All Questions ⁺⁰231295 Questions

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Algebra

The quadratic x^2 - 6x + 60 can be written in the form (x + b)^2 + c, where b and c are constants. What is b + c?

Guest Jan 1, 2022

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194

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Quadratic

In an equation of the form with k = ax^2 + bx + c, the least possible value of k occurs at x = -b/(2a). In the equation k = (6x - 12)(x - 8) , what is the least possible value for k?

Guest Jan 1, 2022

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214

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Number Theory

Find all positive integers n such that n + 7 divides 9n + 7.

Guest Jan 1, 2022

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286

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Geometry

A circle is divided into 4 sectors, the ratio of whose areas is 1 : 2 : 3 : 6. What is the central angle of the largest sector in degrees?

Guest Jan 1, 2022

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284

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Algebra

The values of x such that 2x^2 - 6x + 7 = 0 are m+ni and m-ni, where m and n are positive. What is m*n?

Guest Jan 1, 2022

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302

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Mathematics

Andy has a number of friends who like dressing as zombies for Halloween. Two years ago, four of his friends dressed as zombies. Last year, that number increased by fifty percent. This year, the number increased by one third over last year. How many of Andy’s read more ..

Guest Jan 1, 2022

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281

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Math

Nicole the Robot completed 8 times as many space missions as Astronaut Andy. Nicole completed a total of 48 space missions. How many more space missions has Nicole done than Andy?

Guest Jan 1, 2022

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291

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Coordinates

Line m has the equation y = 3x + 5. Line n has the equation y = kx + 7. Lines m and n intersect at the point (-4, -7). What is the value of k?

Guest Jan 1, 2022

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243

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Counting

Using pennies, nickels, dimes, and quarters. How any ways does it take you to make 69 cents?

Guest Jan 1, 2022

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267

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Absolute value

Given that x < 5, rewrite 8x + 5 - |x - 5| without using absolute value signs.

Guest Jan 1, 2022

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329

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Quadratic

The equation y = -16t^2 - 60t + 54 describes the height (in feet) of a ball thrown downward at 60 feet per second from a height of 54 feet from the ground, where t represents time, measured in seconds. What is the maximum height of the ball? Express your read more ..

Guest Jan 1, 2022

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278

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Algebra

Let a and b be real numbers such that a + b = -1. Compute a^2 - b^2 + 2a.

Guest Jan 1, 2022

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295

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Probability

I am rolling a die, and I must roll a 3 before I roll an even number. What is the probability this happens?

Guest Jan 1, 2022

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185

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Polynomial

The polynomial f(x) satifies the equation f(x)-f(x-2)=5x+1 for all x. If p and q are the coefficients of x^2 and x respectively, in f (x), then what is the value of p+q?

Guest Jan 1, 2022

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284

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Function

If f(x) = a+bx, what are the real values of a and b such that f(f(f(1))) = 14 and f(f(f(0))) = -13.

Guest Jan 1, 2022

Dec 31, 2021

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240

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This is confusing! Help!

Given that $(3,15)$ is on the graph of $y = f(x)$, find a point that must be on the graph of $y = f(x) - 7$. Express your answer as an ordered pair $(a,b)$ where $a$ and $b$ are real numbers.

Guest Dec 31, 2021

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212

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Counting

How many distinct triangles can be formed by selecting three vertices of a regular hexagon? (Triangles with different vertices are considered distinct even if they are congruent.)

Guest Dec 31, 2021

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222

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Sequence

An infinite geometric series has first term 328 and a sum of 2296. What is its common ratio?

Guest Dec 31, 2021

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231

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Trapezoid

What is the perimeter of the trapezoid shown?

Guest Dec 31, 2021

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242

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Polynomial

There is a polynomial which, when multiplied by x^2 + 2x + 3, gives 2x^5 + 3x^4 + 7x^3 + 6x^2 + 15x + 9. What is that polynomial? (Give your answer as a polynomial in which the terms appear in order of decreasing degree. In other words, "x^5 + x + 2" is read more ..

Guest Dec 31, 2021

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176

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Polynomials

Find t if the expansion of the product of x^3 - 4x^2 + 5x - 5 and x^2 + tx - 7 has no x^2 term.

Guest Dec 31, 2021

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276

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Algebra

Let
P = 1/7 + 1/7^2 + 1/7^3 + ...
Then P can be expressed in the form a/b, where a and b are positive integers. Find the smallest possible value of a + b?

Guest Dec 31, 2021

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314

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HEELLPP

Find all values of such that . If you find more than one value, then list your solutions, separated by commas.

Guest Dec 31, 2021

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223

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Geometry

In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 17. What is the greatest possible perimeter of the triangle?

Guest Dec 31, 2021

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282

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Algebra

Solve
(x^2 + 2x + 3)/(x + 4) = x - 5
for x.

Guest Dec 31, 2021

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