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All Questions
^{+0}
234574 Questions
0
1
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+1694
Algebra
Evaluate $a^3 - \dfrac{1}{a^3}$ if $a - \dfrac{1}{a} = 0$.
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ABJeIIy
Aug 3, 2024
Aug 2, 2024
0
6
2
+1694
Algebra
Let
f(x) = \sqrt{x - \sqrt{x}}.
Find the largest three-digit value of $x$ such that $f(x)$ is an integer.
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ABJeIIy
Aug 2, 2024
0
2
0
+779
Number Theory
The number $N$ is a multiple of $7$. The base $2$ representation of $N$ is
10011010011ABC110_2.
Compute the ordered triple of digits $(A,B,C)$.
eramsby1O1O
Aug 2, 2024
0
1
6
+42
Number Theory Question
How many digits are in the whole-number representation of The answer is not 101.
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Umeko1.0
Aug 2, 2024
0
1
3
+2641
Number Theory
Find a six-digit multiple of $64$ that consists only of the digits $2$ and $4$.
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LiIIiam0216
Aug 2, 2024
0
2
0
+2641
Number Theory
Find the number of $7$-digit numbers, where the sum of the digits is divisible by $11.$
LiIIiam0216
Aug 2, 2024
0
2
1
+355
Physics
In the previous problem, we imagined a bathtub draining. Water would leave the tub with a speed of $2.9 \;\mathrm{m/s}$ when the tub is full. Suppose the cross sectional area of the drain is $8.0 \;\mathrm{cm}^2.$ You may assume that all water leaving
read more ..
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Lilliam0216
Aug 2, 2024
0
3
1
+355
When the bathtub is full, water leaves the bath tub at $2.9 \;\mathrm{m/s}$ through the drain. At what speed does water leave the bathtub w
When the bathtub is full, water leaves the bath tub at $2.9 \;\mathrm{m/s}$ through the drain. At what speed does water leave the bathtub when it is half full?
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Lilliam0216
Aug 2, 2024
0
1
1
+820
Counting
In how many ways can the numbers 1, 2, 3, 4, 5, 6 be arranged in a row, so that the product of any two adjacent numbers is at least 5?
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Hi6942O
Aug 2, 2024
-1
3
1
+284
Geometry
In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.
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Stanry
Aug 2, 2024
0
4
1
+756
Geometry
In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?
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RedDragonl
Aug 2, 2024
0
7
0
+864
Geometry
In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.
Rangcr897
Aug 2, 2024
0
1
2
+4
help pls
Given R(-6, 19) and S(15, -5), what are the coordinates of the point on segment RS two-thirds of the distance from R to S?
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Roteuw
Aug 2, 2024
0
2
1
+1694
Geometry
In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$
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ABJeIIy
Aug 2, 2024
0
3
1
+1694
Geometry
Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.
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ABJeIIy
Aug 2, 2024
0
2
1
+1694
Geometry
Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note:
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ABJeIIy
Aug 2, 2024
0
1
1
+1694
Geometry
Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
PA^2 + PB^2 + PC^2 = 3PQ^2 + k.
If $A = (7,-11),$ $B = (10,13),$ and $C = (18,-22)$, then find the constant
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ABJeIIy
Aug 2, 2024
0
1
1
+1694
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 6 from one wall, and a distance of 6 from the other wall. Find the radius of the
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ABJeIIy
Aug 2, 2024
0
7
0
+1694
Geometry
Lines $XQ$ and $XR$ are tangent to a circle, as shown below. If $\angle XTU = 47^\circ$ and $\angle QAU = 65^\circ,$ then find $\angle QXR,$ in degrees.
ABJeIIy
Aug 2, 2024
0
5
1
+1694
Geometry
Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$
read more ..
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ABJeIIy
Aug 2, 2024
0
5
1
+1694
Geometry
We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?
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ABJeIIy
Aug 2, 2024
0
3
1
+1694
Geometry
Altitudes AD and BE of acute triangle ABC intersect at point H. If angle ABH = 30 and angle DAC = 45, then what is angle HCA in degrees?
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ABJeIIy
Aug 2, 2024
0
3
0
+1694
Geometry
In trapezoid EFGH, \overline{EF} \parallel \overline{GH}, and P is the point on \overline{EH} such that EP:PH = 1:2. If the area of triangle PEF is 6, and the area of triangle PGH is 6, then find the area of trapezoid EFGH.
ABJeIIy
Aug 2, 2024
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