All Questions ⁺⁰236043 Questions

-1

35

0

+330

Angles

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

Stanry May 24, 2024

0

17

3

+4

Hi!

How many four-digit, positive integers are there where each digit is a prime number?

Ty to whoever answers :)

IH3ARTPURPL3 May 24, 2024

0

14

1

+842

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. read more ..

RedDragonl May 24, 2024

0

26

1

+842

Geometry

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

RedDragonl May 24, 2024

0

21

0

+842

Algebra

Find all solutions of the equation
|x^2 - 30x - 1| + |x^2 - 30x + 29| = 30

RedDragonl May 24, 2024

0

18

0

+842

Algebra

(1) Let a_1, a_2, a_3 be real numbers such that
|a_1 - a_2| + 2 |a_2 - a_3| + 3 |a_3 - a_1| = 1.
What is the largest possible value of |a_1 - a_2|?

(2) Let a_1, a_2, a_3, \dots, a_{10} be real numbers such that read more ..

RedDragonl May 24, 2024

0

16

1

+842

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 $f$.)

RedDragonl May 24, 2024

0

16

0

+842

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

RedDragonl May 24, 2024

0

12

3

+36

how would i solve this

How many of the first 500 positive integers are multiples of integers 3, 4 or 5?

cheeeeeeese May 24, 2024

0

21

1

+976

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?

Hi6942O May 24, 2024

0

18

1

+976

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 ..

Hi6942O May 24, 2024

0

16

1

+1310

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.

learnmgcat May 24, 2024

0

17

1

+1310

Geometry

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?

learnmgcat May 24, 2024

0

27

0

+1310

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

learnmgcat May 24, 2024

0

22

1

+1310

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.

learnmgcat May 24, 2024

0

8

2

+81

Counting problem involving sets

A set of five positive integers has a mean, median, and range of 7. How many distinct sets whose members are listed from least to greatest could have these properties? Note: {4, 6, 7, 7, 11} is one such set to include.
I know read more ..

moneydude242 May 24, 2024

-6

11

1

+219

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 $5$

BRAlNBOLT May 24, 2024

-6

29

0

+219

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?

BRAlNBOLT May 24, 2024

-5

29

1

+219

Counting

You are given the 4 x 4 grid below.
(a) Find the number of ways of placing 8 counters in the squares (at most one counter per square), so that each row contains exactly two counters.
(b) Find the number of ways read more ..

BRAlNBOLT May 24, 2024

-6

32

0

+219

Counting

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers ($1,$ $2,$ $3,$ $4,$ $5,$ $6,$ and $7$). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

BRAlNBOLT May 24, 2024

-6

18

2

+219

Help meee

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

BRAlNBOLT May 24, 2024

-1

15

1

+219

help help

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

BRAlNBOLT May 24, 2024

-1

28

0

+219

Need help

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 $x$.

BRAlNBOLT May 24, 2024

-1

10

1

+219

Help 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 $S_{70}.$

BRAlNBOLT May 24, 2024

0

8

1

+868

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 ..

eramsby1O1O May 24, 2024

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