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370

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The polynomial $4x^3 - 20x^2 + 19x + 15$ has a root at $x = 3$. Find the other two roots.

AOPS IS HARD

Hint = factor read more ..

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aideniscool Nov 27, 2022

190

Algebra

What is the constant term in the expansion of (sqrt(x) + 5x - 2)^9?

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Guest Nov 27, 2022

177

Circles

Chord YZ of a circle with center O has length 12. The circumference of the circle is 12*pi. Find the length of arc YZ.

Guest Nov 27, 2022

195

angles

The consecutive angles of a particular trapezoid form an arithmetic sequence. If the largest angle measures 140 degrees , what is the measure of the smallest angle?

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Guest Nov 27, 2022

159

Polynomials

When f(x) = ax^3 - 6x^2 + bx - 5 is divided by x - 1, the remainder is -5. When f(x) is divided by x + 2, the remainder is 53. Find the ordered pair (a,b).

Guest Nov 27, 2022

164

Polynomials

If 2x + 7 is a factor of 6x^3 + 29x^2 + cx + 35, find c.

Guest Nov 27, 2022

193

help probability

If I choose four cards from a standard 52-card deck, with replacement, what is the probability that I will end up with four Aces?

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Guest Nov 27, 2022

163

plz help

The graph of y = f(x) is shown below, with one unit between grid lines. Assume f(x) is defined only on the domain shown. What is the sum of all integers c for which the equation f(x) = c has exactly 6 solutions?

read more ..

Guest Nov 27, 2022

171

Algebra

For a real number x, find the number of different possible values of x + (-x).

Guest Nov 27, 2022

168

Complex numbers

Suppose that a and b are positive integers such that (a-bi)^2 = 8 - 6i + 13 - 4i. What is a-bi?

Guest Nov 27, 2022

220

system

Solve for (x,y) in the system of equations
2x + y = -7 + y
x = 4 + 2y + x

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Guest Nov 27, 2022

200

system

Find the ordered pair (s,t) that satisfies the system
s/2 + 5t = 3 + 5t
3t - 6s = 9 + 3t

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Guest Nov 27, 2022

203

help counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color, and at lest three of the squares are red. How many ways are there to color the five squares?

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Guest Nov 27, 2022

Nov 26, 2022

203

+328

A dot is marked at each vertex of a triangle . Then and more dots are marked on the sides and respectively. How many

A dot is marked at each vertex of a triangle . Then and more dots are marked on the sides and respectively. How many triangles have their vertices at these dots?

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Potatobird Nov 26, 2022

221

+328

How many pairs of vertical angles are formed by distinct lines that have a common point of intersection?

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Potatobird Nov 26, 2022

202

How many pairs of vertical angles are formed by distinct lines that have a common point of intersection?

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Guest Nov 26, 2022

204

How many subsets of { } contain at least one prime number?

How many subsets of {} contain at least one prime number?

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Guest Nov 26, 2022

217

+328

At a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one.

At a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur?

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Potatobird Nov 26, 2022

228

18x + 18y = 17 in slope intercept form

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Guest Nov 26, 2022

164

Algebra

Let c be a real number, and consider the system of quadratic equations
y = 6x^2 - 9x + c - x^2 - x
y = 5x^2 - 3x + x^2 + 2x

For which values of c does this system have:
(a) Exactly one real solution (x,y)
(b) More than read more ..

Guest Nov 26, 2022

222

geometry

Triangle ABC has side lengths c = 29, a = 40, and b = 40. Find the inradius of triangle ABC. Find the circumradius of triangle ABC.

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Guest Nov 26, 2022

174

Algebra

Fill in the blank to make the equation true.

13*5*13*___*3 = 13*17

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Guest Nov 26, 2022

198

Parametric curve

The parametric curve (x,y) = (t^2 + t, t), for real numbers t, describes a parabola. Find the vertex of the parabola.

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Guest Nov 26, 2022

230

plz help

Arrange the following numbers in increasing order (smallest first, biggest last):

A = 2*1/2*4*1/6
B = 12*128 read more ..

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Guest Nov 26, 2022

200

Algebra

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 15 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

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Guest Nov 26, 2022

All Questions ⁺⁰237643 Questions

The polynomial $4x^3 - 20x^2 + 19x + 15$ has a root at $x = 3$. Find the other two roots.

Algebra

Circles

angles

Polynomials

Polynomials

help probability

plz help

Algebra

Complex numbers

system

system

help counting

A dot is marked at each vertex of a triangle . Then and more dots are marked on the sides and respectively. How many

How many pairs of vertical angles are formed by distinct lines that have a common point of intersection?

How many pairs of vertical angles are formed by distinct lines that have a common point of intersection?

How many subsets of { } contain at least one prime number?

At a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one.

18x + 18y = 17 in slope intercept form

Algebra

geometry

Algebra

Parametric curve

plz help

Algebra

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