All Questions +0 237417 Questions

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $11,$ and the slope of line segment $\overline{OQ}$ is $13.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

Ibrahin097YT 6 hours ago

0

1

0

+56

Geometry

Ibrahin097YT 6 hours ago

0

1

+56

Geometry

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 1, and the line is y = x.

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.

Ibrahin097YT May 13, 2025

0

1

0

+56

Geometry

Ibrahin097YT May 13, 2025

0

1

0

+56

Geometry

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

Ibrahin097YT May 13, 2025

0

1

0

+56

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

Ibrahin097YT May 13, 2025

0

1

2

+456

Counting

How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, and the sum of the digits is 6?

The following cards are split into four piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
The cards are:
Ace of clubs
Ace of diamonds read more ..

Jasmo May 10, 2025

0

1

0

+458

Counting

bIueb3rry May 10, 2025

0

1

0

+458

Counting

A bag contains red and blue tiles. Each tile has a number from the set \{-1, 0, 1\} written on it. I want to arrange 7 of these tiles in a row, so that the numbers on any three consecutive tiles sum to 3. In how many ways can this be done, assuming that read more ..

bIueb3rry May 10, 2025

0

1

0

+56

i need answer now

Find the number of ways of filling in the squares of a 3 \times 3 grid so that:
* Each square contains a 0 or a 1.
* The sum of the numbers in each row and each column is at most 1.
An example is shown below.

Ibrahin097YT May 10, 2025

0

1

0

+56

plz help now

Find the number of paths from A to B in the grid below, so that
* Each step is down or to the right.
* The path cannot pass through any point more than once.

An example path is shown.
The grid is 3 by 3, with read more ..

Ibrahin097YT May 10, 2025

0

1

+56

help me help help

If an ant crawls from one corner to the other corner of a 3 \times 5 rectangle, then it will cross through seven squares.
If the ant crawls from one corner to the other corner of a 15 \times 16 rectangle, then how many squares will read more ..

A survey conducted among 150 high school students revealed that

* 68 students like Math
* 85 students like English
* 55 students like History
* 20 students like both Math and English
* 15 students like both Math and read more ..

Ibrahin097YT May 10, 2025

0

1

2

+56

help really need help

What is the value of the expression. Express your asnwer as a common fraction.

Ibrahin097YT May 10, 2025

0

1

+9

HELP PLEASE ASAP!!!!

Let ABC be a triangle with side lengths AB = 5, BC = 6, and AC = 9. What is the area of the triangle with side lengths \tan A, \tan B, and \tan C?

Ibrahim097YT May 10, 2025

-1

1

2

+1800

Geometry

Acute triangle ABC has \sin A = \dfrac{2}{5} and \sin B = \dfrac{2}{\sqrt{7}}. What is \sin C?

blackpanther May 9, 2025

-1

1

+1800

Geometry

Find the area of the triangle with side lengths 4, 5, and 8.

blackpanther May 9, 2025

0

1

+1800

Geometry

Triangle ABC has side lengths AB = 8, BC = 10, and AC = 12. Find \dfrac{\cos A}{\cos B}.

blackpanther May 9, 2025

0

1

0

+1800

Geometry

blackpanther May 9, 2025

0

1

0

+608

Counting

A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit.
You are dealt a hand of read more ..

onyuIee May 9, 2025

0

1

0

+608

Counting

Find the number of sequences (a_1, a_2, a_3, \dots, a_8) such that:
* a_i \in \{1, 2, 3, 4, 5, 6, 7, 8\} for all 1 \le i \le 8.
* Every number1, 2, 3, 4, 5, 6, 7, 8 appears at least once in the sequence.

onyuIee May 9, 2025

0

1

0

+608

Counting

A permutation of the numbers (1,2,3,\dots,n) is a rearrangement of the numbers in which each number appears exactly once. For example, (2,5,1,4,3) is a permutation of (1,2,3,4,5).
Find the number of permutations (x_1, x_2, \dots, x_8) read more ..

onyuIee May 9, 2025

0

1

0

+56

How many subsets of \{0, 1, \dots, 9\} have the property

How many subsets of \{0, 1, \dots, 9\} have the property that there are at least two elements and the sum of the two largest elements is 4?

Ibrahin097YT May 9, 2025

0

1

0

+56

We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen).

We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of 5?

Ibrahin097YT May 9, 2025

0

1

0

+56

Find the number of ways of arranging one A, two Bs, three Cs, and four Ds

Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other, no two Cs are next to each other, and no two Ds are next to each other.

Ibrahin097YT May 9, 2025

0

1

0

+4

Trigonometric Laws and Identities

Two students are calculating the exact value of tan(7pi/12)? Choose one of the following to methods to solve.
-Student A says 7pi/12 is half of 7pi/6, and they will use the half-angle identity and the unit of circle to solve.
-Student B says read more ..

blueberiii May 9, 2025

0

1

0

+56

In the diagram below, \overline{AD} and \overline{BE} are angle bisectors

In the diagram below, \overline{AD} and \overline{BE} are angle bisectors of \angle BAC and \angle ABC, respectively, and they intersect at T. We know that BC = 12, AC = 18 and BF = 3 \cdot AF. Find AB.

Ibrahin097YT May 9, 2025

+1

1

+9

What is the value of the expression shown? Express your answer as a common fraction.

How many 7-digit sequences have a digit that appears at least 6 times?
(For example, 3339333 and 0200000 are two such sequences. A sequence is allowed to begin with 0.)

Ibrahim097YT May 9, 2025

+1

1

0

+1271

Counting

Akhain1 May 1, 2025

0

1

+829

Counting

How many positive integers are there whose digits strictly decrease from left to right, and the sum of the digits is 6?

How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, and the sum of the digits is 6?

cooIcooIcooI17 May 1, 2025

0

1

0

+829

Counting

cooIcooIcooI17 May 1, 2025

0

1

0

+56

Geometry

In the diagram, \overline{AD} is an altitude, \overline{BE} is a median, and \overline{AD}, \overline{BE}, and \overline{CF} are concurrent. If AE = 11, BE = 9, and AD = 6\sqrt{2}, what is AF?

PikaPika989 Apr 26, 2025

0

1

0

+56

Geometry

In the diagram below, \overline{AD} and \overline{BE} are angle bisectors of \angle BAC and \angle ABC, respectively, and they intersect at T. We know that BD=12, AE=8, and BF=3+AE. Find AB.

PikaPika989 Apr 26, 2025

0

1

+4

Calculate the best ISO for drone night scenes

If a drone has Max ISO 44000, 12-Bit DNG, how will its night 6K photos be?

How many squares in the plane have at least two points in the lattice below as vertices?

rainyxyb Apr 24, 2025

0

1

+1216

Counting

At a meeting, two scientists, two mathematicians, two historians, and two artists are to be seated around a circular table. In how many ways can they be seated so that all four pairs of people from the same discipline are seated together?

AnswerscorrectIy Apr 23, 2025

0

1

2

+1216

Counting

What is the equation of the reflection of the line y = 2x + 1 across the line y = 5x - 3? Give your answer in slope-intercept form.

AnswerscorrectIy Apr 23, 2025

0

1

+56

Help me plz

In \triangle ABC, we have AB = AC = 4 and \angle BAC = 45^\circ. If M is the midpoint of BC, then find AM^2.

PikaPika989 Apr 23, 2025

0

1

0

+56

Help need help

PikaPika989 Apr 23, 2025

0

2

1

+56

Help geometry

Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of triangle ABC?
A is at (0,0), B is at (1,0), and C is at (1,1).

In the complex plane, z, z2 , z3 form, in some order, three of the vertices of a non-degenerate square. Enter all possible areas of the square, separated by commas.

PikaPika989 Apr 23, 2025

+1

1

+16

Super Hard Algebra 2/Precalculus Question Help Please

Without knowing the relationship between h and x, how is this possible?

PikaPika999 Apr 23, 2025

0

1

+4

Any help appreciated - preferably in simple language for a non mathematician

Let S be a set of distinct integers. What is the smallest number of elements that S must contain, to ensure that S has a nonempty subset, where the sum of the elements in the subset is divisible by 2?

dadtryingtoHelp Apr 22, 2025

0

1

+56

Counting

Vera has 20 white socks, 21 black socks, 22 brown socks, 23 blue socks, 24 red socks, and 25 green socks. How many socks (at a minimum) must she pull out of her sock drawer to ensure at least six matching pairs of different colors?

PikaPika989 Apr 22, 2025

0

1

+56

Counting

Recall that a partition of a positive integer n means a way of writing n as the sum of some positive integers, where the order of the parts does not matter. For example, there are five partitions of 4:
4
3 + 1
2 + 2 read more ..

PikaPika989 Apr 21, 2025

0

1

0

+977

Counting

magenta Apr 20, 2025

0

1

0

+977

Counting

Find the number of ways filling in a 4 \times 4 grid, such that
* Each cell contains a 0 or a 1.
* The sum of the numbers in each row and each column is at least 2.

An example is shown below.
0110 read more ..

magenta Apr 20, 2025

0

1

0

+977

Counting

Consider the set
S = {1, 2, 3, 4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 17, 18, 23, 24, ..., 12345678},
which consists of all positive integers whose digits strictly increase from left to right, and the digits are from 1 to 8. This set is read more ..

magenta Apr 20, 2025

0

1

0

+458

Counting

Find the number of subsets of
S = \{1, 3, 8, 17, 30, 36, 47, 58\},
so that the sum of the elements in the subset is less than 20. (Note that for the empty subset, we take the sum of the elements as 0.)

bIueb3rry Apr 19, 2025

0

3

0

+458

Counting

Find the number of subsets of
S = \{1, 3, 8, 17, 30, 36, 47, 58\},
so that the sum of the elements in the subset is a multiple of 5. (Note that for the empty subset, we take the sum of the elements as 0.)

bIueb3rry Apr 19, 2025

0

3

0

+608

Counting

Adam the ant starts at (0,0). Each minute, he flips a fair coin. If he flips heads, he moves 1 unit up; if he flips tails, he moves 1 unit right.
Betty the beetle starts at (1,1). Each minute, she flips a fair coin. If she flips heads, read more ..

onyuIee Apr 19, 2025

0

2

0

+608

Counting

Consider the sequence
1, 5, 6, 25, 26, 30, 31, ...
which consists of every positive integer that can be expressed as a sum of distinct powers of 5.
What is the first term that is greater than 50?

onyuIee Apr 19, 2025

0

3

0

+608

Counting

Consider the sequence
1, 3, 4, 9, 10, 12, 13, ...
which consists of every positive integer that can be expressed as a sum of distinct powers of 3.
What is the first term that is greater than 20?

onyuIee Apr 19, 2025

0

2

0

+1800

Counting

Find the number of sequences containing three terms, such that
* The second term is equal to the sum of the first term plus one.
* The third term is equal to twice the second term.
* Each term is an integer in \{0, 1, 2, \dots, 100\} read more ..

blackpanther Apr 19, 2025

0

1

+56

Counting

Find the number of arithmetic sequences such that:
* The arithmetic sequence contains three terms
* All the terms are integers in \{0, 1, 2, \dots, 10\}
* The sum of the terms is 9.

Find the number of paths from A to B in the grid below, where each step is down or to the right.
The grid is 3 by 3, with A in the upper-left and B in the lower-right.

PikaPika989 Apr 18, 2025

0

2

0

+56

Counting

PikaPika989 Apr 18, 2025

0

1

+56

Counting

A basket contains 7 green marbles and 6 red marbles. Two marbles are taken from the basket at random without replacement (i.e., the first marble is not put back before the second marble is drawn). What is the probability that the first marble is green, read more ..

In the United States, there are 50 states. Each state is represented by 2 senators. In how many ways can we form a committee with 5 senators, in which no two of the senators are from the same state?

PikaPika989 Apr 18, 2025

0

2

0

+357

Counting

cwimie Apr 17, 2025

0

2

0

+357

Counting

Suppose for this problem (though it may not be accurate in real life) that the Senate has 48 Republicans and 52 Democrats. In how many ways can we form a committee with 5 senators, in which neither party holds all 5 seats?

cwimie Apr 17, 2025

0

2

1

+56

help with counting

Now suppose that not only must Sir Lancelot and Sir Gawain be next to each other, but Sir Galahad and Sir Percival also demand to be next to each other. How many seatings of the 8 knights are possible?

King Arthur's round table has 8 evenly spaced chairs. In how many ways can 8 knights be seated in the chairs, if Sir Lancelot and Sir Gawain insist on being seated next to each other?

PikaPika989 Apr 17, 2025

0

2

0

+56

Counting

PikaPika989 Apr 17, 2025

0

1

0

+56

Counting

In how many ways can 5 balls be placed in 4 boxes, if 2 balls are white and 3 balls are black? (Balls of the same color are indistinguishable. The boxes are indistinguishable.)

PikaPika989 Apr 17, 2025

0

2

1

+56

help with counting

How many zeroes do we write when we write all the integers from 1 to 625 in base 4?

The range of the function is . Let . Find the range of the function .
Thanks!

PikaPika989 Apr 17, 2025

+1

2

3

+16

Help Please Intermediate Algebra

Given a regular octagon, in how many ways can we color one diagonal red and another diagonal blue so that the two colored diagonals intersect at an endpoint? Consider rotations and reflections distinct.

