All Questions ⁺⁰236302 Questions

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Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

cooIcooIcooI17 Jan 2, 2025

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+681

Geometry

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

cooIcooIcooI17 Jan 2, 2025

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+681

Geometry

Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.

cooIcooIcooI17 Jan 2, 2025

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Geometry

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 = 1, and the line is y = x.

cooIcooIcooI17 Jan 2, 2025

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+36

Math

James bought 4/5 kg of flour. He used 1/2 kg of it to bake some cakes and 1/4 of it to bake some cookies. How much four did he have left? Give your answer as a fraction in kilograms.

AskQuestonsInNewYear Jan 2, 2025

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Math

At a sale, a shop was offering a 20% discount for a pair of shoes. Customers can purchase a second pair of shoes at 50% discount. Scott paid $156 for 2 identical pairs of shoes. How much did each pair of shoes cost before the discount?

AskQuestonsInNewYear Jan 2, 2025

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Math

Owen had some fifty-cent and one-dolar coins. 2/7 or his coins were fify-cents coins. His mother gave him 10 one-dollar coins and five-dollars' worth of fifty-cent coins. In the end, he had twice as many one-dollar coins as fifty-cent coins. How many read more ..

AskQuestonsInNewYear Jan 2, 2025

Jan 1, 2025

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+1927

Geometry

Triangle PQR is equilateral. Find AQ.

tomtom Jan 1, 2025

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+1927

Geometry

In triangle ABC, \cos \angle A = \frac{1}{8}. Find the length of angle bisector \overline{AD}.

tomtom Jan 1, 2025

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+1927

Geometry

In the diagram below, \angle XOY = 30^\circ and OA=15. Let B and C be points on rays \overrightarrow{OY}$ and $\overrightarrow{OX}, respectively. Find the area of triangle ABC if OB = 10 and OC = 12.
Triangle ABC is dilated to triangle read more ..

tomtom Jan 1, 2025

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+1927

Geometry

Find \sin C, to two decimal places.

tomtom Jan 1, 2025

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+585

Trig

Let A, B, and C be the angles of a triangle. Given that \tan \frac{A}{2} = \frac{1}{4} and \tan \frac{B}{2} = \frac{1}{3}, find \tan \frac{C}{2}.

Pythagorearn Jan 1, 2025

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+585

Trig

In triangle ABC, \cos A=\sqrt{\frac{2}{5}} and \cos B= 1/2. Find \cos C.

Pythagorearn Jan 1, 2025

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+585

Trig

Let \alpha be an angle in the third quadrant such that $\tan \alpha = \frac{1}{2}$. Find $\cos \alpha.$

Pythagorearn Jan 1, 2025

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+585

Trig

Let \theta be an acute angle such that \cos \theta = \frac{1}{2}. Find $\tan \theta.$

Pythagorearn Jan 1, 2025

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+162

Geometry

What is the sine of an acute angle whose cosine is \frac{5}{7}?

cwimie Jan 1, 2025

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+162

Geometry

Two tangent circles are shown below. One circle is centered at (2,4) with radius 4, and the other circle is centered at with radius . The equation of a common external tangent to the circles can be written in the form $y = mx + b$ with read more ..

cwimie Jan 1, 2025

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+162

Geometry

Two black lines pass through the origin, as shown below. If their slopes are 2 and 8, then find the slope of the red line that bisects the acute angle between these lines.

cwimie Jan 1, 2025

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+162

Algebra

Let x and y be real numbers such that x^2 + y^2 = 2x + 4y. Find the largest possible value of x + y.

cwimie Jan 1, 2025

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+162

Geometry

Consider the grid of points shown below. Find the area of the pink region.

cwimie Jan 1, 2025

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+703

Geometry

Find the area of the region bounded by the lines y=5 and 5x+2y=10 and the coordinate axes.

siIviajendeukie Jan 1, 2025

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+703

Geometry

Two runners start at vertices A and B simultaneously and run clockwise around the perimeter of square ABCD at the same speed. A drone flies so that it is always at the midpoint of the two runners. What is the minimum distance between the two runners? read more ..

siIviajendeukie Jan 1, 2025

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Geometry

Two points, A and B, are on the pavement 6 inches apart. Cassidy the caterpillar traces out a path walking along all the points that are equidistant to ${}A$ as from $B$. Cassidy has red paint on her feet, so she literally traces out the whole path! read more ..

siIviajendeukie Jan 1, 2025

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