt { 2 } } { 2 } | ./MLHME\train_images\train_80.jpg | |
\angle O D B = 9 0 ^ { \circ } | ./MLHME\train_images\train_82.jpg | |
2 \times 3 . 1 4 \times 1 = 6 . 2 8 ( d m ) 3 . 1 4 \times 1 ^ { 2 } = 3 . 1 4 ( d m ^ { 2 } ) | ./MLHME\train_images\train_83.jpg | |
( x ) = x - \frac { 1 } { 2 } s m x - \frac { 1 1 } { 2 } - \frac { 1 } { 2 } s m x | ./MLHME\train_images\train_84.jpg | |
9 0 2 \times 4 7 0 = 4 2 3 9 4 0 1 7 4 \div 4 0 = 4 \cdots 1 4 2 7 5 \div 9 0 = 3 \cdots 5 | ./MLHME\train_images\train_86.jpg | |
= \frac { 2 } { n ( n - 1 ) } ( a _ { n } - 2 a n - 1 + a _ { n } - 2 ) | ./MLHME\train_images\train_87.jpg | |
S _ { \Delta } A D E : S _ { \Delta } A B C = 4 : 2 5 | ./MLHME\train_images\train_88.jpg | |
x - \frac { 3 } { 4 } + \frac { 3 } { 4 } = \frac { 1 } { 4 } + \frac { 3 } { 4 } | ./MLHME\train_images\train_89.jpg | |
\widehat { b } = \frac { \sum _ { i = 1 } ^ { 5 } x i y _ { i } - n \overline { x } \overline { y } } { \sum _ { i = 1 } ^ { 5 } x _ { i } ^ { 2 } - n \overline { x } ^ { 2 } } = \frac { 1 1 2 - 5 \times 6 \times 3 . 4 } { 2 0 0 - 5 \times 3 . 6 } = 0 . 5 | ./MLHME\train_images\train_90.jpg | |
1 2 - 2 ( 2 x - 5 ) = 3 ( 3 - x ) | ./MLHME\train_images\train_91.jpg | |
C u ( O H ) _ { 2 } + 2 H C l = C u C l _ { 2 } + 2 H _ { 2 } O | ./MLHME\train_images\train_92.jpg | |
\angle N F C - \angle N F M = \angle A N F - \angle E N F | ./MLHME\train_images\train_94.jpg | |
\frac { 1 } { 1 0 0 } - \frac { 1 } { 1 0 0 0 } | ./MLHME\train_images\train_95.jpg | |
F / / E B , \Delta D A M \cong \Delta C B F | ./MLHME\train_images\train_96.jpg | |
7 ^ { 2 } = b ^ { 2 } + 5 ^ { 2 } - 2 \times b \times 5 \times \cos 1 2 0 ^ { \circ } | ./MLHME\train_images\train_98.jpg | |
5 0 \div 2 0 0 = \frac { 1 } { 4 } | ./MLHME\train_images\train_99.jpg | |
\frac { 4 } { 1 5 } < \frac { 3 } { 8 } < | ./MLHME\train_images\train_100.jpg | |
\frac { A B } { D E } = \frac { 2 } { \sqrt { 2 } } = \sqrt { 2 } | ./MLHME\train_images\train_101.jpg | |
y = \frac { m } { x } | ./MLHME\train_images\train_102.jpg | |
\sqrt { 1 6 - n ^ { 2 } } \geq 0 , \sqrt { n ^ { 2 } - 1 6 } \geq 0 | ./MLHME\train_images\train_105.jpg | |
( 6 \div 2 ) ^ { 2 } \times 3 . 1 4 \times 6 \times \frac { 1 } { 3 } = 5 6 . 5 2 ( d m ^ { 3 } ) | ./MLHME\train_images\train_106.jpg | |
\frac { 3 - m } { 2 m - 4 } \div ( m + 2 - \frac { 5 } { m - 2 } ) | ./MLHME\train_images\train_108.jpg | |