PikaPika999 Apr 17, 2025

0

2

1

+806

Counting

A survey conducted among 150 high school students revealed that

* 68 students like Math
* 85 students like English
* 55 students like History
* 20 students like both Math and English
* 15 students like both Math and read more ..

crimefightingvigiI Apr 17, 2025

0

1

0

+958

Counting

gnistory Apr 17, 2025

0

2

0

+958

Counting

If an ant crawls from one corner to the other corner of a 3 \times 5 rectangle, then it will cross through seven squares.
If the ant crawls from one corner to the other corner of a 15 \times 16 rectangle, then how many squares will read more ..

gnistory Apr 17, 2025

0

3

1

+22

Using Geo/Trig on an Algebra Problem

What is $xy+yz+xz$ if $x^2+xy+y^2=1$, $y^2+yz+z^2=2$, and $x^2+xz+z^2=3$?

Find the number of paths from A to B in the grid below, so that
* Each step is down or to the right.
* The path cannot pass through any point more than once.

An example path is shown.
The grid is 3 by 3, with read more ..

Xenosmilus Apr 17, 2025

0

2

0

+458

Counting

bIueb3rry Apr 17, 2025

0

2

0

+458

Counting

Find the number of ways of filling in the squares of a 3 \times 3 grid so that:
* Each square contains a 0 or a 1.
* The sum of the numbers in each row and each column is at most 1.
An example is shown below.

bIueb3rry Apr 17, 2025

0

2

0

+458

Counting

How many ordered pairs of positive integers (m,n) satisfy \text{lcm}[m,n] = 360 and \gcd(m,n) = 360?

bIueb3rry Apr 17, 2025

0

2

0

+458

Counting

A bag contains red and blue tiles. Each tile has a number from the set \{-1, 0, 1\} written on it. I want to arrange 7 of these tiles in a row, so that the numbers on any three consecutive tiles sum to 3. In how many ways can this be done, assuming that read more ..

bIueb3rry Apr 17, 2025

0

2

0

+400

Counting

The following cards are split into four piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
The cards are:
Ace of clubs
Ace of diamonds read more ..

Stanry Apr 17, 2025

0

1

0

+400

Counting

How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, and the sum of the digits is 6?

Stanry Apr 16, 2025

0

1

+400

Counting

How many positive integers are there whose digits strictly decrease from left to right, and the sum of the digits is 6?

How many 7-digit sequences have a digit that appears at least 6 times?
(For example, 3339333 and 0200000 are two such sequences. A sequence is allowed to begin with 0.)

Stanry Apr 16, 2025

0

1

+400

Counting

Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other, no two Cs are next to each other, and no two Ds are next to each other.

Stanry Apr 15, 2025

0

1

0

+400

Counting

Stanry Apr 15, 2025

0

4

0

+400

Counting

We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of 5?

Stanry Apr 14, 2025

0

2

0

+400

Counting

How many subsets of \{0, 1, \dots, 9\} have the property that there are at least two elements and the sum of the two largest elements is 4?

Stanry Apr 14, 2025

0

1

0

+400

Counting

A permutation of the numbers (1,2,3,\dots,n) is a rearrangement of the numbers in which each number appears exactly once. For example, (2,5,1,4,3) is a permutation of (1,2,3,4,5).
Find the number of permutations (x_1, x_2, \dots, x_8) read more ..

Stanry Apr 13, 2025

0

1

0

+400

Counting

Find the number of sequences (a_1, a_2, a_3, \dots, a_8) such that:
* a_i \in \{1, 2, 3, 4, 5, 6, 7, 8\} for all 1 \le i \le 8.
* Every number1, 2, 3, 4, 5, 6, 7, 8 appears at least once in the sequence.

Stanry Apr 13, 2025

0

2

0

+400

Counting

A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit.
You are dealt a hand of read more ..

Stanry Apr 13, 2025

0

3

1

+400

Counting

In the array below, in how many different ways can we start with the letter and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCS"?
A read more ..

How many squares in the plane have at least two points in the lattice below as vertices?

Stanry Apr 13, 2025

0

3

0

+400

Counting

Stanry Apr 13, 2025

0

1

2

+400

Counting

At a meeting, two scientists, two mathematicians, two historians, and two artists are to be seated around a circular table. In how many ways can they be seated so that all four pairs of people from the same discipline are seated together?

Triangle ABC has AB = 6. Let D lie on BC such that \overline{AD} bisects \angle BAC. If BD = 3 and CD = 5, what is AC?

Stanry Apr 12, 2025

+1

1

3

+1518

Geometry

CPhill ●●●

learnmgcat Apr 12, 2025

0

1

0

+1518

Geometry

Find an acute angle A such that \sin 4A = \sin A + \sin 2A. Express your answer in degrees.

learnmgcat Apr 12, 2025

0

1

0

+1518

Geometry

What is the distance between the points (\cos 37^{\circ}, \sin 37^{\circ}) and (\cos 127^{\circ}, \sin 127^{\circ})?

learnmgcat Apr 12, 2025

0

1

0

+1518

Geometry

Chris places an orange cone at his current location. Then, he faces west, walks 40 meters, turns 30^{\circ} to his right, and walks 20 meters. How far is Chris from the cone, in meters? Round your answer to the nearest whole number.
(You will need read more ..

learnmgcat Apr 12, 2025

0

1

0

+806

Counting

In a basketball tournament, there are four teams, and each team plays against every other team exactly twice. (So each team plays six games. Also, each team is equally likely to win a game, and there are no ties.) Find the probability read more ..

crimefightingvigiI Apr 12, 2025

0

1

0

+806

Counting

Five standard 6-sided dice are rolled, and the resulting numbers are multiplied together. What is the probability that the product is divisible by 12?

crimefightingvigiI Apr 12, 2025

0

2

0

+806

Counting

Five people check identical suitcases before boarding an airplane. At the baggage claim, each person takes one of the five suitcases at random. What is the probability that exactly one person ends up with the wrong suitcase?

crimefightingvigiI Apr 12, 2025

0

3

0

+806

Counting

Find the number of positive integers that are divisors of at least one of 6^{6}, 10^{10}, 15^{15}, and 30^{30}.

crimefightingvigiI Apr 12, 2025

0

2

0

+806

Counting

I can only remember a seven-digit telephone number if the first three digits (the "prefix") are equal to the next three digits or the last three digits. For example, I can remember 389-3892 and 274-9274.
How many seven-digit telephone numbers can read more ..

crimefightingvigiI Apr 12, 2025

0

2

0

+1800

Counting

In how many ways can we seat 3 pairs of siblings in a row of 10 chairs, so that nobody sits next to their sibling? (Two chairs will be left empty, of course.)

blackpanther Apr 12, 2025

0

1

0

+1800

Counting

A permutation of the numbers (1,2,3,\dots,n) is a rearrangement of the numbers in which each number appears exactly once. For example, (2,5,1,4,3)$ is a permutation of (1,2,3,4,5).
Let \pi = (x_1,x_2,x_3,\dots,x_n) be a permutation read more ..

blackpanther Apr 12, 2025

0

3

0

+1800

Counting

If an ant crawls from one corner to the other corner of a 3 \times 5 rectangle, then it will cross through seven squares.
If the ant crawls from one corner to the other corner of a 15 \times 16 rectangle, then how many squares will read more ..

blackpanther Apr 12, 2025

0

1

0

+1800

Counting

A survey conducted among 150 high school students revealed that

* 68 students like Math
* 85 students like English
* 55 students like History
* 20 students like both Math and English
* 15 students like both Math and read more ..

blackpanther Apr 11, 2025

+1

3

1

+608

Counting

Let P be a point chosen uniformly at random inside ABC. Extend ray BP to hit side AC at D. What is the probability that BD < 4?
The sides of triangle ABC are 3, 5, and 7.

Given a regular octagon, in how many ways can we color one diagonal red and another diagonal blue so that the two colored diagonals intersect at an endpoint? Consider rotations and reflections distinct.

onyuIee Apr 10, 2025

0

2

0

+608

Counting

onyuIee Apr 10, 2025

0

4

0

+608

Counting

Find the number of ways of placing three As, three Bs, and three Cs in a 3 \times 3 grid, so that every square contains one letter, and each diagonals contains one A, one B, and one C.

onyuIee Apr 10, 2025

0

2

1

+164

Counting

How many zeroes do we write when we write all the integers from 1 to 625 in base 4?

In how many ways can 5 balls be placed in 4 boxes, if 2$balls are white and 3 balls are black? (Balls of the same color are indistinguishable. The boxes are indistinguishable.)

HumanBemg Apr 9, 2025

0

2

1

+164

Counting

Now suppose that not only must Sir Lancelot and Sir Gawain be next to each other, but Sir Galahad and Sir Percival also demand to be next to each other. How many seatings of the 8 knights are possible?

HumanBemg Apr 9, 2025

0

1

0

+164

Counting

HumanBemg Apr 8, 2025

0

1

0

+164

Counting

King Arthur's round table has 8 evenly spaced chairs. In how many ways can 8 knights be seated in the chairs, if Sir Lancelot and Sir Gawain insist on being seated next to each other?

HumanBemg Apr 8, 2025

0

1

0

+921

Counting

Suppose for this problem (though it may not be accurate in real life) that the Senate has 48 Republicans and 52 Democrats. In how many ways can we form a committee with 5 senators, in which neither party holds all 5 seats?

booboo44 Apr 8, 2025

0

1

0

+921

Counting

In the United States, there are 50 states. Each state is represented by 2 senators. In how many ways can we form a committee with 5 senators, in which no two of the senators are from the same state?

booboo44 Apr 8, 2025

0

2

1

+921

Counting

A basket contains 7 green marbles and 6 red marbles. Two marbles are taken from the basket at random without replacement (i.e., the first marble is not put back before the second marble is drawn). What is the probability that the first marble is green, read more ..

A basket contains 7 green marbles and 6 red marbles. A marble is taken from the basket at random; its color is recorded, then the marble is returned to the basket. A second marble is then taken from the basket at random, and its color is recorded. read more ..

booboo44 Apr 8, 2025

0

2

1

+921

Counting

Let a_1, a_2, a_3, \dots be an infinite geometric series with positive terms. If a_2 = 10, then find the smallest possible value of
a_1 + a_2 + a_3.

booboo44 Apr 8, 2025

0

2

1

+958

Algebra

Compute
1.11111 + 0.11111 + 0.01111 + 0.00111 + 0.00011 + 0.00001

gnistory Apr 7, 2025

+1

1

2

+958

Algebra

Tackling Friction in Free body diagrams, would appreciate your generous help.
Problem: A block with a mass of 10 kg is placed on a rough inclined plane that makes a 30° angle with the horizontal. The coefficient of static read more ..

gnistory Apr 7, 2025

0

2

1

+448

Free Body Diagram

A and B are two points on a sphere of radius 2. We know the space distance between A and B is 2, What is distance from A to B along the (minor) arc of a great circle?

HiylinLink Apr 7, 2025

+1

1

2

+400

Geometry

Bosco ●●

Stanry Apr 7, 2025

-1

2

+164

Geometry

Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of triangle ABC?
A is at (0,0), B is at (1,0), and C is at (1,1).

In \triangle ABC, we have AB = AC = 4 and \angle BAC = 45^\circ. If M is the midpoint of BC, then find AM^2.

HumanBemg Apr 5, 2025

+1

2

1

+164

Geometry

What is the equation of the reflection of the line y = 2x + 1 across the line y = 5x - 3? Give your answer in slope-intercept form.

HumanBemg Apr 5, 2025

+1

2

1

+164

Geometry

In the diagram below, ABCD is a rectangle with AD=6 and B=10. Point M is the intersection of its diagonals and point E lies on \overline{AD} such that BE=2. Find CE^2. (Diagram not to scale)

HumanBemg Apr 5, 2025

-1

4

1

+958

Geometry

Let R=(a,b) be the image of rotating point P=(7,2) clockwise by 150^\circ degrees around Q=(12,-5). What is b?

gnistory Apr 5, 2025

+1

2

1

+958

Geometry

Let R be the image of rotating point P=(4,0) counterclockwise by 60^\circ$ degrees around Q=(12,-7). What is PR?

gnistory Apr 5, 2025

0

5

0

+958

Geometry

gnistory Apr 5, 2025

0

3

0

+958

Geometry

Point B is the reflection of point A=(2,-1) over the line y=1. Point C is the reflection of point B over the line x + 2y = a. If C=(-5,8), what is a?

gnistory Apr 4, 2025

0

1

+958

Geometry

The area of a cross section of a sphere is 64\% of the largest possible cross sectional area of the sphere. If the sphere has radius 1/2, what is the area of the cross section?

The base of right pyramid ABCDE is a rhombus with side 5. We also know that \triangle ABD \cong \triangle CBD and EA=BA=2. Find the volume of the pyramid.

gnistory Apr 4, 2025

0

2

1

+921

Geometry

In the diagram, \overline{AD} is an altitude, \overline{BE} is a median, and \overline{AD}, \overline{BE}, and \overline{CF} are concurrent. If AB = 11, AC = 12, and AD = 6, what is AF?

booboo44 Apr 4, 2025

0

2

1

+290

Geometry

In the diagram below, \overline{AD} and \overline{BE} are angle bisectors of \angle BAC and \angle ABC, respectively, and they intersect at T. We know that BC = 12, AC = 18 and BF = 3 \cdot AF. Find AB.

AUnVerifedTaxPayer Apr 4, 2025

0

2

1

+400

i need help

The left column contains pairs of triangles with different side-length and angle-measure congruences marked. Match each diagram in the left column with a congruence/similarity criterion in the right column that justifies why the two triangles are congruent/similar. read more ..

