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Questions
253
Réponses
99
256 Questions
128 Answers
0
83
0
+818
Algebra
Let $f(x)$ be a polynomial with integer coefficients. There exist distinct integers $p,$ $q,$ $r,$ $s,$ $t$ such that
\[f(p) = f(q) = f(r) = f(s) = 1\]
and $f(t) > 1.$ What is the smallest possible value of $f(t)?$
maximum
11 déc. 2023
0
67
1
+818
circles
The circles $x^2 + y^2 = 4$ and $(x - 5)^2 + (y - 8)^2 = 60$ intersect in two points $A$ and $B.$ Find the distance $AB$.
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maximum
11 déc. 2023
0
32
1
+818
quadratic
The quadratic equation $x^2-5x+5=-4x+7$ has two roots. Find the absolute difference of these roots.
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maximum
11 déc. 2023
0
61
1
+818
help wth coordinates
Find the number of lattice points that lie on the graph of $x^2-y^2=17-2xy$. (A lattice point is a point in the coordinate plane where both coordinates are integers.)
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maximum
11 déc. 2023
0
31
1
+818
system
The real numbers x and y satisfy x (x+y) = 27 and (x+y) = 54. What is the value of (x+y)^2?
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maximum
11 déc. 2023
0
85
0
+818
plz help quick
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?
maximum
28 nov. 2023
0
70
0
+818
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
maximum
28 nov. 2023
0
54
1
+818
counting problem
In the array below, in how many different ways can we start with the letter A and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?
A
RRR
&
lire plus ..
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maximum
28 nov. 2023
0
87
0
+818
need help
Fill in the blanks with numbers to make a true equation
3x^2 + 12x + 4 - x^3 + 8x - 5x + 7x^2 + 11 = __ (x + __)^3 + __(x + __)^2 + __x + ___
maximum
21 nov. 2023
0
73
1
+818
graphing question
The parabola $y = ax^2 + bx + c$ is graphed below. Find $a + b + c$. (The grid lines are one unit apart.)
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maximum
21 nov. 2023
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24
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20
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#1
+818
-1
Do not post AoPS homework.
maximum
20 janv. 2025
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dernier
11
10
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2
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