PikaPika989

14 Questions
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Geometry

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?

PikaPika989 26.04.2025

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Geometry

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.

PikaPika989 26.04.2025

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Help me plz

What is the equation of the reflection of the line y = 2x + 1 across the line y = 5x - 3? Give your answer in slope-intercept form.

PikaPika989 23.04.2025

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Help need help

In \triangle ABC, we have AB = AC = 4 and \angle BAC = 45^\circ. If M is the midpoint of BC, then find AM^2.

PikaPika989 23.04.2025

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Help geometry

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).

PikaPika989 23.04.2025

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Counting

Let S be a set of distinct integers. What is the smallest number of elements that S must contain, to ensure that S has a nonempty subset, where the sum of the elements in the subset is divisible by 2?

PikaPika989 22.04.2025

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Counting

Vera has 20 white socks, 21 black socks, 22 brown socks, 23 blue socks, 24 red socks, and 25 green socks. How many socks (at a minimum) must she pull out of her sock drawer to ensure at least six matching pairs of different colors?

PikaPika989 21.04.2025

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Counting

Find the number of arithmetic sequences such that:
* The arithmetic sequence contains three terms
* All the terms are integers in \{0, 1, 2, \dots, 10\}
* The sum of the terms is 9.

PikaPika989 18.04.2025

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Counting

Find the number of paths from A to B in the grid below, where each step is down or to the right.
The grid is 3 by 3, with A in the upper-left and B in the lower-right.

PikaPika989 18.04.2025

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Counting

A basket contains 7 green marbles and 6 red marbles. Two marbles are taken from the basket at random without replacement (i.e., the first marble is not put back before the second marble is drawn). What is the probability that the first marble is green, mehr ..

PikaPika989 18.04.2025

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help with counting

Now suppose that not only must Sir Lancelot and Sir Gawain be next to each other, but Sir Galahad and Sir Percival also demand to be next to each other. How many seatings of the 8 knights are possible?

PikaPika989 17.04.2025

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Counting

King Arthur's round table has 8 evenly spaced chairs. In how many ways can 8 knights be seated in the chairs, if Sir Lancelot and Sir Gawain insist on being seated next to each other?

PikaPika989 17.04.2025

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Counting

In how many ways can 5 balls be placed in 4 boxes, if 2 balls are white and 3 balls are black? (Balls of the same color are indistinguishable. The boxes are indistinguishable.)

PikaPika989 17.04.2025

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help with counting

How many zeroes do we write when we write all the integers from 1 to 625 in base 4?

PikaPika989 17.04.2025