Stanry Apr 4, 2025

0

1

+400

help me plz

The left column contains pairs of triangles with different side-length and angle-measure congruences marked. Match each diagram in the left column with a congruence/similarity criterion in the right column that justifies why the two triangles are read more ..

Stanry Apr 4, 2025

0

1

2

+400

need help

A stick is broken at two points, chosen at random. If the length of the stick is 6 units, then what is the probability that all three resulting pieces are shorter than 5 units?
What I've tried so far:
I've treated the stick as read more ..

Stanry Apr 4, 2025

0

2

+71

Counting and Probability, Melody or CPhill help ;-;

In the diagram below, we know \tan \theta = \frac{3}{4}. Find the area of the triangle.
The triangle is right, and the hypotenuse is 80.

Starry Apr 4, 2025

0

3

0

+1518

Geometry

learnmgcat Apr 4, 2025

0

2

1

+1518

Geometry

Find the value of \sin 40^\circ \cdot \cos 50^\circ \cdot \cos 40^\circ \cdot \sin 50^\circ.

Find sin B.
BD = 15, CD = 10, AC = 6

learnmgcat Apr 4, 2025

0

2

0

+458

Geometry

bIueb3rry Apr 4, 2025

0

2

0

+458

Geometry

Find AC in the diagram to the nearest integer.
(You will need to use a calculator. Make sure to use "Degree" instead of "Radian" as the angle unit when computing trigonometric functions.)
AB = 31, angle A = 90 degrees, read more ..

bIueb3rry Apr 4, 2025

0

1

+458

Geometry

In \triangle PQR, we have \angle P = 90^\circ, PQ=3, and QR = 5. Find \tan R.

For a positive integer n, let f(n) denote the integer that is closest to \sqrt[4]{n}. Find the integer m so that
\sum_{n = 1}^m f(n) = 100.

bIueb3rry Apr 4, 2025

0

4

0

+806

Algebra

crimefightingvigiI Apr 3, 2025

0

2

0

+806

Algebra

For how many integer values of a does the equation
x^2 + ax + 12a = 5x + 8
have integer solutions for x?

crimefightingvigiI Apr 2, 2025

0

1

0

+1729

Algebra

Let a and b be positive real numbers. Let
m = \min \left\{ a, \frac{1}{b}, b^2 + \frac{1}{a + 1} \right\}.
Find the largest possible value of m.

parmen Apr 1, 2025

0

3

0

+164

Algebra

The function f : \mathbb{R} \rightarrow \mathbb{R} satisfies
xf(x) + f(1 - x)/x = x^3 + 3x^2 + 14x - 13
for all real x. Find f(x).

HumanBemg Apr 1, 2025

+2

3

1

+6

Hello, guys and gals.

안녕하세요, 여러분. 저는 여러분이 파이에 대해 배우도록 이 글을 찾아오겠습니다. 파이는 정당한 스러울 수 있는 동그라미입니다. 그럼요. 이 문자 그대로 무한한 숫자의 여행을 시작하면 됩니다. 그리고, 위의 경고를 꼭 읽어주세요. 피자는 날씨가 좋으니까요.
1. PI란 무엇인가?
파이는 원의 직경과 원둘레이의 경우입니다. 흥미로운 점은 우주만큼 크든 원자핵만큼 작든 모든 원에 대해 동일하다는 것입니다.
원의 read more ..

Find all complex solutions to the equation z^3 = 8i - (15 + 2i)z^2 + (7 - 4i)z.

xhxmsja Mar 31, 2025

0

5

1

+44

Algebra

Find all complex numbers z such that |z - 1| = |z + 3| + |z - 2i|.

XenosmiIus Mar 30, 2025

0

2

0

+44

Algebra

XenosmiIus Mar 30, 2025

0

1

+44

Algebra

For parts (a) through (d), let f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.
What is the vertex of the parabola y = f(x)?

What is the equation of the line of symmetry of the parabola $y = f(x)$.
f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.

XenosmiIus Mar 30, 2025

0

1

2

+44

Algebra

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

XenosmiIus Mar 30, 2025

-1

2

3

+478

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

MeIdHunter Mar 30, 2025

-1

1

+478

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

MeIdHunter Mar 30, 2025

0

1

+478

Geometry

Find the area of triangle ABC
[asy]
unitsize (2 cm);
pair A, B, C, D, E, F, H;
A = (0,2);
B = (-1,0);<#> C = (1,0);<#> D = (0,0);<#> E = (B + reflect(A,C)*(B))/2;<#> F = (C + reflect(A,B)*(C))/2;<#> read more ..

MeIdHunter Mar 30, 2025

0

2

1

+4

help please

Let x_1, x_2, \dots, x_{100} be real numbers. If
x_1 + 2x_2 + \dots + 100x_{100} = 1,
then find the minimum value of x_1/1 + x_2/2 + \dots + x_{100}/100.

whatthedonut Mar 30, 2025

0

2

0

+44

Algebra

XenosmiIus Mar 30, 2025

0

2

0

+44

Algebra

Let x, y, and z be real numbers. If x^2 + y^2 + z^2 = 1, then find the maximum value of
3x + 4y + 5z + x^3 + \frac{4x^2 y}{z} + \frac{z^5}{xy^2}

XenosmiIus Mar 30, 2025

0

3

0

+44

Algebra

Let x_1, x_2, \dots, x_n be real numbers. If
x_1^2 + 2x_2^2 + \dots + nx_n^2 = 1,
then find the maximum value of (x_1 + x_2/2 + \dots + x_n/n)^2, in terms of n.

XenosmiIus Mar 30, 2025

0

6

0

+44

Help algebra help

Let x_1, x_2, \dots, x_n be real numbers. If
x_1 + 2x_2 + \dots + nx_n = 1,
then find the minimum value of x_1^2/1 + x_2^2/2 + \dots + x_n^2/n, in terms of n.

XenosmiIus Mar 30, 2025

0

2

0

+44

Help me algebra

Let a, b, and c be positive real numbers. Find the minimum value of
(a + 1)^2 + \left( \frac{b}{a} + a + 1 \right)^2 + \left( \frac{c}{b} + abc \right)^2 + \left( \frac{4}{c} + \frac{c}{a} \right)^2.

XenosmiIus Mar 30, 2025

0

4

0

+44

Algebra question

Let x and y be positive real numbers. If
\frac{x^2}{9} + \frac{y^2}{25} = 1,
then find the maximum value of \frac{x^2}{3} \cdot \frac{y^2}{5}.

XenosmiIus Mar 30, 2025

0

3

0

+44

Help with Algebra

Let a, b, and c be positive real numbers. If \frac{a}{2} + b + 3c = 12, then find the maximum value of
\min \left\{ \frac{ab}{2}, ac, 12bc \right\}.

XenosmiIus Mar 30, 2025

+1

4

3

+22

Interesting Range Question; Can use polynomial long division to solve

Find the range of the function

Enter your answer in interval notation.

Find all x such that
(2x)^{\log_{10} 2} = (9x)*{\log_{10} 9} + (5x)^{\log_{10} 9} + \log_x 243

Xenosmilus Mar 29, 2025

0

3

0

+164

Algebra

HumanBemg Mar 29, 2025

0

3

0

+164

Algebra

Let r_1, r_2, r_3, r_4, and r_5 be the complex roots of x^5 - 4x^2 + 7x - 1 = 0. Compute
(r_1^2 + r_1^6 + 2)(r_2^2 + r_2^6 + 2)(r_3^2 + r_3^6 + 2)(r_4^2 + r_4^6 + 2)(r_5^2 + r_5^6 + 2)

HumanBemg Mar 29, 2025

0

2

0

+1800

Algebra

Suppose that f(x) and g(x) are functions which satisfy
f(g(x)) = x^2 \quad \text{and} \quad g(f(x)) = x^4
for all x \ge 1. If g(16) = 1, then compute \log_2 g(2).

blackpanther Mar 27, 2025

0

4

0

+164

Algebra

Suppose f(x) is a rational function such that
3 f \left( \frac{1}{x} \right) - \frac{f(x)}{x} = x
for all $x \neq 0$. Find f(-2).

HumanBemg Mar 27, 2025

0

7

0

+164

Algebra

Let F(x) be the real-valued function defined for all real x except for x = 1 and x = 2 and satisfying the functional equation
F(x) + F \left( \frac{2x - 3}{x - 1} \right) + F \left( \frac{1}{x} \right) = x.
Find the function F(x) satisfying read more ..

HumanBemg Mar 27, 2025

0

4

0

+164

Algebra

The function f(n) is defined for all integers n, such that
f(x) + f(y) = f(x + y) - 4xy - 1 + f(x^2) + f(y^2)
for all integers x and y, and f(1) = 1. Find f(n).

HumanBemg Mar 27, 2025

0

4

0

+164

Algebra

The function f(n) takes the integers to the real numbers such that
f(m + n) + f(m - n) = 2f(m) + 2f(n) + mn
for all integers m and n, and f(1) = 2. Find f(n).

HumanBemg Mar 27, 2025

0

3

1

+1800

Algebra

The function f : \mathbb{R} \rightarrow \mathbb{R} satisfies
f(x) f(y) - f(xy) = -2x - 6y + 10
for all x, y \in \mathbb{R}. Find f(x).

Let f be a function defined on the positive integers, such that
f(xy) = f(x) + f(y)
for all positive integers x and y. Given that f(5) = 6, f(65) = 7, f(86) = 9, f(93) = 10, find (120).

blackpanther Mar 26, 2025

0

4

2

+1800

Algebra

The function f has the following properties:
* f(a,b) is defined for all positive integers a and b
* f(a,1) = a
* f(a,b) = 1 if b > a
* f(a + 1,b) = b[f(a,b) - f(a,b - 1)] read more ..

blackpanther Mar 26, 2025

0

3

1

+1800

Algebra

Fill in the blanks, to make a true equation:
(8x^3 + 24x^2 + 15x + 1)/((x^2 - 1)(x^2 + 3x)) = ___/(x - 1) + ___/(x + 3) + ___/x + ___/(x + 1)

blackpanther Mar 25, 2025

0

2

0

+1800

Algebra

blackpanther Mar 25, 2025

0

1

0

+1800

Algebra

Find the all real numbers that are not in the domain of f(g(x)), where
f(x) = \frac{3x^2 - 10x - 25}{x + 1} and g(x) = \frac{14x - 6}{3x^2 + 5x + 15}

blackpanther Mar 25, 2025

0

2

0

+1800

Algebra

Give a polynomial g(x) so that f(x) + g(x) has a horizontal asymptote of y = 0 as x approaches positive infinity, where
f(x) = \frac{2x^4 - 3x^3 - 8x^2 + 4x - 4}{x^2 + x}.

blackpanther Mar 25, 2025

0

1

0

+1800

Algebra

Fill in the blanks, to make a true equation:
\frac{2x^4 - 3x^3 - x^2 + 4x - 4}{x^2 + x} = ___x^2 + ___x + ___ + ___/x + ___/(x + 1).

blackpanther Mar 25, 2025

0

4

0

+164

Algebra

Find the largest value of x where the plots of
f(x) = - \frac{2x + 5}{x + 3} and g(x) = \frac{12}{x - 1}
intersect.

HumanBemg Mar 25, 2025

0

2

0

+164

Algebra

Fill in the blanks with constants, to make a true equation:
\frac{x^2 - 6x - 3}{x^3 - 4x} = ___/x + ___/(x - 2) + ___/(x + 2)

HumanBemg Mar 25, 2025

0

7

0

+164

Algebra

Let (x,y,z) be the real solution to the system of equations
x + y = \sqrt{4z + 3}
y + z = \sqrt{4x - 1}
z + x = \sqrt{4y + 5}
Find x + y + z.

HumanBemg Mar 25, 2025

0

7

0

+164

Algebra

Find all x such that
sqrt{3x^2 + 2x + 1} + sqrt{3x^2 + 2x - 3} = 20.

HumanBemg Mar 25, 2025

0

6

1

+8

For part b, we solve the answer as 11. The answer given by the book is 44. May i know why is it 44?

Eddie has some white, blue and yellow marbles. He has 4/5 as many white marbles as blue marbles and 120% as many blue marbles as yellow marbles.
(a) Find the ratio of the number of white marbles to the number of blue marbles to the number read more ..

Simplify \frac{6 \sqrt{2]}{\sqrt{2} - \sqrt{3} - \sqrt{5}}

sPpBCdIT Mar 25, 2025

0

6

0

+339

Algebra

jaekg Mar 24, 2025

0

3

1

+339

Algebra

Fill in the blanks.
If f(x) is an even function and g(x) is an even function and h(x) is an even function, then f(x) + g(x) + h(x) is an ___ function.
If f(x) is an odd function and g(x) is an odd function and h(x) read more ..

Find the value of x that maximizes
f(x) = \log (-20x + 16 \sqrt{x} - x).

jaekg Mar 24, 2025

0

3

1

+339

Algebra

If 2^{16^x} = 128*4^x, then find 2^x.

jaekg Mar 24, 2025

0

3

0

+339

Algebra

jaekg Mar 24, 2025

0

3

2

+194

someone helpp

Find an expression for the number of nonnegative integer triples (x, y, z) which are solutions of the equation x + y + z = n, where n is a positive integer.
I believe it has something to do with the hockey stick identity, but read more ..

The function f has the following properties:
* f(x) is defined for x > 0
* f(x) > 0 for all x > 0
* f(x - y) = \sqrt{f(xy) + 4x + 4y + 8} for all x > y > 0

Determine f(1).

