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All Questions
^{+0}
234526 Questions
0
1
1
+665
Number Theory
Find the smallest positive integer $N$ such that
N &\equiv 2 \pmod{5}, \\
N &\equiv 2 \pmod{7}.
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magenta
Aug 14, 2024
+1
3
1
+665
Number Theory
When $N$ is divided by $10$, the remainder is $a$. When $N$ is divided by $2$, the remainder is $b$. What is $N$ modulo $20$, in terms of $a$ and $b$?
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magenta
Aug 14, 2024
0
3
1
+16
Question:
What is the product of the smallest two prime factors of ?
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CelsiusSolving
Aug 14, 2024
Aug 13, 2024
+2
4
2
+16
Difficult Counting Problem
Gracie starts at her house and walkes one block east. After each block she walks, she flips a coin. She walks one block east if the coin lands heads; otherwise one block west. She stops her walk the first time she lands back home. What is the probability
read more ..
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CelsiusSolving
Aug 13, 2024
0
2
0
+593
Number Theory
Brandon spends his afternoon picking apples from an orchard. He notices that if he groups the apples he picked by fives, six, or sevens, then he ends up with $1$ left over. If he groups by eights, he has $1$ left over. If Brandon
read more ..
AnswerscorrectIy
Aug 13, 2024
0
1
0
+593
Number Theory
Find the number of solutions to
N &\equiv 2 \pmod{5}, \\
N &\equiv 2 \pmod{6}, \\
N &\equiv 2 \pmod{7}
in the interval 0 \le N < 1000.
AnswerscorrectIy
Aug 13, 2024
0
4
0
+752
Coefficient
There exists a polynomial $f(x)$ and a constant $k$ such that
(x^2 - 2x - 5) f(x) = 2x^4 + 19x^3 + kx^2 - 15x - 1.
What is $k?$
RedDragonl
Aug 13, 2024
0
3
1
+752
Coefficient
What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?
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RedDragonl
Aug 13, 2024
0
3
7
+9
Help please! Simon's Favorite Factoring Trick
How many integers with can be written as for at least one ordered pair of positive integers ?
This question really confused me because I don't understand what it's asking.
♥️
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anonymousSingularity
Aug 13, 2024
0
1
1
+303
Algebra
Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5.
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onyuIee
Aug 13, 2024
0
2
1
+303
Algebra
Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m.
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onyuIee
Aug 13, 2024
0
2
1
+2633
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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LiIIiam0216
Aug 13, 2024
0
2
1
+2633
Algebra
Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$
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LiIIiam0216
Aug 13, 2024
0
1
1
+1694
Geometry
Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.
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ABJeIIy
Aug 13, 2024
0
2
0
+1694
Geometry
In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid
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ABJeIIy
Aug 13, 2024
0
2
1
+1467
Algebra
Find one ordered pair $(x,y)$ of real numbers such that $x + y = 10$ and $x^3 + y^3 = 162 + x^2 + y^2.$
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parmen
Aug 13, 2024
0
2
1
+1467
Algebra
Find the minimum value of 9^x - 2 \cdot 3^x + 1 over all real numbers x.
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parmen
Aug 13, 2024
0
2
0
+1694
Algebra
I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 600 pounds more than each of her trucks, but no more than 1/2 of the total load her four trucks combined can carry. Based on these
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ABJeIIy
Aug 13, 2024
0
3
0
+1694
Algebra
The product $(3-\sqrt{5})(4+\sqrt{5})(1+6\sqrt{5})$ can be expressed in the form $a+b\sqrt{5}$, where $a$ and $b$ are integers. Find $a+b$.
ABJeIIy
Aug 13, 2024
0
2
2
+38
PLEASE HELP PLEASE
Find the exponential form of the complex number
e^17πi/60+e^27πi/60+e^37πi/60+e^47πi/60+e^57πi/60
with proof.
Could someone help me on this and type out the solving process and the proof please?
Thanks!
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JRFPLSHelp
Aug 13, 2024
0
1
2
+24
Triangle
Triangle ABC has altitudes AD, BE, and CF. and If AD= 12, BE=16, and CF is a positive integer, then find the largest possible value of CF.
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surfz
Aug 13, 2024
0
2
1
+24
Question about triangles
All the sides of a triangle are integers. If the perimeter of the triangle is 16, then how many different possible triangles are there? (Assume that the triangle is non-degenerate. Two triangles are considered the same if they are congruent.)
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surfz
Aug 13, 2024
0
1
0
+1341
Algebra
My street hockey team plays three games each week. My team lost all $9$ games in the first three weeks. Then, my team won one game and lost two games in the fourth week, bringing our record to $1$ win and $11$ losses. Each week after that, my team
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kittykat
Aug 13, 2024
0
1
1
+1341
Algebra
When the same constant is added to the numbers $a,$ $b,$ and $c,$ a three-term geometric sequence arises. If $a = 60,$ $b = 100,$ and $c = 140,$ what is the common ratio of the resulting sequence?
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kittykat
Aug 13, 2024
0
2
0
+1341
Algebra
Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If $a_1 + a_3 = 5$ and $a_2 + a_4 = 6$, then find $a_1$.
kittykat
Aug 13, 2024
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