image imagewidth (px) 2 3.75k | material_type stringclasses 2
values | latex listlengths 1 1 |
|---|---|---|
HW | [
"$\\displaystyle \\frac{2 k}{k-5}+\\frac{4 k-10}{k-5}=-4$"
] | |
HW | [
"$\\displaystyle 2 k+4 k-10=-4 k+20$"
] | |
HW | [
"$\\displaystyle 2 k+4 k-10=-4 k+20$"
] | |
HW | [
"$\\displaystyle 10 k=30$"
] | |
HW | [
"$\\displaystyle k=3$"
] | |
HW | [
"Good!"
] | |
HW | [
"$\\displaystyle 3$"
] | |
HW | [
"$\\displaystyle 3$"
] | |
HW | [
"$\\displaystyle \\sqrt{(3-a)^{2}+(-1-a+1)^{2}}=\\sqrt{(8-a)^{2}+(2-a+1)^{2}}$"
] | |
HW | [
"$\\displaystyle a^{2}-6 a+9+a^{2}=a^{2}-16 a+64+9-6 a+a^{2}$"
] | |
HW | [
"Good!"
] | |
HW | [
"$\\displaystyle 7$"
] | |
HW | [
"$\\displaystyle \\sqrt{(5-t)^{2}+(9)^{2}} \\leq 4$"
] | |
HW | [
"$\\displaystyle (5-t)^{2}+(t-9)^{2} \\leq 16$"
] | |
HW | [
"$\\displaystyle 25-10 t+t^{2}+t^{2}-18 t+81 \\leq 16$"
] | |
HW | [
"$\\displaystyle 2 t^{2}-28 t+106 \\leq 16$"
] | |
HW | [
"$\\displaystyle 2 t^{2}-28 t+106 \\leq 16$"
] | |
HW | [
"$\\displaystyle 2 t^{2}-28 t+90 \\leq 0$"
] | |
HW | [
"$\\displaystyle t^{2}-14 t+45 \\leq 0$"
] | |
HW | [
"$\\displaystyle t^{2}-14 t+45 \\leq 0$"
] | |
HW | [
"$\\displaystyle \\left(\\frac{x_{1}+x_{2}}{3}, \\frac{y_{1}+y_{2}}{3}\\right)\\quad (2, 6)$"
] | |
HW | [
"$\\displaystyle \\frac{x_{1}+x_{2}}{2}=\\frac{6}{2} \\quad \\frac{y_{1}+y_{2}}{2}=\\frac{18}{2}$"
] | |
HW | [
"$\\displaystyle \\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}$"
] | |
HW | [
"$\\displaystyle P(0, b)$"
] | |
HW | [
"$\\displaystyle \\sqrt{5^{2}+(2-b)^{2}}=\\sqrt{1^{2}+(-2-b)^{2}}$"
] | |
HW | [
"$\\displaystyle \\sqrt{5^{2}+(2-b)^{2}}=\\sqrt{1^{2}+(-2-b)^{2}}$"
] | |
HW | [
"$\\displaystyle b=3$"
] | |
HW | [
"$\\displaystyle b=3$"
] | |
HW | [
"$\\displaystyle (0,3)$"
] | |
HW | [
"$\\displaystyle (0,3)$"
] | |
HW | [
" $\\displaystyle A(-5,-1) B(9, 8)$"
] | |
HW | [
" $\\displaystyle A(-5,-1) B(9, 8)$"
] | |
HW | [
"$\\displaystyle =\\sqrt{20a^{2}+50b^{2}}$"
] | |
HW | [
"$\\displaystyle \\overline{A B}= \\sqrt{25 b^{2}+100a^{2}}$"
] | |
HW | [
"$\\displaystyle \\overline{A B}= \\sqrt{25 b^{2}+100a^{2}}$"
] | |
HW | [
"$\\displaystyle \\triangle\\text{OAB} = \\frac{1}{2} \\times 100 a^{2} + 25 b^{2} = 50a^{2}+\\frac{25}{2}b^{2}$"
] | |
HW | [
"$\\displaystyle \\triangle\\text{OAB} = \\frac{1}{2} \\times 100 a^{2} + 25 b^{2} = 50a^{2}+\\frac{25}{2}b^{2}$"
] | |
HW | [
"Good!"
] | |
HW | [
"Good!"
