query stringlengths 1.97k 3.05k | choices listlengths 4 4 | gold listlengths 1 1 |
|---|---|---|
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)24",
"(B)49",
"(C)50",
"(D)99"
] | [
1
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)-4",
"(B)0",
"(C)1",
"(D)3"
] | [
0
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)240",
"(B)140",
"(C)120",
"(D)70"
] | [
3
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)32.4",
"(B)44.0",
"(C)62.0",
"(D)90.0"
] | [
0
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)2",
"(B)3",
"(C)4",
"(D)5"
] | [
3
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)2",
"(B)4",
"(C)5",
"(D)6"
] | [
2
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)$v=30,000-9,000 t$",
"(B)$v=120,000-9,000 t$",
"(C)$v=120,000+9,000 t$",
"(D)$v=120,000-30,000 t$"
] | [
1
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)$y=2 x+3$",
"(B)$y=2 x+4$",
"(C)$y=\\frac{3}{2} x+3$",
"(D)$y=\\frac{3}{2} x+1$"
] | [
3
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)-5",
"(B)-3",
"(C)0",
"(D)12"
] | [
1
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)6",
"(B)10",
"(C)13",
"(D)17"
] | [
2
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)$p=0.5 x$",
"(B)$p=5 x$",
"(C)$p=(0.05)^{x}$",
"(D)$p=(1.05)^{x}$"
] | [
1
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)$\\frac{1}{8} \\operatorname{cup}$",
"(B)$\\frac{1}{4} \\operatorname{cup}$",
"(C)$\\frac{1}{3} \\operatorname{cup}$",
"(D)$\\frac{1}{2} \\operatorname{cup}$"
] | [
1
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)$h(x)=-3(d)^{x}$",
"(B)$h(x)=3(x) d$",
"(C)$h(x)=d(-x)^{3}$",
"(D)$h(x)=d(3)^{x}$"
] | [
3
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)Mean",
"(B)Median",
"(C)Range",
"(D)Standard deviation"
] | [
1
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)The percentages do not add up to $100 \\%$, so any possible conclusions from the poll are invalid.",
"(B)Those who responded to the poll were not a random sample of the population of the United States.",
"(C)There were not $50 \\%$ \"Yes\" responses and $50 \\%$ \"No\" responses.",
"(D)The show did not al... | [
1
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)-30",
"(B)$\\quad-3$",
"(C)3",
"(D)30"
] | [
2
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)$\\cos x^{\\circ}=a$",
"(B)$\\sin \\left(90^{\\circ}-x^{\\circ}\\right)=a$",
"(C)$\\cos \\left(90^{\\circ}-x^{\\circ}\\right)=a$",
"(D)$\\sin \\left(x^{2}\\right)^{\\circ}=a^{2}$"
] | [
2
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)The initial height of the projectile",
"(B)The maximum height of the projectile",
"(C)The time at which the projectile reaches its maximum height",
"(D)The time at which the projectile hits the ground"
] | [
3
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)$f(x)=(x-a)(x-b)$",
"(B)$f(x)=(x+a)(x+b)$",
"(C)$f(x)=(x-a)(x+b)$",
"(D)$f(x)=x(x-a)(x-b)$"
] | [
0
] |
Q: $$(x-6)^{2}+(y+5)^{2}=16$$In the $x y$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{P Q}$ is a diameter of the circle, what are the coordinates of point $Q$ ? Answer Choices: (A)$(2,-5)$ (B)$(6,-1)$ (C)$(6,-5)$ (D)$(6,-9)$
A: Among {} thr... | [
"(A)$y$-coordinate of the vertex",
"(B)$x$-intercept $(\\mathrm{s})$",
"(C)$y$-intercept",
"(D)$x$-intercept of the line of symmetry"
] | [
2
] |
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