All Questions ⁺⁰236048 Questions

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Geometry

Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length AB.

Rangcr897 May 29, 2024

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17

1

+948

Geometry

A semicircle is inscribed in triangle XYZ so that its diameter lies on YZ, and is tangent to the other two sides. If XY = 10, XZ = 10, and YZ = 10*sqrt(2), then find the area of the semicircle.

Rangcr897 May 29, 2024

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16

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+948

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.

Rangcr897 May 29, 2024

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15

1

+551

Algebra

Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)

Pythagorearn May 29, 2024

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12

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+551

Algebra

Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$

Pythagorearn May 29, 2024

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16

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+551

Algebra

Let $f(x) = 3x - 8 + 4x^2$ and $g(x) = 15x + c - 3x^2$. Find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

Pythagorearn May 29, 2024

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29

1

+551

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be an arithmetic sequence. Let $S_n$ denote the sum of the first $n$ terms. If $S_{20} = \frac{1}{5}$ and $S_{10} = 0,$ then find $S_{70}.$

Pythagorearn May 29, 2024

May 28, 2024

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+551

Algebra

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 $20,$ Shirley runs screaming from the room. What number does Laverne say that read more ..

Pythagorearn May 28, 2024

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18

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+551

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10},$ $a_{11},$ $a_{12}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 + a_7 + a_9 + a_{11} = 0$ and $a_2 + a_4 + a_6 + a_8 + a_{10} + a_{12} = 0$, then find $a_1$.

Pythagorearn May 28, 2024

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14

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+551

Algebra

When the same constant is added to the numbers $60,$ $120,$ and $160,$ a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

Pythagorearn May 28, 2024

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22

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+551

Algebra

Find the sum of all positive integers less than $1000$ ending in $3$ or $4$ or $5$.

NotThatSmart ●

Pythagorearn May 28, 2024

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18

1

+551

Algebra

What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?

NotThatSmart ●

Pythagorearn May 28, 2024

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14

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+551

Algebra

There exists a polynomial $f(x)$ and a constant $k$ such that
(x^2 - 2x - 5) f(x) = 2x^4 + 19x^3 + kx^2 - 15x - 1.
What is $k?$

Pythagorearn May 28, 2024

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20

1

+551

Algebra

Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.

Pythagorearn May 28, 2024

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8

2

+36

geometry ish problem

Figure ABCD can be drawn, without retracing, in one continuous pen stroke. If the stroke must begin at A, B, C or D, in how many different ways can this be done?

cheeeeeeese May 28, 2024

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+36

i have an idea for this but i dont know how to actually solve it

In the land of Binaria, the currency consists of coins worth 1¢ , 2¢ , 4¢ , 8¢ , 16¢ , 32¢ and 64¢ . Bina has two of each coin. How many combinations of her coins have a combined value of 50¢ ?
me personally i just brute forced it but read more ..

cheeeeeeese May 28, 2024

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+219

Algebra

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far read more ..

NotThatSmart ●

BRAlNBOLT May 28, 2024

-7

13

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+219

Geometry

Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle BEC if [ABC] = 14.

BRAlNBOLT May 28, 2024

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11

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+219

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

BRAlNBOLT May 28, 2024

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17

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+219

Geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

BRAlNBOLT May 28, 2024

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25

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+842

Medians

A median of a triangle is a line segment joining a vertex of a triangle to the midpoint of the opposite side. Let's try this out with a particular triangle. Consider the triangle ABC with A=(0,0) B=(1,0) C=(0,1).
(a) Let D, E, F be read more ..

RedDragonl May 28, 2024

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19

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+842

Algebra

Find all values of $x$ such that $x^2 - 5x + 4 = -x^2 - 25x - 14$. If you find more than one value, then list your solutions, separated by commas.

NotThatSmart ●

RedDragonl May 28, 2024

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+842

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 the denominator read more ..

RedDragonl May 28, 2024

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14

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+842

Algebra

Evaluate the infinite geometric series
0.4 + 0.036 + 0.0000324 + ...
Express your answer as a fraction with integer numerator and denominator.

RedDragonl May 28, 2024

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14

1

+842

Line

The equation of the line below can be expressed in the form
\frac{x}{a} + \frac{y}{b} = 1.
Find a. read more ..

RedDragonl May 28, 2024

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