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Post New Question
All Questions
+0
235476 Questions
0
1
0
+936
Geometry
In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11
Rangcr897
3 hours ago
0
1
0
+936
Geometry
In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?
Rangcr897
3 hours ago
0
1
0
+290
Algebra
Let a and b be the solutions to 7x^2 + x - 5 = -3x^2 - 9x - 4. Compute (a - 4)/(b - 4) + (b - 4)/(a - 4).
nathanl6656
4 hours ago
0
1
1
+290
Algebra
Seven years ago, Grogg's dad was $9$ times as old as Grogg. Four years ago, Grogg's dad was $6$ times as old as Grogg. How old is Grogg's dad currently?
●
nathanl6656
4 hours ago
0
1
1
+290
Algebra
Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/9 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
●
nathanl6656
4 hours ago
0
1
0
+290
Algebra
Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.
nathanl6656
4 hours ago
0
1
0
+217
Number Theory
Find the 4000th digit following the decimal point in the expansion of \frac{1}{17}.
bIueb3rry
5 hours ago
0
1
0
+217
Number Theory
How many bases b \ge 2 are there such that 100_b + 1_b is prime?
bIueb3rry
5 hours ago
0
1
0
+217
Number Theory
Let $p$ be a prime. What are the possible remainders when $p$ is divided by $17?$ Select all that apply.
bIueb3rry
5 hours ago
0
1
0
+497
Number Theory
Find the number of ordered triples (a,b,c) of positive integers that satisfy
a = \gcd(b,c) + 33
b = \gcd(a,c) + 25
c = \gcd(a,b) + 35
Pythagorearn
5 hours ago
0
1
0
+497
Number Theory
Let a, b, c, d be distinct positive integers such that {lcm}(a, b, c, d) < 1000 and a + b + c + d = 1000. Find the largest possible value of a + b.
Pythagorearn
5 hours ago
0
1
0
+595
Number Theory
Find the largest positive integer n for which there exist positive integers a, b, and c such that
\gcd(a + 3b, b + 3c, c + 3a) = nabc
siIviajendeukie
5 hours ago
0
1
0
+595
Number Theory
Let N be the number of ordered 6-tuples (a_1, a_2, a_3, a_4, a_5, a_6) of positive integers that satisfy
\frac{1}{a_1} + \frac{1}{a_2} + \frac{1}{a_3} + \frac{1}{a_4} + \frac{1}{a_5} + \frac{1}{a_6} = 6.
Find the remainder when N is divided
read more ..
siIviajendeukie
5 hours ago
0
1
0
+595
Number Theory
Let a, b, and c be integers such that 7a + 4b = 3c. Find the largest integer that always divides $abc$.
siIviajendeukie
5 hours ago
0
1
0
+826
Counting
Xavier and Yvonne meet one day at a cafe. For any day that Xavier goes to the cafe, the probability that Xavier goes the next day is $\frac{1}{2},$ and the probability that Xavier returns in two days is $\frac{1}{2}.$ For any day that Yvonne
read more ..
RedDragonl
5 hours ago
0
1
0
+826
Counting
Find the number of subsets S of \{0, 1, 2, 3, \dots, 15\} that have the following property: If n is in S, and m \equiv n + 1 \pmod{16}$ with $0 \le m \le 15,$ then m is also in S.
RedDragonl
5 hours ago
0
1
0
+414
Counting
Let A and B be two fixed points in the plane such that the distance between them is $1.$ Point $P$ is chosen at random on the circle centered at $A$ with radius $1,$ and point $Q$ is chosen at random on the circle centered at $B$ with radius $1.$
read more ..
onyuIee
5 hours ago
0
1
0
+414
Counting
In the $4 \times 4$ grid of points below, each point is one unit away from its closest neighbor. In how many ways are there to choose four of these points, such that the distance between any two chosen points is at most \sqrt{2}?
onyuIee
5 hours ago
0
1
0
+414
Counting
Five workers $A,$ $B,$ $C,$ $D,$ and $E$ at a coffee stand are working out a schedule for the next $10$ days. The schedule must satisfy the following conditions:
* There must be exactly two workers every day, and every pair of workers must be
read more ..
onyuIee
5 hours ago
0
1
0
+136
Geometry
The sides of convex quadrilateral ABCD are AB = 8, BC = 5, $CD = 5,$ and $DA = 8.$ Diagonals $\overline{AC}$ and $\overline{BD}$ intersect at $E$ so that $BE:ED = 1:1.$ Find the area of ABCD.
AUnVerifedTaxPayer
5 hours ago
0
1
0
+136
Geometry
Let H be the orthocenter of acute triangle ABC, and let M be the midpoint of \overline{AC}. Ray $\overrightarrow{MH}$ intersects the circumcircle of triangle $ABC$ at $P.$ If $BC < AB,$ $\angle ABP = 60^\circ,$ $MH = 14,$ and $HP = 3,$ then
read more ..
AUnVerifedTaxPayer
5 hours ago
0
1
0
+475
Geometry
Triangle ABC has a right angle at B. Point D lies on side \overline{AC} such that CD = 6. The circle with diameter $\overline{CD}$ intersects $\overline{AB}$ at two distinct points, $E$ and $F,$ with $AE < AF.$ If AE = 6 and DE = 4,
read more ..
ChiIIBill
5 hours ago
0
1
0
+475
Geometry
In right triangle ABC, \angle ACB = 90^\circ, and the legs are a = BC and b = AC. Let $S$ and $T$ be points on $\overline{AC}$ and $\overline{BC},$ respectively. Let $R$ be the foot of the altitude from $S$ to $\overline{AB},$ and let $U$ be
read more ..
ChiIIBill
5 hours ago
0
1
0
+475
Geometry
In tetrahedron ABCD, AB = AC = AD = 12 and BC = BD = CD = 12. There is a sphere that is tangent to all six edges of the tetrahedron. Find the radius of this sphere.
ChiIIBill
5 hours ago
0
1
0
+510
Algebra
Let the roots of z^{99} = 1 be z_k = x_k + iy_k for 1 \le k \le 99, where $x_k$ and $y_k$ are real. Let $P(z)$ be the monic polynomial whose roots are x_k - iy_k,$ for $1 \le k \le 99.$ Compute P(-2).
cooIcooIcooI17
5 hours ago
0
1
0
+666
Algebra
Find the number of positive integers n \le 10000 that satisfy
\lfloor \log_4 n \rfloor + \lfloor \log_8 n \rfloor + \lfloor \log_{64} n \rfloor = 5
booboo44
5 hours ago
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