3 . 1 \times 1 = \sqrt { 1 0 } | ./MLHME\train_images\train_109.jpg | |
\frac { 1 } { 2 } x = \frac { 1 } { 2 } + \frac { 1 } { 2 ^ { 2 } } + \frac { 1 } { 2 ^ { 3 } } + \frac { 1 } { 2 ^ { 4 } } + \cdots + \frac { 1 } { 2 ^ { 1 0 1 } } - \frac { 1 } { 2 } | ./MLHME\train_images\train_110.jpg | |
C H _ { 4 } - D O _ { 2 } = C O _ { 2 } + 2 H _ { 2 } O | ./MLHME\train_images\train_111.jpg | |
x _ { 1 } = \frac { - 4 \pm \sqrt { 1 6 + 1 6 } } { 2 . } = - 2 \pm 2 \sqrt { 2 } | ./MLHME\train_images\train_112.jpg | |
= 2 ( < O B A + \angle O B C ) | ./MLHME\train_images\train_113.jpg | |
y = \frac { ( \sqrt { 3 } + \sqrt { 2 } ) ^ { 2 } } { ( \sqrt { 3 } + \sqrt { 2 } ) ( \sqrt { 3 } - \sqrt { 2 } ) } = 5 + 2 \sqrt { 6 } | ./MLHME\train_images\train_114.jpg | |
x = \pm \sqrt { 1 4 4 } | ./MLHME\train_images\train_115.jpg | |
\frac { 3 6 0 ^ { \circ } } { n } = 3 0 ^ { \circ } | ./MLHME\train_images\train_116.jpg | |
\frac { 5 } { 3 V } = \frac { 1 0 } { 6 V } \therefore \frac { 3 } { 2 V } < \frac { 5 } { 3 V } | ./MLHME\train_images\train_118.jpg | |
2 \times 7 = 1 4 | ./MLHME\train_images\train_119.jpg | |
- 2 x ^ { 4 } - x ^ { 2 } + 5 = ( - x ^ { 2 } + 1 ) ( x + a ) + b = x ^ { 2 } + a x + 3 x - 3 a - b | ./MLHME\train_images\train_120.jpg | |
x ^ { . } + \frac { \sqrt { 6 } } { 4 } = - \frac { 3 } { 4 } \sqrt { 6 } | ./MLHME\train_images\train_121.jpg | |
A E = A C , \angle 1 = \angle 2 | ./MLHME\train_images\train_122.jpg | |
V _ { 1 } = I _ { 1 } R _ { 1 } = I R _ { 1 } = 0 . 3 A \times 2 0 N = 6 V | ./MLHME\train_images\train_123.jpg | |
\therefore a _ { n + 1 } = \frac { n + 1 } { 2 } a _ { n + 1 } + a _ { n } - \frac { n } { 2 } a _ { n } | ./MLHME\train_images\train_124.jpg | |
0 ^ { - 4 } m ^ { 2 } = 5 8 . 8 N | ./MLHME\train_images\train_126.jpg | |
\tan \angle P A C = \frac { 1 } { 3 } . | ./MLHME\train_images\train_127.jpg | |
\frac { \frac { 1 } { 2 } x } { y + \frac { 1 } { 2 } x } = \frac { O C _ { 1 } } { \frac { 1 } { 2 } x } | ./MLHME\train_images\train_129.jpg | |
x - \frac { 1 } { 2 } = 0 . 2 5 | ./MLHME\train_images\train_130.jpg | |
A l ( O H ) _ { 3 } + O H ^ { - } = A l O _ { 2 } ^ { - } + 2 H _ { 2 } O . | ./MLHME\train_images\train_131.jpg | |
( A B ) = 3 0 ^ { \circ } | ./MLHME\train_images\train_133.jpg | |
4 = 3 \frac { 2 } { 2 } | ./MLHME\train_images\train_134.jpg |
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