All Questions ⁺⁰236187 Questions

0

27

0

+1488

Geometry

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle PBA$, and $\angle ABC - \angle ACB = 24^\circ$. Find $\angle PBC$ in degrees.

kittykat Jun 18, 2024

0

12

2

+1488

Geometry

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

kittykat Jun 18, 2024

0

9

1

+976

Number Theory

Find the first ten digits after the decimal point in the decimal expansion of \frac{13}{29}=0.abcdefghij\ldots without a calculator.
(Express your answer as a ten digit number.)

NotThatSmart ●

Hi6942O Jun 18, 2024

0

12

1

+825

Number Theory

Find the six-digit number abcdef such that
0.\overline{abcdef} = \frac{2}{17},
without a calculator.

NotThatSmart ●

gnistory Jun 18, 2024

0

17

1

+825

Number Theory

Convert 0.29\overline{6} to a fraction in simplest form.

NotThatSmart ●

gnistory Jun 18, 2024

0

11

1

+825

Number Theory

Convert 0.031\overline{4}$ to a fraction in simplest form.

NotThatSmart ●

gnistory Jun 18, 2024

0

19

1

+825

Number Theory

Convert 11012_9 to decimal.

NotThatSmart ●

gnistory Jun 18, 2024

0

15

1

+976

Polygons

A regular hexagon has a perimeter of $p$ (in length units) and an area of $A$ (in square units). If $A = 3,$ then find the side length of the hexagon.

Hi6942O Jun 18, 2024

0

22

0

+976

Polygons

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, and a regular -gon, all with the same side length, also completely read more ..

Hi6942O Jun 18, 2024

0

14

1

+976

Polygons

The number of diagonals in a certain regular polygon is equal to $2$ times the number of sides. How many sides does this polygon have?

Hi6942O Jun 18, 2024

-1

16

1

+330

help geometry

A sphere of radius $4$ inches is inscribed in a cone with a base of radius $8$ inches. In inches, what is the height of the cone? Express your answer as a decimal to the nearest tenth.

Stanry Jun 18, 2024

-1

13

1

+330

help geometry

Rose has a spherical plum of radius $2$ and a spherical watermelon of radius $8$. She builds a glass sphere around the two fruits to contain them, making the sphere as small as possible. When she has done this, she places a golf ball inside read more ..

Stanry Jun 18, 2024

-1

8

1

+330

help geometry

A sphere is inscribed in a cone with height $3$ and base radius $3$. What is the ratio of the volume of the sphere to the volume of the cone?

Stanry Jun 18, 2024

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22

2

+64

help pls asap!

b) For which values of x and y does $(x + y)^2$ equal $x^2 + y^2?$ For which values of x and y does $(x + y)^2$ not equal $x^2 + y^2?$

ghistory Jun 18, 2024

0

18

1

+825

Number Theory

Convert 987_{16} to decimal.

gnistory Jun 18, 2024

0

13

1

+825

Number Theory

Convert 60329_12 to decimal.

gnistory Jun 18, 2024

0

17

1

+825

Number Theory

Convert 35 from base 10 to base 8.

gnistory Jun 18, 2024

0

21

1

+842

Geometry

The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XY = 8$ and $WX = 8,$ find $XY.$

RedDragonl Jun 18, 2024

0

24

0

+825

Algebra

The sum
6\left( 1\cdot1 + 2\cdot2 + \dots + n(n) \right)
is equal to a polynomial f(n) for all n \ge 1.
Write f(n) as a polynomial with terms in descending order of n.

gnistory Jun 18, 2024

0

16

0

+825

Algebra

Find constants A and B such that
(2x + 11)/(x^2 - 6x + 5) = A/(x - 3) + B/(x + 4)
for all x such that x neq 7 and x neq 8

gnistory Jun 18, 2024

0

15

1

+825

Algebra

Let f(x) = lfloor (2 - 3x)/(3x + 8) \rfloor
Evaluate $f(1)+f(2) + f(3) + \dots + f(999)+f(1000).$ (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)

gnistory Jun 18, 2024

0

10

1

+64

halp asap

Solve for the variable x in terms of y and z, assuming $y \neq \frac{1}{2}$: \[xy + x = \frac{3x + 2y + z}{2}.\]

ghistory Jun 18, 2024

-4

28

0

+219

Geometry

Let A1 A2 A3 ... A15 be a regular polygon. A rotation centered at $A_4$ with an angle of $\alpha$ takes $A_3$ to $A_5$. Given that $\alpha < 180^\circ$, find $\alpha,$ in degrees.

BRAlNBOLT Jun 18, 2024

0

19

1

+64

help please

Let's take a look at $(x + y)^2$ and $x^2 + y^2$ . While Beeker believes that these two expressions are equal for all real numbers $x$and $y,$Clod believes they are not! Let's get to the bottom of this!
a) read more ..

ghistory Jun 18, 2024

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