HumenBeing Mar 23, 2025

0

5

0

+806

Algebra

crimefightingvigiI Mar 22, 2025

0

3

0

+806

Algebra

Let f be a function such that
f(x) + f(2x + y) + 5xy = f(4x - y) - x^2 + 5xy - 8x + 17y + 1
for all real numbers x and y. Find f(10).

crimefightingvigiI Mar 22, 2025

0

6

0

+164

Algebra

Let f be a function such that
f(xy) + x = xf(y) + f(x) + xy^2
for all real numbers x and y. If f(-1) = 3, then compute f(100).

HumanBemg Mar 21, 2025

0

4

0

+164

Algebra

Let a, b, and c be positive real numbers. If a + b + c = 1, then find the minimum value of
\frac{1}{a} + \frac{1}{b} + \frac{4}{c*a^2} + \frac{16}{b^4*a} + \frac{32}{a*b^3}

HumanBemg Mar 21, 2025

0

5

0

+164

Algebra

Let a, b, and c be positive real numbers. If a + b + c = 1, then find the minimum value of
\frac{1}{a} + \frac{1}{b} + \frac{1}{c*a^2} + \frac{2}{ab^2} + \frac{8}{c^3}.

HumanBemg Mar 21, 2025

+1

5

3

+116

Algebra

The function f satisfies
f(m + n) = f(m) + f(n) - 2f(mn + m + n + 1) + m^2 + n^2
for all nonnegative integers m and n, and f(1) = 0. Compute f(123).

The function f satisfies
f(a + b) = f(a) + f(b) - ab
for all nonnegative integers a and b, and f(1) = 7. Compute f(123).

coIinqiu Mar 20, 2025

0

2

0

+1216

Algebra

AnswerscorrectIy Mar 20, 2025

0

2

0

+1216

Algebra

The real numbers x_1, x_2, x_3, x_4, and x_5 satisfy
x_1 + x_2 + x_3 + x_4 + x_5 = 8,
x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 = 12,
x_1^3 + x_2^3 + x_3^3 + x_4^3 + x_5^3 = 16.
Let m be the smallest possible value of read more ..

AnswerscorrectIy Mar 20, 2025

0

2

0

+1216

Algebra

(a) Let x, y, and z be positive real numbers. Find the largest possible value of
\sqrt{\frac{3x + 5y + 2z}{6x + 5y + 4z}} + \sqrt{\frac{2x + 5y + z}{6x + 5y + 5z}} + \sqrt{\frac{9x + y + 4z}{6x + 5y + 4z}}.
(b) Find read more ..

AnswerscorrectIy Mar 20, 2025

0

2

0

+1216

Algebra

Let x_1, x_2, \dots, x_{100} be real numbers. If
x_1^2 + 2x_2^2 + \dots + 100x_{100}^2 = 1,
then find the maximum value of x_1/1 + x_2/2 + \dots + x_{100}/100.

AnswerscorrectIy Mar 20, 2025

0

3

0

+1216

Algebra

Let x_1, x_2, \dots, x_{100} be real numbers. If
x_1 + 2x_2 + \dots + 100x_{100} = 1,
then find the minimum value of x_1/1 + x_2/2 + \dots + x_{100}/100.

AnswerscorrectIy Mar 20, 2025

0

4

0

+1216

Algebra

Let x, y, and z be real numbers. If x^2 + y^2 + z^2 = 1, then find the maximum value of
3x + 4y + 5z + x^3 + \frac{4x^2 y}{z} + \frac{z^5}{xy^2}

AnswerscorrectIy Mar 19, 2025

0

6

0

+1216

Algebra

Let x_1, x_2, \dots, x_n be real numbers. If
x_1^2 + 2x_2^2 + \dots + nx_n^2 = 1,
then find the maximum value of (x_1 + x_2/2 + \dots + x_n/n)^2, in terms of n.

AnswerscorrectIy Mar 19, 2025

0

5

0

+1216

Algebra

Let x_1, x_2, \dots, x_n be real numbers. If
x_1 + 2x_2 + \dots + nx_n = 1,
then find the minimum value of x_1^2/1 + x_2^2/2 + \dots + x_n^2/n, in terms of n.

AnswerscorrectIy Mar 19, 2025

0

4

0

+1216

Algebra

Let a, b, and c be positive real numbers. Find the minimum value of
(a + 1)^2 + \left( \frac{b}{a} + a + 1 \right)^2 + \left( \frac{c}{b} + abc \right)^2 + \left( \frac{4}{c} + \frac{c}{a} \right)^2.

AnswerscorrectIy Mar 19, 2025

0

5

0

+116

Algebra

Let x and y be positive real numbers. If
\frac{x^2}{9} + \frac{y^2}{25} = 1,
then find the maximum value of \frac{x^2}{3} \cdot \frac{y^2}{5}.

coIinqiu Mar 19, 2025

0

5

0

+116

Algebra

Let a, b, and c be positive real numbers. If \frac{a}{2} + b + 3c = 12, then find the maximum value of
\min \left\{ \frac{ab}{2}, ac, 12bc \right\}.

coIinqiu Mar 19, 2025

0

3

0

+1216

Algebra

Let x and y be positive real numbers. If x + y = 1, then find the maximum value of xy + y^3.

AnswerscorrectIy Mar 18, 2025

0

2

1

+1216

Algebra

Find the minimum value of
\frac{x^2}{x + 2}
for x > 2.

Find the minimum value of the product
P(x,y,z) = (2x + 3y)(x + 4z) \left( y + \frac{5}{3} z \right),
when xyz = 1, and x, y, z are positive real numbers.

AnswerscorrectIy Mar 18, 2025

0

5

0

+1216

Algebra

AnswerscorrectIy Mar 18, 2025

0

4

0

+116

Algebra

Find the maximum p such that
2x^4 y^2 + \frac{9}{4} y^4 z^2 + \frac{3}{4} z^4 x^2 + 3x^3 y^3 + 10x^3 z^3 + 15y^3 z^3 - px^2 y^2 z^2
is always nonnegative for all real x, y, and z.

coIinqiu Mar 17, 2025

0

5

0

+116

Inequality

Let w, x, y, and z be positive real numbers. If w + 2x + 3y + 6z = 8 - w^2 - x^2 - y^2 - z^2, then what is the maximum value of wxyz?

coIinqiu Mar 17, 2025

0

5

3

+141

Super Confusing Math Problem ( Read Description )

PLEASE READ DESCRIPTION BEFORE ANSWERING
I first picked option A because thats what I think was right and AI and even google was saying its correct... but it ended up being wrong so then I picked option C. because that was my next bet read more ..

Let a and b be positive real numbers. Find the minimum value of
(a + b) \left( \frac{1}{a + 1} + \frac{1}{b + 1} \right)

acyclics Mar 17, 2025

0

3

0

+1216

Algebra

AnswerscorrectIy Mar 17, 2025

0

4

0

+1216

Algebra

Fill in the blanks, to make a true equation.
3/(3^2 - 1) + 3^2/(3^4 - 1) + 3^3/(3^6 - 1) + 3^4/(3^8 - 1) + ... + 3^(2(n - 1))/(3^(2n) - 1) = ___/___
Hint: Let S_n = \frac{3}{3^2 - 1} + \frac{3^2}{3^4 - 1} + \frac{3^3}{3^6 - 1} read more ..

AnswerscorrectIy Mar 17, 2025

0

3

2

+1216

Algebra

Find the number of points of intersection between the graphs of the following equations: \begin{align*}
y = |2x + 5|,
y = -|3x - 2| + |4x - 7| + x.

Let x be a positive real number. Show that
\frac{1}{x} \ge 3 - 2x
Describe when we have equality.

AnswerscorrectIy Mar 16, 2025

0

2

3

+1216

Algebra

Let
f(x) = \frac{x^4 + 2x^3 + 3x^2 + 2x + 1}{x}.
Find the minimum value of x for x > 0.

AnswerscorrectIy Mar 16, 2025

0

2

1

+1216

Algebra

Let $x$ and $y$ be real numbers such that
x^2 + 3xy + 2y^2 = 1 - 12x + 5y.
Find all possible values of x + y. Enter your answer using interval notation.

AnswerscorrectIy Mar 16, 2025

0

1

0

+1216

Algebra

AnswerscorrectIy Mar 16, 2025

0

3

0

+1216

Algebra

Let a and b be real numbers such that
(a^2 + 1)(b^2 + 4) = 14ab + 21.
Find the largest possible value of a^2 + b^2.

AnswerscorrectIy Mar 16, 2025

0

3

0

+1216

Algebra

Let x and y be real numbers satisfying
\frac{x^2y^2 - 1}{2y - 1} = 4x + y.
Find the largest possible value of x.

AnswerscorrectIy Mar 16, 2025

0

4

0

+1216

Algebra

Let x and y be real numbers. Find the maximum value of $(x + y)^2$, if $x$ and $y$ satisfy $x^2 + y^2 = 5 + 2xy$.

AnswerscorrectIy Mar 16, 2025

0

5

0

+1216

Algebra

Find the maximum value of f(a), where a is a positive integer, and
f(x) = \frac{13 + x}{2x + 7 - x^2}.

AnswerscorrectIy Mar 16, 2025

0

2

0

+1216

Algebra

Compute
\sum_{k = 1}^{100} k (\lceil \log_3 k \rceil - \lfloor \log_9 k \rfloor).

AnswerscorrectIy Mar 16, 2025

0

1

0

+1216

Algebra

Find the smallest positive real number x such that
\lfloor x^2 \rfloor - x \lfloor x \rfloor = \lfloor x^3 \rlfoor/x

AnswerscorrectIy Mar 16, 2025

0

6

0

+1216

Algebra

Find all x for which
\Big| x - |x - 2| \Big| = \lfloor x \rfloor + \lfloor 2x \rfloor
Express your answer in interval notation.

AnswerscorrectIy Mar 16, 2025

0

6

0

+1216

Algebra

Find all real numbers x that satisfy the equation
|x + 4| + |x - 7| = 3x - 1 + |3x - 7|.
If you find more than one such value of x, list all of your solutions separated by commas. If you only find one solution, then just enter that so read more ..

AnswerscorrectIy Mar 16, 2025

0

3

1

+1216

Algebra

Compute
\frac{\{\sqrt{3}\} - 4 \{\sqrt{5}\}}{\{\sqrt{3}\}^2 + \{\sqrt{2}\}^2}.

Find the area of the region determined by the system
y \ge |x|, \\
y \le -|2x + 1| + 6.

AnswerscorrectIy Mar 16, 2025

0

7

0

+1216

Algebra

AnswerscorrectIy Mar 15, 2025

0

5

0

+1216

Algebra

Let f be the piecewise function such that
f(x) =
x^2 - 5x - 64 & \text{if} \ x \le 0, \\
x^2 + 3x - 38 & \text{if} \ x > 0.
Find all x such that f(x) = 50.

AnswerscorrectIy Mar 15, 2025

0

9

0

+1216

Algebra

Find the solutions to
|x^2 + 8x| = 9 - |x^4 + 3x^2 + 2|

AnswerscorrectIy Mar 15, 2025

0

5

0

+806

Algebra

What is the horizontal asymptote as x approaches positive infinity of the graph of
y = \sqrt{4x^2 + 5x} - \sqrt{4x^2}?
The horizontal asymptote is in the form y = mx + k.

crimefightingvigiI Mar 15, 2025

+1

3

2

+806

Algebra

Find all real x where
2 \cdot \frac{x - 5}{x - 3} > \frac{2x - 5}{x + 2} + 20.
Give your answer in interval notation.

Find the values of x where the vertical asymptotes of f(g(x)) are located, where
f(x) = \frac{2x - 8}{x^2 - 2x - 3} and g(x) = \frac{x^3 + 2x + 9}{x^2 + 4}.

crimefightingvigiI Mar 15, 2025

0

4

0

+806

Algebra

crimefightingvigiI Mar 15, 2025

0

3

1

+116

Algebra

Fill in the blanks, to make a true equation:
(8x^3 + 24x^2 + 15x + 1)/((x^2 - 1)(x^2 + 3x)) = ___/(x - 1) + ___/(x + 3) + ___/x + ___/(x + 1)

Find the all real numbers that are not in the domain of f(g(x)), where
f(x) = \frac{3x^2 - 10x - 25}{x + 1} and g(x) = \frac{14x - 6}{3x^2 + 5x + 15}

coIinqiu Mar 14, 2025

0

5

0

+116

Algebra

coIinqiu Mar 14, 2025

0

7

0

+116

Algebra

Give a polynomial g(x) so that f(x) + g(x) has a horizontal asymptote of y = 0 as x approaches positive infinity, where
f(x) = \frac{2x^4 - 3x^3 - 8x^2 + 4x - 4}{x^2 + x}.

coIinqiu Mar 14, 2025

0

6

0

+116

Algebra

Fill in the blanks, to make a true equation:
\frac{2x^4 - 3x^3 - x^2 + 4x - 4}{x^2 + x} = ___x^2 + ___x + ___ + ___/x + ___/(x + 1).

coIinqiu Mar 14, 2025

0

8

0

+116

Algebra

Find the largest value of x where the plots of
f(x) = - \frac{2x + 5}{x + 3} and g(x) = \frac{12}{x - 1}
intersect.

coIinqiu Mar 14, 2025

0

3

2

+116

Algebra

Fill in the blanks with constants, to make a true equation:
\frac{x^2 - 6x - 3}{x^3 - 4x} = ___/x + ___/(x - 2) + ___/(x + 2)

Let (x,y,z) be the real solution to the system of equations
x + y = \sqrt{4z + 3}
y + z = \sqrt{4x - 1}
z + x = \sqrt{4y + 5}
Find x + y + z.

coIinqiu Mar 13, 2025

0

7

1

+116

Algebra

Find all x such that
sqrt{3x^2 + 2x + 1} + sqrt{3x^2 + 2x - 3} = 20.

coIinqiu Mar 13, 2025

0

6

0

+116

Algebra

coIinqiu Mar 13, 2025

0

6

0

+116

Algebra

Simplify \frac{6 \sqrt{2]}{\sqrt{2} - \sqrt{3} - \sqrt{5}}

coIinqiu Mar 13, 2025

0

6

0

+116

Algebra

Fill in the blanks.
If f(x) is an even function and g(x) is an even function and h(x) is an even function, then f(x) + g(x) + h(x) is an ___ function.
If f(x) is an odd function and g(x) is an odd function and h(x) read more ..

coIinqiu Mar 12, 2025

0

3

1

+116

Algebra

Find the value of x that maximizes
f(x) = \log (-20x + 16 \sqrt{x} - x).

