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imagewidth (px) 2
3.75k
| material_type
stringclasses 2
values | latex
sequencelengths 1
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HW | [
"$\\displaystyle -2 x-2 y-1=0$"
] |
|
HW | [
"$\\displaystyle -2 x-2 y-1=0$"
] |
|
HW | [
"$\\displaystyle 2 x+2 y-1=0$"
] |
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HW | [
"$\\displaystyle 2x+2y-1=0$ !!"
] |
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HW | [
"$\\displaystyle a+b+c=-3+2+13=12$"
] |
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HW | [
"$\\displaystyle a+b+c=-3+2+13=12$"
] |
|
HW | [
"$\\displaystyle 9-a^{2}=-a+5$"
] |
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HW | [
"$\\displaystyle 9-a^{2}=-a+5$"
] |
|
HW | [
"$\\displaystyle a^{2}-a-4=0$"
] |
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HW | [
"$\\displaystyle 5 y=-2(-x)^{2}+5$"
] |
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HW | [
"$\\displaystyle =-2 x^{2}+5$"
] |
|
HW | [
"$\\displaystyle 2 x^{2}+5 y-5=0$"
] |
|
HW | [
"$\\displaystyle 2 x^{2}+5 y-5=0$"
] |
|
HW | [
"$\\displaystyle 2 x^{2}+5 y-5=0$"
] |
|
HW | [
"$\\displaystyle 2 x^{2}+5 y-5=0$"
] |
|
HW | [
"$\\displaystyle 4 x=4 y-2$"
] |
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HW | [
"$\\displaystyle 4 x=4 y-2$"
] |
|
HW | [
"$\\displaystyle x^{2}+y^{2}-10 x+8=0$"
] |
|
HW | [
"$\\displaystyle (x-5)^{2}+y^{2}=17$"
] |
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HW | [
"$\\displaystyle (x-1)^{2}+(y-2)^{2}=17$"
] |
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HW | [
"$\\displaystyle y=-2 x^{2}+8 x-2$"
] |
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HW | [
"$\\displaystyle =-2\\left(x^{2}-4 x\\right)-2$"
] |
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HW | [
"$\\displaystyle (-2,0)$"
] |
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HW | [
"$\\displaystyle (a,-1) \\rightarrow(1,-a) \\rightarrow(-1,-a+1)=(-1, b)$"
] |
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HW | [
"$\\displaystyle \\therefore a+b=1$"
] |
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HW | [
"$\\displaystyle \\therefore a+b=1$"
] |
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HW | [
"$\\displaystyle \\frac{a-1}{2}=4 . \\quad \\frac{b+2}{2}=-4 .$"
] |
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HW | [
"$\\displaystyle \\frac{a-1}{2}=4 . \\quad \\frac{b+2}{2}=-4 .$"
] |
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HW | [
"$\\displaystyle a=9, \\quad b=-10$"
] |
|
HW | [
"$\\displaystyle -90$"
] |
|
HW | [
"$\\displaystyle P(0, a)$"
] |
|
HW | [
"$\\displaystyle P(0, a)$"
] |
|
HW | [
"$\\displaystyle P(0,3)$"
] |
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HW | [
"$\\displaystyle P(0,3)$"
] |
|
HW | [
"$\\displaystyle \\overline{OA}=\\sqrt{5^{2}+3^{2}}=\\sqrt{34}$"
] |
|
HW | [
"$\\displaystyle \\overline{O B}=\\sqrt{(5+a)^{2}+(-2)^{2}}=3 \\sqrt{34}$"
] |
|
HW | [
"$\\displaystyle a=\\sqrt{302}-5(\\because a>0)$"
] |
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HW | [
"$\\displaystyle a=\\sqrt{302}-5(\\because a>0)$"
] |
|
HW | [
"$\\displaystyle \\sqrt{302}-5$"
] |
|
HW | [
"$\\displaystyle \\sqrt{302}-5$"
] |
|
HW | [
"$\\displaystyle x \\rightarrow x-2,\\quad y \\rightarrow y-m$"
] |
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HW | [
"$\\displaystyle 3-m=0-4, \\quad m=7$"
] |
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HW | [
"$\\displaystyle 3-m=0-4, \\quad m=7$"
] |
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HW | [
"$\\displaystyle x \\rightarrow x-7$"
] |
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HW | [
"$\\displaystyle x \\rightarrow x-7$"
] |
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HW | [
"$\\displaystyle 3=-(-n)+1, \\quad n=2$"
] |
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HW | [
"$\\displaystyle 3=-(-n)+1, \\quad n=2$"
] |
|
HW | [
"$\\displaystyle m \\times n=7 \\times 2=14$"
] |
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HW | [
"$\\displaystyle 14$"
] |
|
HW | [
"$\\displaystyle x^{2}+y^{2}-6 x+8 y+2=0$"
] |
|
HW | [
"$\\displaystyle x^{2}+y^{2}-6 x+8 y+2=0$"
] |
|
HW | [
"$\\displaystyle (x-3)^{2}+(y+4)^{2}+2-9-16=0$"
] |
|
HW | [
"$\\displaystyle 24$"
] |
|
HW | [
"$\\displaystyle \\sqrt{(5-1)^{2}+(7-10)^{2}}=16+9=\\sqrt{25}=5$"
] |
|
HW | [
"$\\displaystyle (5+a)^{2}=297$"
] |
|
HW | [
"$\\displaystyle a=-5+\\sqrt{33}(\\because a>0)$"
] |
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HW | [
"$\\displaystyle a=-5+\\sqrt{33}(\\because a>0)$"
] |
|
HW | [
"$\\displaystyle -5+\\sqrt{33}$"
] |
|
HW | [
"$\\displaystyle -5+\\sqrt{33}$"
] |
|
HW | [
"$\\displaystyle P$"
] |
|
HW | [
"$\\displaystyle \\sqrt{5}$"
] |
|
HW | [
"good."
