Datasets:
HamAndCheese82
/
mathocr-v2

Dataset card Data Studio Files Community
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HW
[ "$\\displaystyle Q(-3,6)$" ]
HW
[ "$\\displaystyle \\sqrt{(6+3)^{2}+(3-6)^{2}}=\\sqrt{81+9}=3 \\sqrt{10}$" ]
HW
[ "$\\displaystyle \\sqrt{(6+3)^{2}+(3-6)^{2}}=\\sqrt{81+9}=3 \\sqrt{10}$" ]
HW
[ "$\\displaystyle 3\\sqrt{10}$" ]
HW
[ "$\\displaystyle 3\\sqrt{10}$" ]
HW
[ "$\\displaystyle 3(-y)+2(-x)-3=0$" ]
HW
[ "$\\displaystyle 3(-y)+2(-x)-3=0$" ]
HW
[ "$\\displaystyle 2 x+3 y+3=0$" ]
HW
[ "$\\displaystyle 2 x+3 y+3=0$" ]
HW
[ "$\\displaystyle 2 x+3 y+3=0$" ]
HW
[ "$\\displaystyle 2(-x)+2(-y)+k=0$" ]
HW
[ "$\\displaystyle 2(-x)+2(-y)+k=0$" ]
HW
[ "$\\displaystyle 2 x+2 y-k=0$" ]
HW
[ "$\\displaystyle 2 x+2 y-k=0$" ]
HW
[ "$\\displaystyle \\frac{|2 \\times 5+2 \\times 1-k|}{\\sqrt{2^{2}+2^{2}}}=2$" ]
HW
[ "$\\displaystyle \\frac{|2 \\times 5+2 \\times 1-k|}{\\sqrt{2^{2}+2^{2}}}=2$" ]
HW
[ "$\\displaystyle k=12 \\pm 4 \\sqrt{2}$" ]
HW
[ "$\\displaystyle k=12 \\pm 4 \\sqrt{2}$" ]
HW
[ "$\\displaystyle -3 y-3 x-4=0$" ]
HW
[ "$\\displaystyle 3 x+3 y+4=0$" ]
HW
[ "$\\displaystyle y-3=-(x+2)^{2}+4(x+2)-1$" ]
HW
[ "$\\displaystyle y=-x^{2}+6$" ]
HW
[ "$\\displaystyle y=-x^{2}+6$" ]
HW
[ "$\\displaystyle (x+2)^{2}+(y-4)^{2}=k^{2}$" ]
HW
[ "$\\displaystyle (x+2)^{2}+(y-4)^{2}=k^{2}$" ]
HW
[ "$\\displaystyle k=q$" ]
HW
[ "$\\displaystyle 2-a=25 \\rightarrow a=-23$" ]
HW
[ "$\\displaystyle 2-a=25 \\rightarrow a=-23$" ]
HW
[ "$\\displaystyle b=-2$" ]
HW
[ "$\\displaystyle b=-2$" ]
HW
[ "$\\displaystyle -25$" ]
HW
[ "$\\displaystyle -25$" ]
HW
[ "$\\displaystyle y=-x^{2}+\\frac{1}{6} x-\\frac{1}{6}$" ]
HW
[ "$\\displaystyle y=-x^{2}+\\frac{1}{6} x-\\frac{1}{6}$" ]
HW
[ "$\\displaystyle a=-8, \\quad 8=-1$" ]
HW
[ "$\\displaystyle a=-8, \\quad 8=-1$" ]
HW
[ "$\\displaystyle 4 x+y-6=0$" ]
HW
[ "$\\displaystyle 4 x+y+10=0$" ]
HW
[ "$\\displaystyle 4 x+y+10=0$" ]
HW
[ "11" ]
HW
[ "11" ]
HW
[ "$\\displaystyle (x+1)^{2}+(y-5)^{2}=1$" ]
HW
[ "$\\displaystyle (x+1)^{2}+(y-5)^{2}=1$" ]
HW
[ "$\\displaystyle y=(x-4)-2+m$" ]
HW
[ "$\\displaystyle 3=-3+m, m=6$" ]
HW
[ "$\\displaystyle mn=12$" ]
HW
[ "$\\displaystyle mn=12$" ]
HW
[ "$\\displaystyle 12$" ]
HW
[ "$\\displaystyle 12$" ]
HW
[ "$\\displaystyle \\overline{O A}=\\sqrt{4^{2}+1^{2}}=\\sqrt{17}$" ]
HW
[ "$\\displaystyle \\overline{O A}=\\sqrt{4^{2}+1^{2}}=\\sqrt{17}$" ]
HW
[ "$\\displaystyle (a+4)^{2}=104$" ]
HW
[ "$\\displaystyle a+4=2 \\sqrt{26}(\\because a>0)$" ]
HW
[ "$\\displaystyle a=2 \\sqrt{26}-4$" ]
HW
[ "$\\displaystyle a=2 \\sqrt{26}-4$" ]
HW
[ "$\\displaystyle 2 \\sqrt{26}-4$" ]
HW
[ "$\\displaystyle 5.$" ]
HW
[ "$\\displaystyle 5.$" ]
HW
[ "$\\displaystyle 2 X-2 B=2 A+4 B$" ]
HW
