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LiIIiam0216
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LiIIiam0216
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1247
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Questions
312
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16
312 Questions
16 Answers
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Geometry
Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.
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LiIIiam0216
19 mai 2024
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counting
In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are $3$ skaters, including $3$ Americans, in how many ways can the medals be awarded to three of the $3$ skaters if exactly
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LiIIiam0216
19 mai 2024
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+1247
Counting
Dogs in the GoodDog Obedience School win a blue ribbon for learning how to sit, a green ribbon for learning how to roll over, and a white ribbon for learning how to stay. There are $100$ dogs in the school.
$62$ have blue ribbons, $55$
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LiIIiam0216
19 mai 2024
0
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+1247
Counting
Find the number of positive integers that satisfy both the following conditions:
- Each digit is a 1 or a 2 or a 3
- The sum of the digits is 5
LiIIiam0216
19 mai 2024
0
1
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+1247
Counting
In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?
LiIIiam0216
19 mai 2024
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+1247
Geometry
In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $CY = 6$, find $BZ$.
LiIIiam0216
19 mai 2024
0
1
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+1247
Algebra
The temperature of a point (x,y) in the plane is given by the expression x^2 + y^2 - 4x + 2y - 12x + 14y + 26. What is the temperature of the coldest point in the plane?
LiIIiam0216
18 mai 2024
0
1
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+1247
Algebra
Let x and y be nonnegative real numbers. If xy = \frac{2}{5}, then find the minimum value of 6x + \frac{3}{5y}.
LiIIiam0216
18 mai 2024
0
1
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+1247
Algebra
Let x and y be nonnegative real numbers. If x^2 + 3y^2 = 18, then find the maximum value of x + y.
LiIIiam0216
18 mai 2024
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1
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+1247
Geometry
A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point $P$ on the edge of the table (as shown below) has a distance of $10$ from one wall, and a distance of $13$ from the other wall. Find the radius
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LiIIiam0216
18 mai 2024
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+1247
Geometry
The two circles below are externally tangent. A common external tangent intersects line $PQ$ at $R.$ Find $QR.$
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LiIIiam0216
18 mai 2024
0
1
0
+1247
Geometry
In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $1$ and $BC = \sqrt{3}$, then find $AB$.
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LiIIiam0216
18 mai 2024
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