All Questions ⁺⁰237643 Questions

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223

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help counting

In how many ways can the numbers 1 through 5 be entered once each into the five boxes below so that all the given inequalities are true?

Guest Dec 26, 2022

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201

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counting problem

We want to divide 10 dogs (including Fluffy and Nipper) into three groups, one with 3 dogs, one with 5 dogs, and one with 2 dogs. How many ways can we form the groups such that Fluffy is in the 2-dog group and Nipper is in the read more ..

Guest Dec 26, 2022

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204

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Help is appreciated :)

1. What is the smallest positive integer value of n such that (sqrt3/2 - i/2)^n is real?

2. If x + x^-1 = sqrt2, find x^20
read more ..

Guest Dec 26, 2022

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207

1

geometry

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area read more ..

Guest Dec 26, 2022

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191

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geometry

Let T be a point inside square EFGH such that TE = sqrt6, TF = 2sqrt3, and TG = 3sqrt2. Find angle ETF in degrees.

Guest Dec 26, 2022

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193

1

geometry

Let G be the center of equilateral triangle XYZ. A dilation centered at G with scale factor -4/3 is applied to triangle XYZ to obtain triangle X'Y'Z'. Let A be the area of the region that is contained in both triangles XYZ and X'Y'Z'. Find read more ..

Guest Dec 26, 2022

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199

1

Angle bisectors

Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF, which intersect at I. If DI = 3, BD = 4, and BI = 8, then find the area of triangle ABC.

Guest Dec 26, 2022

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184

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Function

Let F(x) be the real-valued function defined for all real x except for x = 1 and x = 2 and satisfying the functional equation
F(x) + F((2x - 3)/x) = x.
Find the function F(x) satisfying these conditions. Write F(x) as read more ..

Guest Dec 26, 2022

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225

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Geometry

Let AB be a diameter of a circle, and let C be a point on the circle such that AC=8 and BC=14 The angle bisector of ACB intersects the circle at point M Find CM.

Guest Dec 26, 2022

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211

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Counting

In how many ways can you distribute 10 indistinguishable balls among 8 distinguishable boxes, if at least one of the boxes must be empty?

Guest Dec 26, 2022

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166

0

help counting

How many solutions are there to the equation
u + v + w + x + y + z = 18
where u, v, w, x, y, and z are nonnegative integers, and x is at most 10?

Guest Dec 26, 2022

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170

0

Complex numbers

Describe all solutions to zw - 3w - 2iw + 4z = 7iw + 5w + 11iz - 13 + 15i
where z and w are complex numbers.

Guest Dec 26, 2022

Dec 25, 2022

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207

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geometry

In the diagram below, D is a point on segment CE such that segments AD and BE are parellel and point A is not on segment BC. Line segments AD and BC intersect at point P.

If angle CAD = 67 degrees, then what is angle read more ..

Guest Dec 25, 2022

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