All Questions ⁺⁰236397 Questions

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184

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Probability

Two two-digit counting numbers (from 10 to 99, inclusive) were chosen randomly.These two integers could be the same or different. What is the probability that thedifference between these two numbers is at most 3?

Guest May 7, 2022

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196

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Graphing functions

The graph of y = f(x) is shown in red below. Find f(2). Assume grid lines are spaced 1 unit apart.

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302

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Polynomial Divison

Find a polynomial f(x) of degree 5 such that both of these properties hold:

f(x) is divisible by .
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240

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Counting

How many 4-digit numbers are there where any two consecutive digits have different parity?

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289

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triangle problem

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172

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help quadratic

The quadratic ax^2 + bx + c can be expressed in the form (x - 4)^2 + 8. When the quadratic is expressed in the form 3ax^2 + 2bx + c, what is n(x - h)^2 + k, what is h?

Guest May 7, 2022

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252

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Perfect Squares

Find the number of positive integers 1<=n<=1000 such that n^n is a perfect square.

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279

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Geometry

The sides of triangle XYZ are XY = XZ = 25 and YZ = . A semicircle is inscribed in triangle XYZ so that its diameter lies on YZ and is tangent to the other two sides. Find the area of the semicircle.

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193

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Conics

The ellipse x^2 + 4y^2 = 4 and the hyperbola x^2 - my^2 = 1 are tangent. Compute m.

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260

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Coordinates

Let B be the reflection of A over the line $y = \frac{1}{2} x + 2$. Find the coordinates of B.

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171

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Inequality

My street hockey team plays three games each week. My team lost all 12 games in the first four weeks. Then, my team won two games and lost one game in the fifth week, bringing our record to 2 wins and 13 losses. Each week after that, my team won two read more ..

Guest May 7, 2022

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312

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Algebra

Determine the value of the infinite product
Enter your answer in the form "\sqrt[a]{b}"

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236

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Probability

Ben twuce chooses a random integer between 1 and 50 inclusive, twice (and he may choose the same integer both times). What is the probability that at least one of the numbers Ben chooses is a multiple of ?

Guest May 7, 2022

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278

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Algebra

Five times a number is divided by 7 more than the original number. If the result is , then what was the original number?

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230

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trig

In right triangle ABC with angle B = 90, we have sin A = cos A. What is cos A?

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278

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help geometry

Let G be the center of equilateral triangle XYZ. A dilation centered at G with scale factor 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 A/[XYZ] read more ..

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241

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Geometry

In quadrilateral AC, we have AB = 3, BC = 6, CD = 4, and DA = .

If the length of diagonal is an integer, what are all the possible values for AC? Explain your answer in complete sentences.

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289

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Number Theory

The number 2^1993 + 3 is a multiple of 5. What is the units digit of the quotient (2^1993 + 3)/5?

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287

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Floor function

Let f(x) = x + floor(x).

(a) Find all x >= 0 such that f(x) = 1.
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242

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Reflections

In the diagram below, Y is reflected over XZ to Y'. Find YY'.

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368

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math probem

John counts up from 1 to 13, and then immediately counts down again to 1, and then back up to 13, and so on, alternately counting up and down: What is the integer in his list?

Guest May 7, 2022

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231

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math problem

Jacob’s little brother bragged that he could add all numbers from from 1 to 10 (55).Not to be outdone, Jacob said he could add all numbers from 1 to 100 (the answer is 5050).Perhaps because Jacob was a bit too smuck about it, Jacob’s little brother gave read more ..

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243

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Please help

Hello, I really need help with the question below. I don't understand how to approach it.

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190

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Algebra

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t^2 + 90t gives the height h of the ball after t seconds.
What is the maximum height of the ball?

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Let $P(x)$ be a nonconstant polynomial, where all the coefficients are nonnegative integers. Prove that there exist infinitely many positive

Let $P(x)$ be a nonconstant polynomial, where all the coefficients are nonnegative integers. Prove that there exist infinitely many positive integers $n$ $P(n)$ such that is composite.

Guest May 7, 2022

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