] | |
HW | [
"$\\displaystyle \\left(\\frac{a+c}{2}, \\frac{b+d}{2}\\right)=(1,3)$"
] | |
HW | [
"$\\displaystyle \\left(\\frac{a+c}{2}, \\frac{b+d}{2}\\right)=(1,3)$"
] | |
HW | [
"$\\displaystyle (\\frac{a+c+e}{3}, \\frac{b+d+f}{3})=(7,7)$"
] | |
HW | [
"$\\displaystyle (\\frac{a+c+e}{3}, \\frac{b+d+f}{3})=(7,7)$"
] | |
HW | [
"$\\displaystyle e=19 \\quad f=15$"
] | |
HW | [
"$\\displaystyle (-2,4)$"
] | |
HW | [
"$\\displaystyle Q: \\frac{18-4}{2+1}=\\frac{14}{3},~~ \\frac{16+2}{2+1}=6$"
] | |
HW | [
"$\\displaystyle Q: \\frac{18-4}{2+1}=\\frac{14}{3},~~ \\frac{16+2}{2+1}=6$"
] | |
HW | [
"$\\displaystyle y-1=-4(x-6)$"
] | |
HW | [
"$\\displaystyle y-1=-4(x-6)$"
] | |
HW | [
"$\\displaystyle y=-4 x+23$"
] | |
HW | [
"$\\displaystyle \\frac{|0+3 k+9|}{\\sqrt{1+9}}=\\frac{|3 k+9|}{\\sqrt{10}}$"
] | |
HW | [
"$\\displaystyle \\frac{|0-k-2|}{\\sqrt{9+1}}=\\frac{|-k-2|}{\\sqrt{10}}$"
] | |
HW | [
"$\\displaystyle \\frac{|0-k-2|}{\\sqrt{9+1}}=\\frac{|-k-2|}{\\sqrt{10}}$"
] | |
HW | [
"$\\displaystyle -k-2=3 k+9$"
] | |
HW | [
"$\\displaystyle -4 k=11$"
] | |
HW | [
"$\\displaystyle -4 k=11$"
] | |
HW | [
"$\\displaystyle k=-\\frac{11}{4}$"
] | |
HW | [
"$\\displaystyle \\therefore k=-\\frac{11}{4}$"
] | |
HW | [
"$\\displaystyle \\therefore k=-\\frac{11}{4}$"
] | |
HW | [
"$\\displaystyle a x+4 y+b=0$"
] | |
HW | [
"$\\displaystyle 2 x+4 y+1=0$"
] | |
HW | [
"$\\displaystyle 2 x+4 y+1=0$"
] | |
HW | [
"$\\displaystyle (3,-2) \\quad b-a$"
] | |
HW | [
"$\\displaystyle x=-12$"
] | |
HW | [
"$\\displaystyle x=-12$"
] | |
HW | [
"Good~!!"
] | |
HW | [
"$\\displaystyle \\frac{|2 \\times 3+2 \\times 4-1|}{\\sqrt{2^{2}+2^{2}}}=\\frac{13}{\\sqrt{8}}$"
] | |
HW | [
"$\\displaystyle \\frac{|2 \\times 3+2 \\times 4-1|}{\\sqrt{2^{2}+2^{2}}}=\\frac{13}{\\sqrt{8}}$"
] | |
HW | [
"$\\displaystyle \\frac{13}{\\sqrt{8}}=\\frac{13 }{2 \\sqrt{2} }=\\frac{13 \\sqrt{2}}{4}$"
] | |
HW | [
"$\\displaystyle \\frac{13}{\\sqrt{8}}=\\frac{13 }{2 \\sqrt{2} }=\\frac{13 \\sqrt{2}}{4}$"
] | |
HW | [
"$\\displaystyle \\sqrt{2}$"
] | |
HW | [
"$\\displaystyle \\sqrt{2}$"
] | |
HW | [
"$\\displaystyle \\sqrt{2}$"
] | |
HW | [
"$\\displaystyle \\frac{13}{2 \\sqrt{2}}$"
] | |
HW | [
"$\\displaystyle \\frac{13}{2 \\sqrt{2}}$"
] | |
HW | [
"$\\displaystyle 2 m+3 \\times \\square=-1$"
] | |
HW | [
"$\\displaystyle 2 m+3 \\times \\square=-1$"
] | |
HW | [
"g o o d"
] | |
HW | [
"g o o d"
] | |
HW | [
"$\\displaystyle k=86$"
] | |
HW | [
"$\\displaystyle y-8=2(x-9)$"
] | |
HW | [
"$\\displaystyle y=2 x-18+8$"
] | |
HW | [
"$\\displaystyle y=2 x-10$"
] | |
HW | [
"$\\displaystyle y=2 x-10$"
] | |
HW | [
"$\\displaystyle y=2 x-10$"
] | |
HW | [
"$\\displaystyle y=6 x-9$"
] | |
HW | [
"$\\displaystyle y=6 x-9$"
] | |
HW | [
"$\\displaystyle y=6 x-9$"
] | |
HW | [
"$\\displaystyle y-2=\\frac{8-2}{7-3}(x-3)$"
] | |
HW | [
"$\\displaystyle y=\\frac{3}{2} x-\\frac{5}{2}$"
] | |
HW | [
"$\\displaystyle 13$"
] | |
HW | [
"Good!"
] | |
HW | [
"Good!"
] | |
HW | [
"$\\displaystyle y=2x+4$"
] | |
HW | [
"$\\displaystyle y=2x+4$"
] | |
HW | [
"$\\displaystyle P(a, 2 a-4)$"
] | |
HW | [
"$\\displaystyle P(a, 2 a-4)$"
] | |
HW | [
"$\\displaystyle \\frac{a+14}{8}=x \\quad\\frac{2 a-4+28}{8}=y$"
] | |
HW | [
"$\\displaystyle 8 x-4y-2=0$"
] | |
HW | [
"$\\displaystyle 8 x-4y-2=0$"
] |
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