If 2^{16^x} = 128*4^x, then find 2^x.

coIinqiu Mar 12, 2025

0

3

1

+116

Algebra

Express 2 + sqrt(2) + 1/(2 + sqrt(3)) + 1/(sqrt(5) - 2) in simplest form.

coIinqiu Mar 12, 2025

0

4

1

+116

Algebra

For each of the following functions, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain. Select all the properties that apply.
f(x) = x + 2 \lfloor x \rfloor + sqrt{x} - \frac{1}{|x|}

coIinqiu Mar 12, 2025

0

6

0

+1216

Algebra

AnswerscorrectIy Mar 11, 2025

0

7

0

+1216

Algebra

For each of the following functions, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain. Select all the properties that apply.
f(x) = \frac{x}{\sqrt{x^2 + 1}} + \frac{1}{x^2} - \frac{x}{x^2 - 1 read more ..

AnswerscorrectIy Mar 11, 2025

0

7

0

+1216

Algebra

For each of the following functions, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain. Select all the properties that apply.
f(x) = \frac{\sqrt{|x|}}{x} + x + \frac{1}{x^2}

AnswerscorrectIy Mar 11, 2025

0

7

0

+1216

Algebra

For each of the following functions, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain. Select all the properties that apply.
f(x) = \frac{1}{\sqrt{x^2 + 1}} - \frac{1}{x}

AnswerscorrectIy Mar 11, 2025

+1

3

2

+116

Algebra

For each of the following functions, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain. Select all the properties that apply.
f(x) = sqrt{10 - x} + \sqrt{x + 10}

For each of the following functions, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain. Select all the properties that apply.
f(x) = x^3 - 3x^2 + 10x - 15

coIinqiu Mar 11, 2025

+1

3

1

+116

Algebra

Find all real numbers a and b such that
a + b = 14
a^3 + b^3 = 812 + a^2 + b^2

coIinqiu Mar 11, 2025

0

6

2

+116

Algebra

Factor (ab + ac + bc)^3 - a^3 b^3 - a^3 c^3 - b^3 c^3 + (a^2 + b^2 + c^2)^3 - 3(a^3 + b^3 + c^3)^2 as much as possible.

coIinqiu Mar 11, 2025

+1

6

0

+116

Algebra

coIinqiu Mar 11, 2025

0

9

0

+116

Algebra

Let P = \log_8 3 and Q = \log_3 5. Express \log_{15} 72 in terms of P and Q. Your answer should no longer include any logarithms.

coIinqiu Mar 11, 2025

0

4

0

+806

Algebra

Let x, y, and z be positive real numbers with x > y > z > 1 such that
\log_x y + \log_y z + \log_z x = \frac{13}{2},
\log_x z + \log_z y = 8.

Find \log_z x.

crimefightingvigiI Mar 11, 2025

0

4

1

+806

Algebra

The equation
\sqrt[5]{7} x^{\log_7 x} = x^{\log_5 x}
has two positive roots a and b. Compute ab.

Find \frac{a}{b} when 2 log(a - 2b) = log a + log (2b) - log(a + b).

crimefightingvigiI Mar 11, 2025

0

5

1

+1216

Algebra

If the two numbers \log_x 3 + \log_x 9 and \log_x 27 are equal, then what is their common value?

AnswerscorrectIy Mar 10, 2025

0

5

1

+1216

Algebra

Given that log_{4n} 40 sqrt(3) = log_{2n} 10, find n^4.

AnswerscorrectIy Mar 10, 2025

0

3

1

+1216

Algebra

Let x, y, and z all exceed 1, and let w be a positive number such that \log_x w = 24, \log_x yx = 40, and \log_{xy^2} zw = 12. Find \log_z w.

AnswerscorrectIy Mar 10, 2025

0

5

1

+806

Algebra

crimefightingvigiI Mar 10, 2025

+1

4

1

+7

Two squares are inscribed in a semi-circle, as shown below. Find the radius of the semi-circle.

Let P = \log_8 3 and Q = \log_3 5. Express \log_{15} 72 in terms of P and Q. Your answer should no longer include any logarithms.

Tigergaming2464 Mar 9, 2025

0

3

1

+806

Algebra

Factor (ab + ac + bc)^3 - a^3 b^3 - a^3 c^3 - b^3 c^3 + (a^2 + b^2 + c^2)^3 - 3(a^3 + b^3 + c^3)^2 as much as possible.

crimefightingvigiI Mar 8, 2025

0

7

0

+806

Algebra

crimefightingvigiI Mar 8, 2025

0

4

2

+806

Algebra

Find all real numbers a and b such that
a + b = 14
a^3 + b^3 = 812 + a^2 + b^2

Find x if \log_2 x^2 + \log_{1/2} x + 3 \log_4 x = 5.

crimefightingvigiI Mar 8, 2025

0

9

0

+164

Algebra

HumanBemg Mar 8, 2025

0

8

0

+164

Algebra

Simplify 25^{\frac{1}{2} - \log 5 + \sqrt{3}}.

HumanBemg Mar 8, 2025

0

6

1

+164

Algebra

Compute
\log_4 5 + \log_5 6 + \log_6 7+ \log_{2047} 2048 + \log_{2048} 2049

Fill in the blanks, to make a true equation.
3/(3^2 - 1) + 3^2/(3^4 - 1) + 3^3/(3^6 - 1) + 3^4/(3^8 - 1) + ... + 3^(2(n - 1))/(3^(2n) - 1) = ___/___

HumanBemg Mar 8, 2025

0

6

0

+164

Algebra

HumanBemg Mar 8, 2025

0

6

0

+164

Counting

Let S be the set {1, 2, 3, \dots, 10, 11, 12}. How many subsets of the set S have no two consecutive primes as members?

HumanBemg Mar 7, 2025

0

5

0

+164

Algebra

Let
A_0 = 0
A_1 = 1
A_n = A_{n - 1} + A_{n - 2} for n ge 2
There is a unique ordered pair (c,d) such that c \alpha^n + d \beta^n is the closed form for sequence A_n. Find the ordered pair (c,d).

HumanBemg Mar 7, 2025

0

4

0

+164

Algebra

Find the ordered pair (p,q) such that
F_n = p \alpha^n + q \beta^n.

HumanBemg Mar 7, 2025

0

3

1

+164

Algebra

The Fibonacci sequence, is defined by F_0 = 0, F_1 = 1, and F_n = F_{n - 2} + F_{n - 1}. It turns out that
F_n = \frac{\alpha^n - \beta^n}{\sqrt{5}},
where \alpha = \frac{1 + \sqrt{5}}{2} and \beta = \frac{1 - \sqrt{5}}{2}.
The read more ..

Find a closed form for
S_n = 1! \cdot (1^2 + 1) + 2! \cdot (2^2 + 2) + \dots + n! \cdot (n^2 + n).\]
for any integer n \ge 1. Your response should have a factorial.

HumanBemg Mar 7, 2025

0

5

1

+164

Algebra

For a positive integer k, let
S_k = 1 \cdot 1! \cdot 2 + 2 \cdot 2! \cdot 3 + \dots + k \cdot k! \cdot (k + 1).
Find a closed form for S_k.

HumanBemg Mar 7, 2025

0

4

0

+164

Algebra

HumanBemg Mar 7, 2025

0

10

0

+21

Algebra

Find
\sum_{k = 1}^{20} k(k^2 - 10k - 20)(k^2 + 1)

co1inqiu Mar 7, 2025

0

5

1

+806

Algebra

Compute
1.11111 + 0.11111 + 0.01111 + 0.00111 + 0.00011 + 0.00001

Let a_1, a_2, a_3, \dots be an infinite geometric series with positive terms. If a_2 = 10, then find the smallest possible value of
a_1 + a_2 + a_3.

crimefightingvigiI Mar 7, 2025

0

6

1

+806

Algebra

Let
a + ar + ar^2 + ar^3 + \dotsb
be an infinite geometric series. The sum of the series is 9. The sum of the cubes of all the terms is 36. Find the common ratio.

crimefightingvigiI Mar 7, 2025

0

3

0

+806

Algebra

crimefightingvigiI Mar 7, 2025

0

4

1

+806

Algebra

Let A = x^4 + x^3 + x^2 + x + 1 and B = x^4 - x^3 + x^2 - x + 1. Simplify A + B.

The closed form sum of
12 \left[ 1 \cdot 2^2 \cdot 3 + 2 \cdot 3^2 \cdot 4 + \dots + n (n + 1)^2 (n + 2) \right]
for n \ge 1 is n(n + 1)(n + 2) p(n) for some polynomial p(n). Find p(n).

crimefightingvigiI Mar 7, 2025

0

8

0

+1216

Algebra

AnswerscorrectIy Mar 7, 2025

0

4

0

+1216

Algebra

The sum
6 (1 \cdot 3 \cdot 5 + 2 \cdot 4 \cdot 6 + \dots + n(n + 2)(n + 4))
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.

AnswerscorrectIy Mar 7, 2025

0

1

+1216

Algebra

A sequence a_1, a_2, a_3, \dots of positive integers has the following properties:
* The first three terms are in geometric progression.
* The second, third, and fourth terms are in arithmetic progression.
* In general, for all $i\ge1$, read more ..

A sequence of real numbers (a_n) is defined as follows: a_0 = 1, a_2 = 2, and
a_{n + 2} = \frac{a_{n + 1}}{a_n}
for n = 0, 1, 2, \dots. Find a_0 + a_1 + a_2 + \dots + a_{100}.

AnswerscorrectIy Mar 7, 2025

0

9

0

+1216

Algebra

AnswerscorrectIy Mar 6, 2025

0

2

1

+1216

Algebra

Let
P = 3^{1/3} \cdot 9^{1/9} \cdot 27^{1/27} \cdot 81^{1/81}.
Then P can be expressed in the form \sqrt[a]{b}, where $a$ and $b$ are positive integers. Find the smallest possible value of $a + b.$

Let
P = 2^{1/2} \cdot 4^{1/4} \cdot 8^{1/8} \cdot 16^{1/16}
Then P can be expressed in the form \sqrt[a]{b}, where $a$ and $b$ are positive integers. Find the smallest possible value of $a + b.$

AnswerscorrectIy Mar 6, 2025

0

7

1

+1216

Algebra

Let r be a real number such that |r| < 1. Express
\sum_{n = 0}^{\infty} n*r^n*(n + 1)*(n + 2)
in terms of r.

AnswerscorrectIy Mar 6, 2025

0

10

1

+164

Algebra

Find
\sum_{k = 0}^{10} (k + 3) \cdot 2^k \cdot (k - 3)

HumanBemg Mar 6, 2025

0

7

1

+164

Algebra

Simplify \frac{1 + 3 + 5 + ... + 1999 + 2001 + 2003}{2 + 4 + 6 + ... + 2000 + 2002 + 2004 + 2006 + 2008 + 2010}.

HumanBemg Mar 6, 2025

0

3

2

+164

Algebra

Find the sum
\frac{1}{7} + \frac{2}{7^2} + \frac{3}{7^3} + \frac{1}{7^4} + \frac{2}{7^5} + \frac{3}{7^6}

HumanBemg Mar 6, 2025

+1

6

1

+164

Algebra

Let a_1, a_2, a_3, \dots be an infinite geometric series with positive terms. If a_2 = 10, then find the smallest possible value of
a_1 + a_2 + a_3.

HumanBemg Mar 6, 2025

0

3

1

+116

Algebra

Let
a + ar + ar^2 + ar^3 + \dotsb
be an infinite geometric series. The sum of the series is 9. The sum of the cubes of all the terms is 36. Find the common ratio.

coIinqiu Mar 5, 2025

0

6

1

+116

Algebra

Let A = x^4 + x^3 + x^2 + x + 1 and B = x^4 - x^3 + x^2 - x + 1. Simplify A + B.

coIinqiu Mar 5, 2025

0

4

1

+116

Algebra

thatgirlaj ●

coIinqiu Mar 5, 2025

0

11

1

+116

Algebra

Compute
1.11111 + 0.11111 + 0.01111 + 0.00111 + 0.00011 + 0.00001

Simplify (x^4 + x^3 + x^2 + x + 1) + (x^4 - x^3 + x^2 - x + 1).

coIinqiu Mar 4, 2025

0

6

1

+116

Algebra

Find all real numbers a such that the roots of the polynomial
x^3 - 3x^2 + 17x + a
form an arithmetic progression and are not all real.

coIinqiu Mar 4, 2025

0

10

0

+806

Algebra

crimefightingvigiI Mar 4, 2025

0

10

0

+806

Algebra

Find the sum of the series
1 + \frac{1}{2} + \frac{1}{10} + \frac{1}{30} + \frac{1}{60} + ,..
where we alternately multiply by $\frac 12$ and $\frac 15$ and $\frac{1}{3}$ to get successive terms.

crimefightingvigiI Mar 4, 2025

0

4

1

+806

Algebra

The sum of the first three terms of a geometric sequence of integers is equal to seven times the first term, and the sum of the first four terms is $30$. What is the first term of the sequence?

