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Post New Question
All Questions
+0
234503 Questions
0
10
0
+1467
Counting
Find the number of ways of choosing three circles below, so that no two circles are next to each other.
parmen
Jun 12, 2024
0
6
0
+1015
Algebra
The graphs of x = y^4 and x + y^2 = 1 + x^2 - y^3 intersect at two points. The distance between these points is of the form sqrt(u + v*sqrt(5)), where u and v are integers. Find the ordered pair (u,v).
learnmgcat
Jun 12, 2024
0
6
1
+1015
Algebra
A right triangle with integer leg lengths is called cool if the number of square units in its area is equal to five times the number of units in the sum of the lengths of its legs. What is the sum of all the different possible areas of cool right
read more ..
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learnmgcat
Jun 12, 2024
0
9
1
+1015
Algebra
Let a and b be positive real numbers such that a + b = 1. Find the set of all possible values of a/b.
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learnmgcat
Jun 12, 2024
-3
8
1
+161
Geometry
Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.
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BRAlNBOLT
Jun 12, 2024
-3
6
1
+161
Geometry
In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.
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BRAlNBOLT
Jun 12, 2024
-3
13
1
+161
Geometry
In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.
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BRAlNBOLT
Jun 12, 2024
0
5
1
+56
halp pls asap
Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/5 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
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ghistory
Jun 12, 2024
Jun 11, 2024
-3
11
0
+161
Geometry
In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.
BRAlNBOLT
Jun 11, 2024
0
9
1
+16
how?
The x intercepts of a circle are -3 and 10. One of the y intercepts is 5. What is the other y intercept? What is
the area of the circle?
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Pearsse
Jun 11, 2024
-4
9
0
+161
Geometry
Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$,
read more ..
BRAlNBOLT
Jun 11, 2024
-4
7
1
+161
Geometry
Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$,
<
read more ..
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BRAlNBOLT
Jun 11, 2024
+1
3
1
+276
Help me!
Find the largest integer k such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.
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BRAINBOLT
Jun 11, 2024
0
7
0
+1467
Geometry
Altitudes $\overline{AP}$ and $\overline{BQ}$ of an acute triangle $\triangle ABC$ intersect at point $H$. What is the area of triangle $ABC$?
parmen
Jun 11, 2024
0
6
1
+1307
Counting
The six faces of a cube are painted black. The cube is then cut into 6^3 smaller cubes, all the same size. One of the small cubes is chosen at random, and rolled. What is the probability that when it lands, the face on the top is black?
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blackpanther
Jun 11, 2024
0
8
2
+85
Quadratics
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PurpleWasp
Jun 11, 2024
0
4
2
+1307
Counting
A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is times the probability that a freshman is elected. Everyone on the junior varsity
read more ..
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blackpanther
Jun 11, 2024
0
8
1
+1307
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
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blackpanther
Jun 11, 2024
0
6
2
+1307
Algebra
Let x \mathbin{\spadesuit} y = \frac{x^2}{y} for all x and y such that y\neq 0. Find all values of $a$ such that $a \mathbin{\spadesuit} (a + 1) = 9$. Write your answer as a list separated by commas.
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blackpanther
Jun 11, 2024
0
7
1
+85
Quadratics
The two positive integer solutions of the equation x^2-mx+n are k and t, where m and n are both prime numbers and k>t. What is the value of ?
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PurpleWasp
Jun 11, 2024
0
2
2
+28
NUMERO
Given that is a prime number, evaluate
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wassyo
Jun 11, 2024
0
8
1
+1307
Algebra
Suppose $a(x) = 2x + 5 - 3x^2 + x^3$ and $b(x) = 4 - x^2 + 4x^4$. Find $(a\circ b)(3) - (b\circ a)(3).$
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blackpanther
Jun 11, 2024
+1
10
2
+28
Number Theory
How many ways are there to fill in the tens digit and hundreds digit of 1_ _4 so that it is divisible by 11?
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wassyo
Jun 11, 2024
0
9
1
+2633
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 BC, then find AC + BC + AB.
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LiIIiam0216
Jun 11, 2024
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