All Questions ⁺⁰232819 Questions

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Geometry

The line $y = mx$ bisects the angle between the two lines shown below. Find $m$.
The two lines are y = x and y = 2x.

RedDragonl May 28, 2024

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+412

Help math

Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
x^2 + y^2 = 4x + 2y
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.

NotThatSmart ●

RedDragonl May 28, 2024

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+412

Math

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 20.
The line is y = -4.

RedDragonl May 28, 2024

May 27, 2024

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+461

Counting

In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are $3$ skaters, including $3$ Americans, in how many ways can the medals be awarded to three of the $3$ skaters if exactly read more ..

Rangcr897 May 27, 2024

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+461

Counting

Dogs in the GoodDog Obedience School win a blue ribbon for learning how to sit, a green ribbon for learning how to roll over, and a white ribbon for learning how to stay. There are $100$ dogs in the school.
$62$ have blue ribbons, $55$ read more ..

Rangcr897 May 27, 2024

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+461

Counting

Find the number of positive integers that satisfy both the following conditions:
- Each digit is a 1 or a 2 or a 3
- The sum of the digits is 5

Rangcr897 May 27, 2024

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+461

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

Rangcr897 May 27, 2024

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+385

Algebra

The temperature of a point (x,y) in the plane is given by the expression x^2 + y^2 - 4x + 2y - 12x + 14y + 26. What is the temperature of the coldest point in the plane?

Pythagorearn May 27, 2024

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+385

Algebra

Let x and y be nonnegative real numbers. If xy = \frac{2}{5}, then find the minimum value of 6x + \frac{3}{5y}.

Pythagorearn May 27, 2024

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+4

HELP PLEASE

Find the number of ways that Magnus can give out 12 identical stickers to 4 of his friends. (Not everyone has to get a sticker.)

Frogperson May 27, 2024

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+385

Algebra

Let x and y be nonnegative real numbers. If x^2 + 3y^2 = 18, then find the maximum value of x + y.

Pythagorearn May 27, 2024

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+657

Algebra

Find all values of x such that \frac{x}{x - 5} = \frac{4}{2x - 4} + \frac{2}{x + 3}.

eramsby1O1O May 27, 2024

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+657

Algebra

Find all ordered pairs $(x,y)$ of real numbers such that $x + y = 10$ and $x^2 + y^2 = 64 + xy$.

eramsby1O1O May 27, 2024

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+657

Algebra

Find one ordered pair (x,y) of real numbers such that x + y = 6 and x^3 + y^3 = 162 - (x^2 + y^2).

eramsby1O1O May 27, 2024

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+36

Triangle DEF is inscribed in circle G. In circle G, angle EDF=29 and arc DF has a measure of 132. If the circumference of circle G is 24

Triangle DEF is inscribed in circle G. In circle G, angle EDF=29 and arc DF has a measure of 132. If the circumference of circle G is 24 units, what is the length of arc DE? Express your answer as a common fraction.

RedDragon1 May 27, 2024

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+628

Algebra

For what real values of $c$ is $x^2 - 8x - 14x + c$ the square of a binomial?

NotThatSmart ●

learnmgcat May 27, 2024

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+628

Algebra

Find all real values of $s$ such that $x^2 + sx + 144 - 44$ is the square of a binomial.

learnmgcat May 27, 2024

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+628

Algebra

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2mn - 21m + 6n + mn - 9m + ___

learnmgcat May 27, 2024

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+628

Geometry

Our badminton team has finished $60\%$ of its season. So far, we have won $40\%$ of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

learnmgcat May 27, 2024

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+385

Geometry

In the diagram below, each side of convex quadrilateral $ABCD$ is trisected. (For example, $AP = PQ = QB.$) The area of convex quadrilateral $ABCD$ is $180.$ Find the area of the shaded region.

Pythagorearn May 27, 2024

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+385

Geometry

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.
An equilateral triangle, a regular dodecagon, a square, and a regular n-gon, all with the same side length, also read more ..

Pythagorearn May 27, 2024

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+171

Math

The graph of y=f(x) is a parabola whose vertex is at (1,-2). The graph of y=3f(x+5)/2-8 is also a parabola. Where is the vertex of the graph of y=3f(x+5)/2-8

BRAlNBOLT May 27, 2024

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+171

Math

Suppose f(3)=4. Name a point that must be on the graph of y=2f(x/3)+17

BRAlNBOLT May 27, 2024

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+171

Geometry

The distance between the points $A$ and $B$ is $\sqrt{34}.$ If $A = (a,4)$ and $B = (-20,33),$ then find the sum of all possible values of $a.$

BRAlNBOLT May 27, 2024

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+603

Counting

How many ways can you write two different letters chosen from
A B C D E F G H I J K L M N O P
so that they are in alphabetical order, and the first letter is a vowel? For example, AF and EN count, but DE and KC do not.

Hi6942O May 27, 2024

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