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(2/x + x/2).
What is the domain of g?

crimefightingvigiI Mar 4, 2025

0

9

0

+806

Algebra

crimefightingvigiI Mar 4, 2025

0

10

0

+806

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(x - 4x^2)
What is the domain of g?

crimefightingvigiI Mar 4, 2025

0

5

0

+806

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = 5 - f(x) + f(5/x).
What is the domain of g?

crimefightingvigiI Mar 4, 2025

0

7

0

+806

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f((x + 1)(x - 2)).
What is the domain of g?

crimefightingvigiI Mar 4, 2025

0

10

0

+21

Algebra

Let t be a root of f(x) = x^3 - x + 3. Evaluate t^6 - 4t^5 + 7t^4 - 3t^2 + 10t - 13.

co1inqiu Mar 4, 2025

+1

3

1

+21

Algebra

Let r, s, and t be solutions of the equation x^3 - 4x^2 - 7x + 12 = 0. Compute
\frac{rs}{t^2} + \frac{rt}{s^2} + \frac{st}{r^2}

Let r, s, and t be solutions of the equation x^3 + 2x^2 - 5x + 15 = 0. Compute
\frac{1}{r - 2s - 2t} + \frac{1}{s - 2r - 2t} + \frac{1}{t - 2r - 2s}

co1inqiu Mar 4, 2025

0

6

0

+21

Algebra

co1inqiu Mar 4, 2025

0

4

1

+21

Algebra

Suppose r and s are the values of x that satisfy the equation
x^2 - 2mx + (m^2 - 6m + 11) = 0
for some real number m. Find the minimum real value of (r - s)^2.

Let be a complex number so that
Find z, then calculate .

co1inqiu Mar 4, 2025

+1

6

2

+11

Complex numbers... Help needed!

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2mn - 18m + 7n - 3mn + 15m + 8n + ___

Mathematix1981 Mar 3, 2025

0

5

1

+164

Algebra

Fill in the blanks, to complete the factorizaion:
(a^2 + b^2 - c^2)^2 - 4a^2 b^2 - 4a^2 c^2 + 4b^2 c^2 = (a + ___)(a + ___)(a + ___)(a + ___)

HumanBemg Mar 3, 2025

0

5

0

+164

Algebra

HumanBemg Mar 3, 2025

0

12

0

+164

Algebra

Let r_1, r_2, r_3, r_4, and r_5 be the complex roots of x^5 - 4x^2 + 7x - 1 = 0. Compute
(r_1^2 + r_1^6 + 2)(r_2^2 + r_2^6 + 2)(r_3^2 + r_3^6 + 2)(r_4^2 + r_4^6 + 2)(r_5^2 + r_5^6 + 2)

HumanBemg Mar 3, 2025

0

12

0

+164

Algebra

Factor 3xy - 4x^2 + 18y - 24x + 5x^2*y - 8y^3 + 20.

HumanBemg Mar 3, 2025

0

7

0

+1800

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 $a_1$.

blackpanther Mar 3, 2025

0

5

1

+1800

Algebra

The system of equations
\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 2
has exactly one solution. What is $z$ in this solution?

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{3}.

blackpanther Mar 3, 2025

0

3

1

+1800

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 ..

blackpanther Mar 3, 2025

0

2

1

+1800

Algebra

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

blackpanther Mar 3, 2025

0

5

1

+977

Algebra

The equation of the line below can be expressed in the form
\frac{x}{a} + \frac{y}{b} = 1.
Find a.
The lines passes through (5,8) and (-4,17).

magenta Mar 3, 2025

0

5

1

+977

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 sends read more ..

magenta Mar 3, 2025

+1

2

1

+977

Algebra

Triangle ABC is a 30-60-90 right triangle with right angle at C, angle ABC = 60 degrees, and hypotenuse of length 2. Let P be a point chosen at random inside ABC, and extend ray BP to hit side AC at D. What is the probability that BD < √2?
<read more ..

magenta Mar 3, 2025

0

4

1

+194

New question :) someone help me please T_T

Guys, look at these guidelines: https://web2.0calc.com/questions/some-guidlines-for-question-askers
I think everyone on this site who asks a question should in fact show what they have tried. This is not a website to magically read more ..

HumenBeing Mar 3, 2025

+1

7

0

+37

Question Askers

Kromy Mar 2, 2025

+1

3

2

+806

Algebra

Evaluate
1 + \frac{i}{3} - \frac{1}{9} - \frac{i}{27} + \frac{1}{81},
where $i$ is the imaginary unit.

Evaluate
2 + \frac{6}{7} +\frac {18}{49} + \frac{54}{343} + 1 + \frac{2}{14} + \frac{3}{98}.

crimefightingvigiI Mar 2, 2025

0

8

2

+806

Algebra

CPhill ●●

crimefightingvigiI Mar 2, 2025

+1

6

1

+806

Algebra

Evaluate \sum_{n = 1}^{33} (5n + 2 - 4n + n^2 + 17).

Evaluate 21 + 27 + 33 + ... + 267 + ... + 6021.

crimefightingvigiI Mar 2, 2025

0

3

2

+806

Algebra

Let be real numbers such that
Find the maximum value of in terms of
I originally got the answer of 1 but it was wrong! Thanks for helping!

crimefightingvigiI Mar 2, 2025

0

7

1

+36

Algebra

Thanks for helping!
Let be real numbers such that
and is minimized. Find

crimefightingvigil Mar 2, 2025

0

5

1

+36

HELP Pls

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 $S_{70}.$

crimefightingvigil Mar 2, 2025

0

4

2

+972

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 sends read more ..

Rangcr897 Mar 2, 2025

0

4

1

+972

Algebra

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

Rangcr897 Mar 2, 2025

0

3

1

+1518

Algebra

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

learnmgcat Mar 2, 2025

0

9

1

+1556

Algebra

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 15$, find $BZ$.

kittykat Mar 2, 2025

0

6

1

+806

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 15$, find $BC$.

crimefightingvigiI Mar 2, 2025

0

8

1

+806

Geometry

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are read more ..

crimefightingvigiI Mar 2, 2025

0

7

2

+339

help with counting

Each face of a cube is painted randomly one of the colors red, orange, yellow, green, blue or purple. What is the probability that the cube has at least one pair of faces that share an edge and are the same color? Express your answer as a decimal to the read more ..

jaekg Mar 2, 2025

0

1

2

+34

Counting and Probability

Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 2.

colinqiu Mar 2, 2025

0

4

1

+1800

Algebra

Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 4.

blackpanther Mar 2, 2025

0

5

1

+1800

Algebra

Let a, b, c be the roots of p(x) = x^3 + 7x^2 + 10x - 13 - 5x^3 + 25x^2 + 44x - 15. Find the value of
1/(ab + ac) + 1/(ab + bc) + 1/(ac + bc)

blackpanther Mar 2, 2025

0

5

1

+1800

Algebra

Suppose the polynomial p(x)=x^3+ax^2+bc+c has the property that the mean of its zeroes, the product of its zeroes, and the sum of its coefficients are all equal. If the y-intercept of the graph of y=p(x) is 0, what is b?

blackpanther Mar 2, 2025

+1

5

1

+413

Algebra

Find all (real or nonreal) x satisfying
(x - 3)^4 + (x - 5)^4 = -8 + 6(x - 3)(x - 5)^3 - 11(x - 3)^3 (x - 5).

nathanl6656 Mar 2, 2025

0

6

1

+413

Algebra

Express x^8 + x^4 y^4 - x^6 y^2 + x^3 y^5 - 4xy^7 - y^8 as the product of two polynomials of degree 2, and a polynomial of degree 4.

nathanl6656 Mar 2, 2025

0

5

1

+413

Algebra

Find the constant k so that
2x^2 + 5xy - 8y^2 + 7x + 25y + k
can be expressed as the product of two linear factors of the form ax + by + c.

nathanl6656 Mar 2, 2025

0

9

1

+413

Algebra

Let
p(a, b, c) = a^5 + b^5 + c^5 + k(a^3 + b^3 + c^3)(a^4 + b^4 + c^4 - 2a^2 b^2 - 2a^2 c^2 - 2b^2 c^2).
Find the constant k so that p(a,b,c) is divisible by a + b + c.

nathanl6656 Mar 2, 2025

+1

6

1

+478

Algebra

If z is a complex number satisfying
z + \frac{1}{z} = \sqrt{5},
calculate
z^{10} + \frac{1}{z^{10}}. read more ..

MeIdHunter Mar 2, 2025

0

6

0

+478

Algebra

MeIdHunter Mar 2, 2025

0

3

1

+478

Algebra

In this multi-part problem, we will consider this system of simultaneous equations:
3x + 4y + 30z = -60,
2xy + 42xz - 16yz = 68,
5xyz = 56.
Let a = x/2, b = 5y and c = -4z.
Determine the monic cubic polynomial in terms of read more ..

In this multi-part problem, we will consider this system of simultaneous equations:
3x + 4y + 30z = -60,
2xy + 42xz - 16yz = 68,
5xyz = 56.
Let a = x/2, b = 5y and c = -4z.
Determine the monic cubic polynomial in terms of read more ..

MeIdHunter Mar 2, 2025

0

7

0

+478

Algebra

MeIdHunter Mar 2, 2025

0

4

0

+958

Algebra

If (x,y) satisfies the simultaneous equations
3xy - 4x^2 + 18y - 24x + 5x^2*y - 8y^3 + 20.
x^2 - y^2 = 7 + 4xy
where x and y may be complex numbers, determine all possible values of y^2.

gnistory Mar 2, 2025

0

5

0

+958

Algebra

Factor 3xy - 4x^2 + 18y - 24x + 5x^2*y - 8y^3 + 20.

gnistory Mar 2, 2025

0

9

0

+958

Algebra

Factor x^2 - 2x - y^2 + 2yz + 5z^2 as the product of two polynomials of degree 1.

gnistory Mar 2, 2025

0

9

0

+456

Algebra

Suppose the real numbers $a$, $b$, $x$, and $y$ satisfy the equations
ax + by = 3,
ax^2 + by^2 = 5,
ax^3 + by^3 = 17,
ax^4 + by^4 = 23.<#> Evaluate ax^5 + by^5.

Jasmo Mar 2, 2025

0

9

0

+456

Algebra

Let a, b, c, and d be distinct real numbers such that
a = \sqrt{4 + \sqrt{5 + a}},
b = \sqrt{4 - \sqrt{7 + b}},
c = \sqrt{4 + \sqrt{9 - c}},
d = \sqrt{4 - \sqrt{11 - d}}.
Compute abcd.

Jasmo Mar 2, 2025

0

5

0

+456

Algebra

If a_1, a_2, ..., a_19 satisfy
a_1 + a_2 + a_3 + a_4 = 1,
a_2 + a_3 + a_4 + a_5 = 2,
a_3 + a_4 + a_5 + a_6 = 3,
...
a_{16} + a_{17} + a_{18} + a_{19} = 16,
a_{17} + a_{18} + a_{19} + read more ..

Jasmo Mar 1, 2025

0

9

0

+456

Algebra

Let a = 3(x - y), b = 3(y - z), and c = 3(z - x), where x, y, z are real numbers, and assume ab + ac + bc \ne 0. Compute
(a^3 + b^3 + c^3)/(ab + ac + bc).

Jasmo Mar 1, 2025

0

7

1

+900

Algebra

Let r_1, r_2, r_3, r_4, and r_5 be the complex roots of x^5 - 4x^2 + 7x - 1 = 0. Compute
(r_1^2 + r_1^6 + 2)(r_2^2 + r_2^6 + 2)(r_3^2 + r_3^6 + 2)(r_4^2 + r_4^6 + 2)(r_5^2 + r_5^6 + 2)

Fill in the blanks, to complete the factorizaion:
(a^2 + b^2 - c^2)^2 - 4a^2 b^2 - 4a^2 c^2 + 4b^2 c^2 = (a + ___)(a + ___)(a + ___)(a + ___)

eramsby1O1O Mar 1, 2025

0

11

0

+900

Algebra

eramsby1O1O Mar 1, 2025

0

11

1

+900

Algebra

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2mn - 18m + 5n - mn + 20m + 4n + ___

Let t be a root of f(x) = x^3 - x + 3. Evaluate t^6 - 4t^5 + 7t^4 - 3t^2 + 10t - 13.

eramsby1O1O Mar 1, 2025

0

8

0

+900

Algebra

eramsby1O1O Mar 1, 2025

0

8

0

+458

Algebra

Find the foci of the ellipse shown below.
Enter your answer as a list of ordered pairs separated by commas.
Points on the ellipse are (-4,9), (-7,2), (-5,2), (-7, 1)

bIueb3rry Mar 1, 2025

0

6

0

+458

Algebra

The real numbers x and y satisfy
x^2 + y^2 - 8x + 6y + 23 = 0.
Find the largest possible value of x + y.

bIueb3rry Mar 1, 2025

0

6

0

+458

Algebra

Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 2.

bIueb3rry Mar 1, 2025

0

8

0

+458

Algebra

Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 4.

bIueb3rry Mar 1, 2025

0

12

0

+357

Algebra

Let a, b, c be the roots of p(x) = x^3 + 7x^2 + 10x - 13 - 5x^3 + 25x^2 + 44x - 15. Find the value of
1/(ab + ac) + 1/(ab + bc) + 1/(ac + bc)

cwimie Mar 1, 2025

0

7

1

+357

Algebra

Suppose the polynomial p(x)=x^3+ax^2+bc+c has the property that the mean of its zeroes, the product of its zeroes, and the sum of its coefficients are all equal. If the y-intercept of the graph of y=p(x) is 0, what is b?

