All Questions ⁺⁰237785 Questions

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Polygons

The measures of the interior angles of a convex 9-gon form an arithmetic sequence and, measured in degrees, are all distinct integers. What is the measure of the largest possible angle if the smallest angle is 100 degrees?

Guest Jul 22, 2022

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255

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Number Theory

What is the sum of all positive integers n that satisfy
lcm[n,100]=gcd(n,100)+500

Guest Jul 22, 2022

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286

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URGENT HELLPPPP

Find the ordered triple that satisfies the following system:
x-2y=0
y-2z=0
x+z=5
read more ..

Guest Jul 22, 2022

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252

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number theory

Let A be the product of the divisors of 300!. What is the sum of the distinct prime divisors of A?

Guest Jul 22, 2022

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286

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NEED FAST HELP

Find all values for which there exists an ordered pair satisfying the following system of equations:
a+ab^2=40b
a-ab^2=-32b
List only the values for a

Guest Jul 22, 2022

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299

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geometry problem

Ari draws twelve circles of diameter 2 inches that all pass through the same point, so that the angles formed by the diameters of any two consecutive circles are congruent, as in the image shown. What is the distance between point A and read more ..

Guest Jul 22, 2022

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228

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Complex numbers

The four complex roots of
2z^4 + 8iz^3 + (-9 - 9i)z^2 + (-12 - 4i)z + (8 - 2i) = 0
when plotted in the complex plane, form a rhombus. Find the area of the rhombus.

Guest Jul 22, 2022

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198

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Complex numbers

Let a, b, c be complex numbers, with a real, such that
a + b + c = ab + ac + bc
abc = 3/a + 3/b + 3/c
a = b + c read more ..

Guest Jul 22, 2022

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271

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Inequality

Solve the inequality 4t^2 <= 9t - 2 + 7t - 4.

Guest Jul 22, 2022

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218

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Inequality

Solve the inequality 2x - 5 <= -x + 12 + 5x - 8.

Guest Jul 22, 2022

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376

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Probability

A machine randomly generates one of the nine numbers 1, 2, 3, … , 9 with equal likelihood. What is the probability that when Tsuni uses this machine to generate four numbers their product is divisible by 4? Express your answer as a common fraction. read more ..

Guest Jul 22, 2022

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220

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Game

Three players are sitting at a round table playing a dice game with these rules. Each player starts with three tokens. On each turn, the player rolls one regular six-sided die and does one of the following actions based on the number rolled:
read more ..

Guest Jul 22, 2022

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283

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counting question

Amos counts out loud by 8 beginning with 0. Sarah counts out loud by 7 also beginning with 0. Between 2000 and 3000 inclusive, how many of the numbers do both Sarah and Amos say out loud?

Guest Jul 22, 2022

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220

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Probability problem

Consider the regular octahedron as shown. Each edge of the octahedron has a length of 1. An ant starts at the vertex A and crawls a total distance of 3 units along the edges of the octahedron. Any time the ant reaches a vertex of the octahedron, it randomly read more ..

Guest Jul 22, 2022

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218

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optimization problem

A factory manufactures two types of gadgets: regular and premium.
Each gadget requires two stages, assembly, and finishing, and there are at most 120 hours available for each operation (that is, 120 hours for assembly, and 120 hours read more ..

Guest Jul 22, 2022

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256

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Inequality

Find all x such that x^2 < 4 + 2x. Give your answer in interval notation.

Guest Jul 22, 2022

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248

1

Proportion

Suppose that a^2 varies inversely with b^3 If a=7 when b=6, find the value of a^2 when b=3

Guest Jul 22, 2022

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252

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Proportion

The square of a and the square root of b vary inversely. If a=2 when b=48, then find b when ab=81.

Guest Jul 22, 2022

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296

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number theory

Find the largest integer n for which 12^n evenly divides 20! + 12!.

Guest Jul 22, 2022

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205

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help math

The faces of a standard die are numbered 1, 2, 3, 4, 5, and 6 such that the sum of the numbers on any two opposite faces is 7. Tia writes one number on each vertex of the die such that the number on each face of the die is the greatest common divisor of read more ..

Guest Jul 22, 2022

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285

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trig

In triangle PQR, we have P = 90 degrees, QR = 20, and tan R = 2 sin R. What is PR?

Guest Jul 22, 2022

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214

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Operations

For any two real numbers x and y, define
x \star y = ax + by + cxy,
where a, b, and c are constants. It is known that 1 \star 2 = 4, 2 \star 3 = 1, and there is a non-zero real number $d$ read more ..

Guest Jul 22, 2022

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312

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Thermodynamics need help asap

I think second one is right.
pls answer read more ..

Guest Jul 22, 2022

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255

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Algebra

No matter where Sasha is in the country, the pre-tax price of a cup of coffee at a paritcular coffee retailer is 5.00. However, sales tax varies by region. In Atlanta there is a 8.5% sales tax, while in Chicago there is a 10% sales tax. read more ..

Guest Jul 22, 2022

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254

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Probability

Hans is staying at a hotel that has five floors, numbered 1 through 5, and 10 rooms per floor, numbered 1 through 10. Hans forgets where his room is, but knows that it is on an odd numbered floor and the room nujmber is divisible by 3. If Hans read more ..

Guest Jul 22, 2022

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