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All Questions
^{+0}
234574 Questions
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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 ..
Rangcr897
Jul 19, 2024
0
5
0
+601
Number Theory
Let $S$ be the set of numbers of the form
n(n + 1)(n + 3)(n + 4)(n + 8)(n + 10)(n + 12)
where $n$ is any positive integer.
What is the GCD of the elements of $S$?
AnswerscorrectIy
Jul 19, 2024
0
7
0
+601
Number Theory
There is a single sequence of integers $a_2,$ $a_3,$ $a_4,$ $a_5,$ $a_6,$ $a_7$ such that
\frac{a_2}{2!} + \frac{a_3}{3!} + \frac{a_4}{4!} + \frac{a_5}{5!} + \frac{a_6}{6!} + \frac{a_7}{7!} = \frac{3}{128}
and $0 \le a_i < i$ for $i = 2,$
read more ..
AnswerscorrectIy
Jul 19, 2024
0
5
0
+601
Number Theory
Find the unique triple $(x,y,z)$ of positive integers such that $x < y < z$ and
\frac{1}{x} - \frac{1}{xy} - \frac{1}{xyz} = \frac{1}{3}
AnswerscorrectIy
Jul 19, 2024
0
4
0
+601
Number Theory
Find the largest positive integer $n$ such that $n^3$ divides 15.
AnswerscorrectIy
Jul 19, 2024
-1
2
0
+165
Number Theory
Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim
read more ..
BRAlNBOLT
Jul 19, 2024
-1
2
1
+165
Number Theory
A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest terrific positive integer?
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BRAlNBOLT
Jul 19, 2024
+1
2
1
+276
I might know the answer...
A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest number of primes that could divide a terrific positive integer?
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BRAINBOLT
Jul 19, 2024
0
3
1
+601
Counting
At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if each scientist must sit next to a mathematician? (Two seatings are considered equivalent
read more ..
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AnswerscorrectIy
Jul 19, 2024
0
2
1
+601
Counting
Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if
read more ..
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AnswerscorrectIy
Jul 19, 2024
0
3
0
+601
Counting
I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are
read more ..
AnswerscorrectIy
Jul 19, 2024
+1
1
2
+7
Help!
Solve for the variable in terms of and :
CPhill
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MellowJello
Jul 19, 2024
0
5
1
+8
Trigonometric Identities
I need help solving this problem!
Ishiaki
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Ishiaki
Jul 19, 2024
Jul 18, 2024
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6
0
+467
Algebra
Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator
read more ..
ChiIIBill
Jul 18, 2024
0
3
1
+467
Algebra
Sophie's favorite (positive) number is a two-digit number. If she reverses the digits, the result is 72 less than her favorite number. Also, one digit is 1 less than double the other digit. What is Sophie's favorite number?
NotThatSmart
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ChiIIBill
Jul 18, 2024
0
5
1
+8
Precalc
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abc12345678
Jul 18, 2024
0
4
1
+601
Algebra
For certain values of k and m the system
a + 2b &= -3, \\
a + 2b &= k + 5a - mb
has infinitely many solutions (a,b) What are k and m?
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AnswerscorrectIy
Jul 18, 2024
0
2
2
+601
Algebra
Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$
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AnswerscorrectIy
Jul 18, 2024
0
2
2
+601
Algebra
Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___
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AnswerscorrectIy
Jul 18, 2024
0
4
1
+601
Algebra
Write the equation of the line below in the form Ax+By=C, where A, B, and C are integers with greatest common divisor 1 and A is positive.
The line passes through (-2,5) and (9,1).
chess4math
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AnswerscorrectIy
Jul 18, 2024
0
3
2
+601
Algebra
The system of equations
\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 2
has exactly one solution. What is $z$ in this solution?
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AnswerscorrectIy
Jul 18, 2024
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