All Questions ⁺⁰236027 Questions

-1

31

2

+1521

coeffcient

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

blackpanther Dec 8, 2023

-1

34

0

+1521

polynomials

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 $k?$

blackpanther Dec 8, 2023

-1

34

0

+1521

polynomial

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

blackpanther Dec 8, 2023

0

26

2

+8

Find the number of integers $n$ that satisfy $n^2 < 64.$

Find the number of integers that satisfy

apples1ices Dec 8, 2023

0

25

1

+1911

Geometric

In a geometric sequence, the $23$rd term is $16$ and the $26$th term is $18$. What is the $24$th term?

tomtom Dec 8, 2023

0

59

0

+1911

Arithmetic

In an arithmetic sequence, the $23$rd term is $\frac{1}{4},$ and the $24$th term is $\frac{2}{4}$. What is the $25$th term?

tomtom Dec 8, 2023

-1

36

1

+1521

Absolute value

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

blackpanther Dec 8, 2023

-1

59

0

+1521

Inequalities

(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 ..

blackpanther Dec 8, 2023

0

49

0

+4

calculate swap amountIn

I have a swap from USD to ETH (doesn't matter what exactly) I need to get 0.0012 ETH after the swap, but the swap has a 0.3% commission.
For example:
price - 1 ETH = 1870 USD
commission = 0.3% read more ..

soypxx Dec 8, 2023

0

53

0

+1911

Floor function

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 $f$.)

tomtom Dec 8, 2023

0

54

0

+1911

Floor function

Find all values of $t$ such that $\lfloor t \rfloor = 3t - \lfloor 2t \rfloor$. If you find more than one value, then list the values you find in increasing order, separated by commas.

tomtom Dec 8, 2023

0

56

0

+1911

Function

The function is defined for 1 \le x \le 5 as follows:
f(x) = -2x + 4 + 5 - x + 9 - 2x + 6 - x if x < 2 3 4 5
Find all real numbers x such that f(x) = x

tomtom Dec 8, 2023

0

68

0

+1911

constants

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

tomtom Dec 8, 2023

0

59

0

+1911

function

The function $f(x)$ is defined by
f(x) = lfloor 4x rfloor + 3 - x + x^2 if x pi 5.2
Find f(f(\sqrt{2})).

tomtom Dec 8, 2023

0

62

0

+1911

floor function

Find the number of positive integers $n$ that satisfy $\lfloor \sqrt{n} \rfloor = 7 + n.$

tomtom Dec 8, 2023

Dec 7, 2023

0

54

0

+1678

polygon

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 hexagon.

wiseowl Dec 7, 2023

0

59

0

+1678

polygons

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

wiseowl Dec 7, 2023

0

64

0

+1678

square

In the diagram, $ABCD$ is a square. Find $PR^2.$

wiseowl Dec 7, 2023

0

61

0

+1678

polygon

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 $IJKLMN$.

wiseowl Dec 7, 2023

0

34

1

+1678

diagonals

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?

wiseowl Dec 7, 2023

0

64

0

+1678

help with 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 $n$-gon, all with the same side length, also completely read more ..

wiseowl Dec 7, 2023

0

68

0

+1678

hexagon

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.

wiseowl Dec 7, 2023

0

60

0

+1678

polygon

In a certain regular polygon, the measure of each interior angle is $2$ times the measure of each exterior angle. Find the number of sides in this regular polygon.

wiseowl Dec 7, 2023

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