CInsbstnkng

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Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of triangle ABC?
A is at (0,0), B is at (1,0), and C is at (1,1).

CInsbstnkng 27 июл. 2025 г.

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In the diagram below, \overline{AD} and \overline{BE} are angle bisectors of \angle BAC and \angle ABC, respectively, and they intersect at T. We know that BD=12, AE=8, and BF=3+AE. Find AB.

CInsbstnkng 26 июл. 2025 г.

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In the diagram, \overline{AD} is an altitude, \overline{BE} is a median, and \overline{AD}, \overline{BE}, and \overline{CF} are concurrent. If AE = 11, BE = 9, and AD = 6\sqrt{2}, what is AF?

CInsbstnkng 25 июл. 2025 г.

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How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, and the sum of the digits is 6?

CInsbstnkng 25 июл. 2025 г.

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How many positive integers are there whose digits strictly decrease from left to right, and the sum of the digits is 6?

CInsbstnkng 25 июл. 2025 г.

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Right triangles ABC, ADE, EFG, and GHC are all similar. Also, $[ADE] = 1,$ $[EFG] = 1,$ and $[GHC] = 1.$ Find the area of the red region.

CInsbstnkng 25 июл. 2025 г.

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Let f(x) be a polynomial such that f(0) = 4, f(1) = 8, and f(2) = -6. Find the remainder when f(x) is divided by x.

CInsbstnkng 24 июл. 2025 г.

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The polynomial
g(x) = x^3 - x^2 - (m^2 + m + 18) x + 2m^2 - 14m - 6
is divisible by x - 5 and all of its zeroes are integers. Find all possible values of m.

CInsbstnkng 24 июл. 2025 г.

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Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other, no two Cs are next to each other, and no two Ds are next to each other.

CInsbstnkng 24 июл. 2025 г.

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The correct answer is n = 14.

CInsbstnkng27 июл. 2025 г.