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Jasmo
Username
Jasmo
Score
189
Membership
Stats
Questions
47
Answers
0
47 Questions
0 Answers
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+189
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 $BXA$.
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Jasmo
10 hours ago
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+189
Geometry
The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XY = 8$ and $WX = 8,$ find $XY.$
Jasmo
Feb 9, 2025, 3:01:58 PM
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Geometry
Let ABCD be a trapezoid with bases AB and CD. Let P be a point on side CD, and let X, Y be the feet of the altitudes from P to AD, BC respectively. Prove that if AD = 5, BC = 7, AB = 6, CD = 12, and CP/PD = 1, then PX = 12*sqrt(6)/5 and PY =
read more ..
Jasmo
Feb 9, 2025, 3:01:40 PM
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Number Theory
A terminal zero is a $0$ that appears at the end of a number. For example, the number $3,800$ has two terminal zeros.
How many terminal zeroes does $40 \cdot 6 \cdot 75 \cdot 12$ have?
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Jasmo
Feb 8, 2025
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Number Theory
The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$
What is the smallest positive integer that has exactly $2$ perfect square divisors?
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Jasmo
Feb 8, 2025
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Number Theory
A positive integer is called nice if it is a multiple of $6.$
A certain nice positive integer $n$ has exactly $8$ positive divisors. What is the smallest possible value of $n$?
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Jasmo
Feb 8, 2025
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Number Theory
A positive integer is called nice if it is a multiple of $6.$
A certain nice positive integer $n$ has exactly $8$ positive divisors. How many prime numbers are divisors of $n?$
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Jasmo
Feb 8, 2025
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+189
Number Theory
A positive integer is called terrific if it has exactly 5 positive divisors. What is the smallest terrific positive integer?
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Jasmo
Feb 8, 2025
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+189
Number Theory
A positive integer is called terrific if it has exactly 5 positive divisors. What is the largest number of primes that could divide a terrific positive integer?
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Jasmo
Feb 8, 2025
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+189
Number Theory
A positive integer is called terrific if it has exactly 5 positive divisors. What is the smallest number of primes that could divide a terrific positive integer?
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Jasmo
Feb 8, 2025
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+189
Counting
Starting with the A moving one letter at a time vertically, horizontally, or diagonally, how many different paths spell ARCH?
A
RRR
CCCCC
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Jasmo
Feb 7, 2025
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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?
Jasmo
Feb 7, 2025
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+189
Counting
In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving at least four pieces each?
Jasmo
Feb 6, 2025
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+189
Counting
Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $6,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)
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Jasmo
Feb 6, 2025
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+189
Counting
A baking club wants to form an executive committee. There are $15$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people, not including Mark?
Jasmo
Feb 6, 2025
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Algebra
Real numbers a and b satisfy
a + ab = 250
a - ab = -240
Enter all possible values of a, separated by commas.
Bosco
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Jasmo
Feb 6, 2025
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+189
Algebra
Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___
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Jasmo
Feb 6, 2025
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