[ "$\\displaystyle =7x^{2}+xy+6 y^{2}+3(-3x^{2}+5xy $" ]
HW
[ "$\\displaystyle =7x^{2}+xy+6 y^{2}+3(-3x^{2}+5xy $" ]
HW
[ "$\\displaystyle \\left.+6 4^{2}\\right)$" ]
HW
[ "$\\displaystyle =-2 x^{2}+16 x y+24 y^{2}$" ]
HW
[ "⑫ $\\displaystyle x^{4}+5x^{3}+11x^{2}+15x+9=A\\left(x^{2}+3x+4\\right)+4x+5$" ]
HW
[ "⑫ $\\displaystyle x^{4}+5x^{3}+11x^{2}+15x+9=A\\left(x^{2}+3x+4\\right)+4x+5$" ]
HW
[ "$\\displaystyle x^{4}+5 x^{3}+11 x^{2}+11 x+4=A\\left(x^{2}+3 x+4\\right) .$" ]
HW
[ "$\\displaystyle A=x^{2}+2 x+1$" ]
HW
[ "$\\displaystyle 5 x-5 x^{2}-2+17 x^{3}$" ]
HW
[ "$\\displaystyle 5 x-5 x^{2}-2+17 x^{3}$" ]
HW
[ "$\\displaystyle 17 x^{3}-5 x^{2}+5 x-2$" ]
HW
[ "$\\displaystyle 17 x^{3}-5 x^{2}+5 x-2$" ]
HW
[ "Good!!" ]
HW
[ "Good!!" ]
HW
[ "$\\displaystyle (3 x-2)(3 x+2)\\left(3^{2} x^{2}+2^{2}\\right)\\left(3^{4} x^{4}+2^{4}\\right)=\\left(3^{2} x^{2}-2^{2}\\right)\\left(3^{2} x^{2}+2^{2}\\right)\\left(3^{4} x^{4}+2^{4}\\right)=\\left(3^{4}x^{4}-2^{4}\\right)\\left(3^{4} x^{4}+2^{4}\\right)=$" ]
HW
[ "$\\displaystyle (3 x-2)(3 x+2)\\left(3^{2} x^{2}+2^{2}\\right)\\left(3^{4} x^{4}+2^{4}\\right)=\\left(3^{2} x^{2}-2^{2}\\right)\\left(3^{2} x^{2}+2^{2}\\right)\\left(3^{4} x^{4}+2^{4}\\right)=\\left(3^{4}x^{4}-2^{4}\\right)\\left(3^{4} x^{4}+2^{4}\\right)=$" ]
HW
[ "perfect!!" ]
HW
[ "49. ① $\\displaystyle -16ab(4a+4b-4c)$" ]
HW
[ "49. ① $\\displaystyle -16ab(4a+4b-4c)$" ]
HW
[ "$\\displaystyle =-64 a^{2} b-64 a b^{2}+64 a b c$" ]
HW
[ "$\\displaystyle =-64 a^{2} b-64 a b^{2}+64 a b c$" ]
HW
[ "② $\\displaystyle {(4 a)}^{3}+{(4 b)}^{3}+{(-4 c)}^{3}-3(-64 a b c)$" ]
HW
[ "$\\displaystyle =64 a^{3}+64 b^{3}-64 c^{3}+192 a b c$" ]
HW
[ "$\\displaystyle =64 a^{3}+64 b^{3}-64 c^{3}+192 a b c$" ]
HW
[ "$\\displaystyle -64 a b^{2}+236 a b c$" ]
HW
[ "$\\displaystyle x^{3}+\\frac{1}{x^{3}}=\\left(x+\\frac{1}{x}\\right)^{3}-3\\left(x+\\frac{1}{x}\\right)$" ]
HW
[ "$\\displaystyle x^{2}+\\frac{1}{x^{2}}=\\left(x+\\frac{1}{x}\\right)^{2}-2=12$" ]
HW
[ "$\\displaystyle x^{2}+\\frac{1}{x^{2}}=\\left(x+\\frac{1}{x}\\right)^{2}-2=12$" ]
HW
[ "$\\displaystyle \\left(x+\\frac{1}{x}\\right)^{2}=14, ~~x+\\frac{1}{x}=\\sqrt{14} .$" ]
HW
[ "$\\displaystyle x^{3}+\\frac{1}{x^{3}}=14 \\sqrt{14}-3 \\sqrt{14}$" ]
HW
[ "$\\displaystyle x^{3}+\\frac{1}{x^{3}}=14 \\sqrt{14}-3 \\sqrt{14}$" ]
HW
[ "$\\displaystyle =11 \\sqrt{14}$" ]
HW
[ "$\\displaystyle 11 \\sqrt{14}$" ]
HW
[ "$\\displaystyle 11 \\sqrt{14}$" ]
HW
[ "$\\displaystyle x^{3}-9 x^{2}+20 x-12$" ]
HW
[ "$\\displaystyle x^{3}-9 x^{2}+20 x-12$" ]
HW
[ "$\\displaystyle =a^{2}+2 a b+b^{2}-4 a b$" ]
HW
[ "$\\displaystyle =(a+b)^{2}-4 a b$" ]
HW
[ "$\\displaystyle =(a+b)^{2}-4 a b$" ]
HW
[ "$\\displaystyle =16+40=56$" ]
HW
[ "good" ]