Find all (real or nonreal) x satisfying
(x - 3)^4 + (x - 5)^4 = -8 + 6(x - 3)(x - 5)^3 - 11(x - 3)^3 (x - 5).

cwimie Mar 1, 2025

0

5

1

+357

Algebra

Express x^8 + x^4 y^4 - x^6 y^2 + x^3 y^5 - 4xy^7 - y^8 as the product of two polynomials of degree 2, and a polynomial of degree 4.

cwimie Mar 1, 2025

0

11

0

+456

Algebra

Jasmo Feb 27, 2025

0

9

1

+456

Algebra

Find the constant k so that
2x^2 + 5xy - 8y^2 + 7x + 25y + k
can be expressed as the product of two linear factors of the form ax + by + c.

Let
p(a, b, c) = a^5 + b^5 + c^5 + k(a^3 + b^3 + c^3)(a^4 + b^4 + c^4 - 2a^2 b^2 - 2a^2 c^2 - 2b^2 c^2).
Find the constant k so that p(a,b,c) is divisible by a + b + c.

Jasmo Feb 27, 2025

0

9

0

+357

Algebra

cwimie Feb 27, 2025

0

7

1

+357

Algebra

If z is a complex number satisfying
z + \frac{1}{z} = \sqrt{2},
calculate
z^{10} + \frac{1}{z^{10}}. read more ..

In this multi-part problem, we will consider this system of simultaneous equations:
3x + 4y + 30z = -60,
2xy + 42xz - 16yz = 68,
5xyz = 56.
Let a = x/2, b = 5y and c = -4z.
Determine the monic cubic polynomial in terms of read more ..

cwimie Feb 27, 2025

0

5

1

+357

Algebra

In this multi-part problem, we will consider this system of simultaneous equations:
3x + 4y + 30z = -60,
2xy + 42xz - 16yz = 68,
5xyz = 56.
Let a = x/2, b = 5y and c = -4z.
Determine the monic cubic polynomial in terms of read more ..

cwimie Feb 26, 2025

0

8

1

+357

Algebra

If (x,y) satisfies the simultaneous equations
3xy - 4x^2 + 18y - 24x + 5x^2*y - 8y^3 + 20.
x^2 - y^2 = 7 + 4xy
where x and y may be complex numbers, determine all possible values of y^2.

cwimie Feb 26, 2025

0

8

0

+456

Algebra

Jasmo Feb 26, 2025

0

5

0

+456

Algebra

Factor 3xy - 4x^2 + 18y - 24x + 5x^2*y - 8y^3 + 20.

Jasmo Feb 26, 2025

0

11

0

+456

Algebra

Let r_1, r_2, r_3, r_4, and r_5 be the complex roots of x^5 - 4x^2 + 7x - 1 = 0. Compute
(r_1^2 + r_1^6 + 2)(r_2^2 + r_2^6 + 2)(r_3^2 + r_3^6 + 2)(r_4^2 + r_4^6 + 2)(r_5^2 + r_5^6 + 2)

Jasmo Feb 25, 2025

0

8

0

+456

Algebra

Fill in the blanks, to complete the factorizaion:
(a^2 + b^2 - c^2)^2 - 4a^2 b^2 - 4a^2 c^2 + 4b^2 c^2 = (a + ___)(a + ___)(a + ___)(a + ___)

Jasmo Feb 25, 2025

0

10

0

+456

Algebra

Factor x^2 - 2x + 7 - y^2 - 10yz - 13z^2 as the product of two polynomials of degree 1.

Jasmo Feb 25, 2025

0

9

2

+456

Algebra

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2mn - 18m + 7n - 3mn + 15m + 8n + ___

Factor x^2 - 2x - y^2 + 2yz + 5z^2 as the product of two polynomials of degree 1.

Jasmo Feb 25, 2025

0

10

1

+357

Algebra

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2mn - 18m + 5n - mn + 20m + 4n + ___

cwimie Feb 25, 2025

0

10

0

+357

Algebra

cwimie Feb 25, 2025

0

9

1

+357

Algebra

Let r, s, and t be solutions of the equation 3x^3 - 4x^2 - 2x + 12 = 0. Compute
\frac{rs}{t^2} + \frac{rt}{s^2} + \frac{st}{r^2}.

history ●

cwimie Feb 25, 2025

+1

12

0

+357

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

cwimie Feb 25, 2025

+1

3

1

+357

Geometry

Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-1$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$ Let $A$ be the area of the region that is contained in both triangles $XYZ$ and $X'Y'Z'.$ Find read more ..

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

cwimie Feb 25, 2025

+1

7

2

+357

Geometry

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

cwimie Feb 25, 2025

+1

12

0

+357

Geometry

cwimie Feb 25, 2025

+1

7

1

+36

Trig help (no random guests allowed)

Problem:
Find AC.
[asy] size(300); pair A,B,C,O; A=origin; B=6*sqrt(3)*dir(150); C=(5,0);draw(A--B--C--cycle); dot("$A$",A,SW); dot("$B$",B,NW); dot("$C$",C,SE); label("$150^\circ$",A,dir(75)); label("$9$",A--B,SW); label("$7\sqrt{3}$",C--B,NE);read more ..

The graph shows that Anna and Boris begin walking at the same time. Find Boris's speed. Edit: I know that this forum is mostly about the Aops class ciriculum.This problem comes from a different ciriculum. As a new member who lacks the knowledge of this read more ..

skibidibrain901 Feb 25, 2025

+1

6

1

+10

HELP ME!!111

Suppose r and s are the values of x that satisfy the equation
x^2 - 2mx + (m^2 - 6m + 11) = 0
for some real number m. Find the minimum real value of (r - s)^2.

Chiccen Feb 24, 2025

0

7

1

+456

Algebra

Let r, s, and t be solutions of the equation x^3 + 2x^2 - 5x + 15 = 0. Compute
\frac{1}{r - 2s - 2t} + \frac{1}{s - 2r - 2t} + \frac{1}{t - 2r - 2s}

Jasmo Feb 24, 2025

0

5

1

+456

Algebra

Let r, s, and t be solutions of the equation x^3 - 4x^2 - 7x + 12 = 0. Compute
\frac{rs}{t^2} + \frac{rt}{s^2} + \frac{st}{r^2}

Jasmo Feb 24, 2025

0

5

3

+456

Algebra

Let t be a root of f(x) = x^3 - x + 3. Evaluate t^6 - 4t^5 + 7t^4 - 3t^2 + 10t - 13.

Jasmo Feb 24, 2025

0

7

0

+456

Algebra

Jasmo Feb 24, 2025

+1

6

1

+357

Geometry

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point.
An equilateral triangle, a regular decagon, and a regular n-gon, all with the same side length, also completely surround a read more ..

Quadrilateral ABCD is a parallelogram. Let E be a point on \overline{AB}, and let F be the intersection of lines DE and BC. The area of triangle EBF is 1, and the area of triangle BCE is 2. Find the area of parallelogram ABCD.

cwimie Feb 24, 2025

0

4

1

+357

Geometry

In trapezoid EFGH, \overline{EF} \parallel \overline{GH}, and P is the point on \overline{EH} such that EP:PH = 1:2. If the area of triangle PEF is 6, and the area of triangle PGH is 6, then find the area of trapezoid EFGH.

cwimie Feb 24, 2025

+1

6

1

+357

Geometry

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$ read more ..

cwimie Feb 24, 2025

0

7

1

+357

Geometry

what is the answer 38x+74-92=-18

cwimie Feb 24, 2025

+3

5

1

+113

algebra!

please help me with this question!

thatgirlaj Feb 24, 2025

+1

6

1

+17

Help!

what is the answer 65x+17-98=-4

cwinnie Feb 24, 2025

+2

6

1

+113

algebra

Bosco ●

thatgirlaj Feb 23, 2025

+2

7

1

+113

algebra

what is the answer 23x-79+4=-41

Let p, q, r, and s be the roots of g(x) = 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 + 11x^2 + 18x - 14.
Compute p^2 qrs + pq^2 rs + pqr^2 s + pqrs^2.

thatgirlaj Feb 23, 2025

+1

7

2

+456

Algebra

Let p, q, r, and s be the roots of g(x) = 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 + 11x^2 + 18x - 14.
Compute p^2 + q^2 + r^2 + s^2.

Jasmo Feb 23, 2025

+1

5

2

+456

Algebra

Let p, q, r, and s be the roots of g(x) = 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 + 11x^2 + 18x - 14.
Compute \frac{1}{p} + \frac{1}{q} + \frac{1}{r} + \frac{1}{s}.

Jasmo Feb 23, 2025

+1

3

2

+456

Algebra

For parts (a)-(d), let p, q, r, and s be the roots of g(x) = 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 + 11x^2 + 18x - 14.
Compute pqr + pqs + prs + qrs.

Jasmo Feb 23, 2025

+1

7

1

+456

Algebra

Suppose p(x) is a monic cubic polynomial with real coefficients such that p(2 - 3i) = 8 and p(0) = -5 and p(4 + 7i) = 11.
Determine p(x) (in expanded form).

Jasmo Feb 23, 2025

+1

9

1

+456

Algebra

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

Jasmo Feb 23, 2025

+1

6

1

+456

Geometry

Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.

Jasmo Feb 23, 2025

+1

7

1

+456

Geometry

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

Jasmo Feb 22, 2025

0

7

1

+456

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

Jasmo Feb 22, 2025

0

11

0

+456

Geometry

Jasmo Feb 22, 2025

0

2

1

+252

What is the total area of the region between the curves y=6x^2-18x and y=-6x from x=1 to x=3?

What is the total area of the region between the curves y=6x^2-18x and y=-6x from x=1 to x=3?
I keep getting 4, but it's not right. How do you do this?

ikleyn ●

Blizzardshine Feb 22, 2025

0

10

0

+456

Algebra

Let f(x) = \left \lfloor \frac{2 - 3x}{x + 3} + x^2 \right \rfloor.
Find f(1) + f(2) + f(3) + ... + f(999) + f(1000).

Jasmo Feb 22, 2025

0

3

1

+456

Algebra

Find the minimum value of \frac{x^2}{x - 1 + x^3} for x > 1

Bosco ●

Jasmo Feb 22, 2025

0

7

0

+456

Algebra

Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 4.

Jasmo Feb 22, 2025

0

12

0

+456

Algebra

Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 2.

Jasmo Feb 22, 2025

0

9

0

+305

Algebra

Let a, b, c be the roots of p(x) = x^3 + 7x^2 + 10x - 13 - 5x^3 + 25x^2 + 44x - 15. Find the value of
1/(ab + ac) + 1/(ab + bc) + 1/(ac + bc)

rtsdylifdts Feb 22, 2025

0

9

0

+305

Algebra

Let a, b, c be the roots of p(x) = x^3 + 7x^2 + 10x - 13 - 5x^3 + 25x^2 + 44x - 15.

rtsdylifdts Feb 22, 2025

0

6

1

+456

Geometry

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

Tottenham10 ●

Jasmo Feb 22, 2025

0

14

0

+456

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

Jasmo Feb 22, 2025

0

8

0

+789

Algebra

Find the conic section represented by the equation
4x^2 - 8y^2 - 28x + 49 = 4x^2 + 5x - 11y + 20

bingboy Feb 22, 2025

0

8

0

+789

Algebra

Determine the sum of all real numbers x satisfying
(x^2 - 6x + 4)(x^2 - 8x + 5) = 1.

bingboy Feb 22, 2025

0

5

1

+789

Algebra

The real numbers x and y satisfy
x^2 + y^2 - 8x + 6y + 23 = 0.
Find the largest possible value of x + y.

Find the foci of the ellipse shown below.
Enter your answer as a list of ordered pairs separated by commas.
Points on the ellipse are (-4,9), (-7,2), (-5,2), (-7, 1)

bingboy Feb 22, 2025

0

8

0

+789

Algebra

bingboy Feb 22, 2025

0

8

1

+357

Algebra

Parts (a)-(c) refer to the graph of
-4x^2 + y^2 - 2y = -3y^2 + 8x + 9y + 15
which is a hyperbola.
Find the center of the hyperbola.

Find the vertices of the hyperbola from part (a).
-4x^2 + y^2 - 2y = -3y^2 + 8x + 9y + 15

cwimie Feb 22, 2025

0

11

0

+357

Algebra

cwimie Feb 22, 2025

0

10

0

+357

Algebra

Find the asymptote of the hyperbola from part (a) with positive slope.
Enter your answer as an equation of the form $y = mx + b$.
-4x^2 + y^2 - 2y = -3y^2 + 8x + 9y + 15

cwimie Feb 22, 2025

0

8

0

+357

Algebra

Find the constant k so that the equation
4x^2 + 9y^2 - 8x + 54y + k = 2x^2 + 5y^2 - 12x + 34y
represents an ellipse which has an area of 6 \pi.

cwimie Feb 22, 2025

0

8

0

+1518

Algebra

An ellipse and a hyperbola have the same foci, $A$ and $B$, and intersect at four points. The ellipse has major axis $24,$ and minor axis $13.$ The distance between the vertices of the hyperbola is $5$. Let $P$ be one of the points of intersection read more ..

learnmgcat Feb 22, 2025

0

5

0

+1518

Algebra

Find the quotient and remainder when p(x) is divided by q(x), where p(x) = x^2 + 2 and q(x) = x^4 + 11x^2 - 7x + 10.

learnmgcat Feb 22, 2025

0

10

0

+1518

Algebra

Find the quotient and remainder when p(x) is divided by q(x), where p(x) = 9x^4 + x^3 - 12x + 21 and q(x) = x.

learnmgcat Feb 22, 2025

0

3

1

+1518

Algebra

Find the quotient and remainder when p(x) is divided by q(x)$, where p(x) = x^4 - x^2 + 3x - 7 and q(x) = x^2 + 2x - 5.

