All Questions ⁺⁰237783 Questions

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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?

LiIIiam0216 Jan 15, 2025

Jan 14, 2025

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12

2

+460

Algebra

Fill in the blanks with numbers to make a true equation.
3x^2 + 12x - 4 - 2x^2 + 6x + 7 = ___ (x + ___ )^2 + ___

Dragononweb2.0calc ●●

MEMEG0D Jan 14, 2025

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26

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+460

Algebra

The parabola y = ax^2 + bx + c is graphed below. Find a + b + c. (The grid lines are one unit apart.)
The parabola passes through (-2,8), (0,0), and (2,8).

MEMEG0D Jan 14, 2025

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21

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+460

Algebra

Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.

MEMEG0D Jan 14, 2025

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+30

Roots of Unity

Let be the roots of unity and let be the roots of unity. Compute
The hint is: What is the root of unity?

Chadly Jan 14, 2025

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31

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+2729

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

LiIIiam0216 Jan 14, 2025

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32

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+2729

Algebra

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

LiIIiam0216 Jan 14, 2025

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25

1

+2729

Algebra

A geometric sequence has $400$ terms. The first term is $500$ and the common ratio is $-\frac{1}{20}.$ How many terms of this sequence are greater than $1?$

LiIIiam0216 Jan 14, 2025

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26

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+2729

Algebra

All members of our painting team paint at the same rate. If $15$ members can paint a specific wall in $45$ minutes, then how long would it take $20$ members to paint the same wall, in minutes?

LiIIiam0216 Jan 14, 2025

+1

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+7

(1+sin2𝛼)/(sin𝛼+cos𝛼)−sin𝛼 please explain

(1+sin2𝛼)/(sin𝛼+cos𝛼)−sin𝛼
please explain

xknmvs Jan 14, 2025

Jan 13, 2025

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39

0

+460

Algebra

Let
f(x) = \left\lfloor\frac{2 - 3x}{3x + 1}\right\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.)

MEMEG0D Jan 13, 2025

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39

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+460

Algebra

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

MEMEG0D Jan 13, 2025

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28

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+2729

Geometry

In the diagram, \overline{BE} bisects \angle ABC, and $\overline{CE}$ bisects $\angle ACD.$ Compute $\angle BAC,$ in degrees.

LiIIiam0216 Jan 13, 2025

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28

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+2729

Geometry

Two angle bisectors of triangle ABC, $\overline {BE}$ and $\overline {CF}$, intersect at $P$. What is $\angle A$ in degrees?

LiIIiam0216 Jan 13, 2025

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33

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+2729

Geometry

Let A_1 A_2 A_3 \dotsb A_{12} be a regular polygon. If the area of A_1 A_2 A_3 \dotsb A_{12} is 1, then find the area of the blue region.

LiIIiam0216 Jan 13, 2025

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18

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+2729

Geometry

A square is divided into five rectangles, and all the rectangles have the same area. Given that $AB = 1,$ find the side length of the square.

LiIIiam0216 Jan 13, 2025

Jan 12, 2025

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40

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+823

Parametric Curves

The parametric equations
x = vt \cos \theta,
y = vt \sin \theta - \frac{1}{2} gt^2,
describe the path of a projectile fired at an angle of $\theta,$ where $v$ is the initial velocity, $g$ denotes acceleration due to gravity, and $t$ denotes read more ..

crimefightingvigiI Jan 12, 2025

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48

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+823

Counting

How many solutions are there to the equation
u + v + w + x + y + z = 6
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $8$ and $y$ is even?

crimefightingvigiI Jan 12, 2025

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45

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+823

Counting

There is a group of five children, where two of the children are twins. In how many ways can I distribute $12$ identical pieces of candy to the children, if the twins must get an equal amount of candy?

crimefightingvigiI Jan 12, 2025

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