] |
|
HW | [
"$\\displaystyle (5+a)^{2}+4=261 \\rightarrow 5+a=\\sqrt{257}(\\because a>0$"
] |
|
HW | [
"$\\displaystyle (5+a)^{2}+4=261 \\rightarrow 5+a=\\sqrt{257}(\\because a>0$"
] |
|
HW | [
"$\\displaystyle a=-5+\\sqrt{257}$"
] |
|
HW | [
"$\\displaystyle a=-5+\\sqrt{257}$"
] |
|
HW | [
"$\\displaystyle -5+\\sqrt{257}$"
] |
|
HW | [
"$\\displaystyle (-1,-9)$"
] |
|
HW | [
"$\\displaystyle (-1,-9)$"
] |
|
HW | [
"$\\displaystyle y-2=-(x+4)^{2}+3(x+4)+2$"
] |
|
HW | [
"$\\displaystyle y-2=-(x+4)^{2}+3(x+4)+2$"
] |
|
HW | [
"$\\displaystyle y=-x^{2}-8 x-16+3 x+12+2+2$"
] |
|
HW | [
"$\\displaystyle y=-x^{2}-8 x-16+3 x+12+2+2$"
] |
|
HW | [
"$\\displaystyle =-x^{2}-5 x$"
] |
|
HW | [
"$\\displaystyle y=-x^{2}=5 x$"
] |
|
HW | [
"$\\displaystyle x \\rightarrow x+y$"
] |
|
HW | [
"$\\displaystyle y\\rightarrow y-3$"
] |
|
HW | [
"$\\displaystyle y=(x+6)^{2}-6$"
] |
|
HW | [
"$\\displaystyle (a, b)=(-6,-6)$"
] |
|
HW | [
"$\\displaystyle a-b=0$"
] |
|
HW | [
"$\\displaystyle a-b=0$"
] |
|
HW | [
"$\\displaystyle 0$"
] |
|
HW | [
"$\\displaystyle 0$"
] |
|
HW | [
"$\\displaystyle (0,5) \\rightarrow(0,-5)$"
] |
|
HW | [
"$\\displaystyle (0,5) \\rightarrow(0,-5)$"
] |
|
HW | [
"$\\displaystyle (0,-5)$"
] |
|
HW | [
"$\\displaystyle \\frac{|12+2 a-7|}{\\sqrt{3^{2}+2^{2}}}=\\sqrt{13} \\Rightarrow|12+2 a-7|=13$"
] |
|
HW | [
"$\\displaystyle \\frac{|12+2 a-7|}{\\sqrt{3^{2}+2^{2}}}=\\sqrt{13} \\Rightarrow|12+2 a-7|=13$"
] |
|
HW | [
"$\\displaystyle a=12 \\quad b=-4$"
] |
|
HW | [
"$\\displaystyle a=12 \\quad b=-4$"
] |
|
HW | [
"$\\displaystyle a b=-48$"
] |
|
HW | [
"$\\displaystyle a b=-48$"
] |
|
HW | [
"$\\displaystyle (-4,10)$"
] |
|
HW | [
"$\\displaystyle (x-1)^{2}+(y-1)^{2}=-a+2$"
] |
|
HW | [
"$\\displaystyle (x-1)^{2}+(y-1)^{2}=-a+2$"
] |
|
HW | [
"$\\displaystyle a+b=-6$"
] |
|
HW | [
"ok"
] |
|
HW | [
"$\\displaystyle (6,-3)$"
] |
|
HW | [
"$\\displaystyle P(6,3)$"
] |
|
HW | [
"$\\displaystyle Q(-3,6)$"
] |
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