All Questions ⁺⁰236251 Questions

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Algebra

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and read more ..

parmen Dec 27, 2024

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+1573

Algebra

Let
a + ar + ar^2 + ar^3 + \dotsb
be an infinite geometric series. The sum of the series is 3. The sum of the squares of all the terms is 10. Find the common ratio.

parmen Dec 27, 2024

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+1573

Algebra

Compute the sum
1 + 1/5 + 2/25 + 4/25 + 8/125.

parmen Dec 27, 2024

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+1573

Algebra

Evaluate the infinite geometric series
0.4 + 0.016 + ...
Express your answer as a fraction with integer numerator and denominator.

parmen Dec 27, 2024

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+5

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts,

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds Shirley runs screaming from the room. What number does Laverne say that sends Shirley screaming read more ..

hemii18675 Dec 27, 2024

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+585

Geometry

A circle is centered at O and has tangent \overline{AB}. Find the area of the circle.

Pythagorearn Dec 27, 2024

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+585

Geometry

Find the radius of the circle if AB is 12 and CD is 10.

Pythagorearn Dec 27, 2024

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+585

Geometry

Equilateral triangle ABC is inscribed in a circle. Let $M$ and $N$ be the midpoints of sides $\overline{AB}$ and $\overline{AC},$ respectively. Line $MN$ intersects the circle at $P$ and $Q.$ Compute MB/MC.

Pythagorearn Dec 27, 2024

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+585

Geometry

Chords \overline{PQ} and \overline{RS} of a circle meet at $X$ inside the circle. If $RS = 38$, $PX = 38$, and $QX = 36$, then what is the smallest possible value of $RX$?

Pythagorearn Dec 27, 2024

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+348

Geometry

A circle is drawn inside triangle ABC, tangent to $\overline{AC},$ $\overline{BC},$ and the semicircle with diameter $\overline{AB}.$ The radius of the circle is $1,$ and $\angle BAC = 60^\circ.$ Find the area of triangle $ABC.$

MEMEG0D Dec 27, 2024

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+24

Math

The cost of a corn is at $1.80 per cob. A snack bar is selling per cob at a profit of 40%. The number of corns sold on last Sunday was 50% as many as the total number sold on last Friday and Saturday. The ratio of the number of corns sold on last Friday read more ..

BilalKrol28282 Dec 27, 2024

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+348

Geometry

Two circles, centered at A and B, are externally tangent to each other, and tangent to a line $\ell.$ A third circle, centered at $C,$ is externally tangent to the first two circles, and the line $\ell.$ If the radii of circle $A$ and circle $B$ are $9$ read more ..

MEMEG0D Dec 27, 2024

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+348

Geometry

Given regular heptagon $ABCDEFG$, a circle can be drawn that is tangent to $\overline{DC}$ at $C$ and to $\overline{EF}$ at $F$. What is radius of the circle if the side length of the heptagon is 1?

MEMEG0D Dec 27, 2024

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+348

Geometry

In the diagram, a semicircle is centered at O, and \overline{AB} is tangent to the semicircle at $B.$ Find $\angle BCD,$ in degrees.

MEMEG0D Dec 27, 2024

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+303

Geometry

Angles \angle A : \angle P : \angle ASP are in ratio 1:8:15. Find the degree measure of \angle BSA.

bIueb3rry Dec 27, 2024

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+305

Probability

Not including the identity transformation, the eleven transformations that preserve the regular hexagon shown are counterclockwise rotations by and reflections across the six dashed lines shown. Kristina randomly picks six transformations and with read more ..

Imcool Dec 27, 2024

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+303

Geometry

Circle O has radius 5. Segment $\overline{AS}$ has length $5$ and is tangent to circle $O$ at $A$. If $P$ is the projection of A onto OS, find length PS.

bIueb3rry Dec 27, 2024

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+303

Geometry

Compute \angle AGD, in degrees.
In triangle AGD, A = 30 degrees and D = 70 degrees.

bIueb3rry Dec 27, 2024

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+303

Geometry

What kinds of quadrilaterals are always cyclic? Select all that apply.
AB = CD
AB = 2*CD
AB + BC = AD + DC read more ..

bIueb3rry Dec 27, 2024

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+303

Geometry

In the figure, MR=MK. What is \angle RPK, in degrees?

bIueb3rry Dec 27, 2024

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+911

Geometry

A circle is centered at O. Compute \angle BPC, in degrees.

magenta Dec 27, 2024

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+911

Geometry

In the diagram, \text{minor arc } AB: \text{minor arc } BC : \text{major arc } CA = 1:1:1. What is \angle ABC in degrees?

magenta Dec 27, 2024

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+911

Geometry

Grogg draws the following figure. It so happens that \angle SAP is 124^\circ less than \angle PSO. Find the degree measure of \angle SAP.

magenta Dec 27, 2024

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+911

Geometry

In a circle, \overline{AP} is a diameter of length 17 and $\overline{PS}$ is a chord of length 17. What is the length of chord $\overline{AS}$?

magenta Dec 27, 2024

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+493

Geometry

Find the degree measure of arc PS. (The angle above arc AP indicates its degree measure.)

crimefightingvigiI Dec 27, 2024

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