Find an ordered pair of constants (a,b) such that the polynomial f(x)=x^3+ax^2+(b+2)x+1 is divisible by x^2-3.
Enter your answer as an ordered pair in the format $(a,b)$, where $a$ and $b$ are replaced by appropriate numbers. read more ..

learnmgcat Feb 22, 2025

0

7

0

+56

Algebra

NotThatSmartTwo Feb 22, 2025

0

12

0

+56

Algebra

Given that x = 2 is a root of p(x) = x^4 - 3x^3 + 11x^2 - 25x + k for some constant k, find all the roots of p(x) (real and nonreal).
Enter your answer as a list of numbers separated by commas.

NotThatSmartTwo Feb 22, 2025

0

11

0

+56

Algebra

The polynomial
g(x) = x^3 - x^2 - (m^2 + m + 18) x + 2m^2 - 14m - 6
is divisible by x - 5 and all of its zeroes are integers. Find all possible values of m.

NotThatSmartTwo Feb 22, 2025

0

8

0

+56

Algebra

Let f(x) be a polynomial such that f(0) = 4, f(1) = 8, and f(2) = -6. Find the remainder when f(x) is divided by x.

NotThatSmartTwo Feb 22, 2025

0

8

0

+864

Algebra

Let f(x) = x^{10}+5x^9-8x^8+4x^7-x^6-33x^5+4x^4-22x^3+8x^2-3x-5.
Without using long division (which would be horribly nasty!), find the remainder when f(x) is divided by x^2 - 4.

RedDragonl Feb 22, 2025

0

5

0

+864

Algebra

Suppose P(x) is a polynomial of smallest possible degree such that:
* P(x) has rational coefficients.
* P(-2) = P(\sqrt{5}) = P(\sqrt{7}) = P(\sqrt{17}) = 0.
* P(-1) = 13.
Determine the value of P(0).

RedDragonl Feb 22, 2025

0

8

0

+864

Algebra

Find a monic quartic polynomial f(x) with rational coefficients whose roots include x = 1 + \sqrt{5} - 7 + \sqrt{3}. Give your answer in expanded form.

RedDragonl Feb 22, 2025

0

7

0

+864

Algebra

There are integers b, c for which both roots of the polynomial x^2 - x - 3 are also roots of the polynomial x^3 - bx^2 - c. Determine the ordered pair (b,c).

RedDragonl Feb 22, 2025

0

6

0

+413

Algebra

Solve the system of equations
x + y + 2z = 1
-2x - 4y + 2z = 7
10x - 17x + 13z = 8 read more ..

nathanl6656 Feb 22, 2025

0

9

0

+413

Algebra

Solve the system of equations
5x + 3z = 1
-x + y - z = 0
2x - 3y + 7z = -4

nathanl6656 Feb 22, 2025

0

6

0

+413

Algebra

Given that
5a - 7b + 3c = 19
4a + 2b - 8c = 4
7a + 5b + 3c = -11 read more ..

nathanl6656 Feb 22, 2025

0

10

0

+413

Algebra

Find all values of z such that z^4 - 4z^2 + 3 = 5z^2 + 11z^3 - 40.

nathanl6656 Feb 22, 2025

0

13

0

+458

Algebra

Find all values of x satisfying
sqrt(4x - 3) + 40/sqrt(4x - 3) = 12x + 14.

bIueb3rry Feb 22, 2025

0

10

0

+458

Algebra

What is the domain of the function f(x) = sqrt(6x - 3 + x^2)?

bIueb3rry Feb 22, 2025

+1

3

1

+458

Algebra

What is the domain of the function f(x) = sqrt(5 - 8x + x^2)?

What is the range of the function f(x) = sqrt(5 - 8x + x^2)?

bIueb3rry Feb 22, 2025

0

5

1

+458

Algebra

What is the domain of the function g(x) = (6x + 7)(2x - 3)?

bIueb3rry Feb 22, 2025

0

5

1

+1271

Algebra

What is the range of the function g(x) = (6x + 7)(2x - 3)?

Akhain1 Feb 22, 2025

0

8

0

+1271

Algebra

Akhain1 Feb 22, 2025

0

3

0

+1271

Algebra

The domain of the function p(x) = x^2 + 8x + 7x^3 is (-infty,infty). What is the range?

Akhain1 Feb 22, 2025

0

10

0

+1271

Algebra

The domain of the function q(x) = x^4 + 8x^2 + 7x^3 is (-infty,infty). What is the range?

Akhain1 Feb 22, 2025

0

10

0

+613

Algebra

The domain of the function r(x) = (x^2 + 1)/(1 - x)^2 is (-infty,1) U (1,infty). What is the range?

Pythagorearn Feb 22, 2025

0

10

0

+613

Algebra

Find all values of t such that t - 1, t + 1, and 6 - t could be the lengths of the sides of a right triangle.

Pythagorearn Feb 22, 2025

0

6

0

+613

Algebra

Give an example of a quadratic function that has zeroes at x = 2 and x = -2, and that takes the value 0 when x = 2.

Pythagorearn Feb 22, 2025

0

10

0

+613

Algebra

Suppose f is a function such that f(f(x)) = x for all x in the domain of f, and suppose that f(-3) = 0. If f(x) = ax + b, then find a and b. Find all solutions to f(x) = 5.

Pythagorearn Feb 22, 2025

0

11

0

+608

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(x - 4x^2)
What is the domain of g?

onyuIee Feb 22, 2025

0

7

0

+608

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = 5 - f(x) + f(5/x).
What is the domain of g?

onyuIee Feb 22, 2025

0

9

0

+608

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(2/x + x/2).
What is the domain of g?

onyuIee Feb 22, 2025

0

8

0

+608

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f((x + 1)(x - 2)).
What is the domain of g?

onyuIee Feb 22, 2025

0

10

0

+478

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(sqrt(x)/sqrt(-x)).
What is the domain of g?

MeIdHunter Feb 22, 2025

0

11

0

+478

Algebra

Suppose f(x) = \frac{9}{5} x - 4 + x^2. Does f have an inverse? If so, find f^{-1}(0). If not, enter "undef".

MeIdHunter Feb 22, 2025

0

7

0

+478

Algebra

Suppose f(x) = -3x^2 + 6x - 17 + 3x^2 + 2x - 14. Does f have an inverse function? If so, find f^{-1}(-41). If not, enter "undef".

MeIdHunter Feb 22, 2025

0

10

0

+478

Algebra

Suppose f(x) = \frac{1}{\sqrt{x}} + x^2 for x > 0. Does f have an inverse? If so, find f^{-1}(2). If not, enter "undef".

MeIdHunter Feb 22, 2025

0

11

0

+1000

Algebra

Functions that aren't invertible can be made invertible by restricting their domains. For example, the function $x^2$ is invertible if we restrict $x$ to the interval $[0,\infty)$, or to any subset of that interval. In that case, the inverse function is read more ..

Hi6942O Feb 22, 2025

0

12

0

+1000

Algebra

The function
f(x) = \frac{cx}{x - 1}
satisfies f(f(x)) = x for all real numbers x \neq 1. Find the value of c.

Hi6942O Feb 22, 2025

0

8

0

+1000

Algebra

Compute
(2 + 3i) + (2 - 3i) + (-2 + 3i) + (-2 - 3i).

Hi6942O Feb 22, 2025

0

10

0

+1000

Algebra

Compute 1 + i + i^2 + i^3 + i^4 + \dots + i^{2000} + \dots + i^{2025}.

Hi6942O Feb 22, 2025

0

10

0

+1800

Algebra

Express
\cfrac{1}{1 - \cfrac{1}{2 + \cfrac{1}{i}}}
in the form a+bi, where a and b are real numbers.

blackpanther Feb 22, 2025

0

9

0

+1800

Algebra

Find all complex numbers $z$ satisfying the equation
\frac{z + 1}{z - 1} = 1 + i + \frac{5 + 2i}{z}.

blackpanther Feb 22, 2025

0

12

0

+1800

Algebra

Find all complex numbers z satisfying the equation
\frac{z + 1}{z - 1} = 2 + i + \frac{-7 + 3z}{z}.

blackpanther Feb 22, 2025

0

11

0

+1800

Algebra

Find a complex number $z$ such that the real part and imaginary part of $z$ are both integers, and such that
z^2 + 2z = -53 + 8i.

blackpanther Feb 22, 2025

0

9

0

+750

Algebra

Compute (-5 + 4i) + (-5 - 4i).
Express your answer in the form $a+bi$, where $a$ and $b$ are real numbers.

siIviajendeukie Feb 22, 2025

0

7

0

+750

Algebra

Simplify (i + 1)(100) - (i - 1)(100).

siIviajendeukie Feb 22, 2025

0

11

0

+750

Algebra

Find all complex solutions to the equation z^2 = -55 - 48i + 40 + 63i.

siIviajendeukie Feb 22, 2025

0

9

0

+750

Algebra

Find all complex solutions to the equation z^3 = 8i - (15 + 2i)z^2 + (7 - 4i)z.

siIviajendeukie Feb 22, 2025

0

8

0

+977

Algebra

Find all complex numbers z such that |z - 1| = |z + 3| + |z - 2i|.

magenta Feb 22, 2025

0

10

0

+977

Algebra

For parts (a) through (d), let f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.
What is the vertex of the parabola y = f(x)?

magenta Feb 22, 2025

0

11

0

+977

Algebra

Find the solutions x of the equation
2ix^2 + x + 15i = 7ix - 4

magenta Feb 22, 2025

0

7

0

+977

Algebra

Find all solutions $x$ to the equation
5(2x + 1) + 5*2 = 5*x + 5(x + 3).

magenta Feb 22, 2025

0

5

0

+339

Algebra

Determine the set of all real x satisfying
x^2 + 3x >= -2 - 5x^2 + 10x - 13.
Enter your answer in interval notation.

jaekg Feb 22, 2025

0

16

0

+339

Algebra

Determine the set of all real x satisfying
x^3 - 2x^2 - 3x < -25x^2 + 17x.
Enter your answer in interval notation.

jaekg Feb 22, 2025

0

9

0

+339

Algebra

Determine the set of all real x satisfying
(x^2 - 5x + 3)^2 < 9 + 6x + x^2
Enter your answer in interval notation.

jaekg Feb 22, 2025

0

7

0

+339

Algebra

Find all nonzero constants $a$ such that
ax^2 + 7x + 2 = 5x^2 + 23x - 12
has only one distinct root.

jaekg Feb 22, 2025

0

5

0

+456

Algebra

Find all complex solutions to the equation z^4 = -64 - 16z^2.
Enter all the solutions in the form $a + bi$, where $a$ and $b$ are real numbers.

Jasmo Feb 22, 2025

0

8

0

+456

Algebra

Find all complex solutions to the equation z^8 + 16 = 17z^4 - 8z^6 - 8z^2.

Jasmo Feb 22, 2025

0

9

0

+456

Algebra

Determine the range of the function $(x) = -4x^2-8x-6 + 3x^2 - 17x + 10. Enter your answer in interval notation.

Jasmo Feb 22, 2025

0

9

0

+456

Algebra

Determine the range of the function g(x) = 5x^2 - 2x + 1 + 3x^2 + 20x + 18. Enter your answer in interval notation.

Jasmo Feb 22, 2025

0

10

0

+458

Algebra

Let P(x) be a polynomial of the form
P(x) = 2x^3 + ax^2 - 23x + c,
such that 12 and 7 are roots of P(x). What is the third root?

For the polynomial in part (a), compute the ordered pair (a,c).

bIueb3rry Feb 22, 2025

0

12

0

+458

Algebra

Let P(x) be a polynomial of the form
P(x) = 2x^3 + ax^2 - 23x + c,
such that 3 and 1 are roots of P(x). What is the third root?
For the polynomial in part (a), compute the ordered pair (a,c).

bIueb3rry Feb 22, 2025

0

5

1

+31

Geometry question (again)

In triangle ABC, AB=AC, and angle A is equal to 36. Point D is on AC so that BD bisects ABC.
(a) Prove that BC = BD = AD.
(b) Let x = BC and let y = CD. Using similar triangles BCD and ABC, write an equation involving x and y. read more ..

Quadrilateral PQRS is a trapezoid with bases PQ and RS. The median MN meets the diagonals PQ and QS at X and Y, respectively, with X between M and Y as shown below. Find PQ. <read more ..

Jasino Feb 22, 2025

0

9

2

+31

Geometry question

Let a and b be integer such that (2 + sqrt(5))(137) = a + b sqrt(5). Compute a^2 - 5b^2.

Jasino Feb 22, 2025

0

9

0

+458

Algebra

bIueb3rry Feb 22, 2025

0

3

1

+458

Algebra

Let (2 + \sqrt{5})(137) = a + b \sqrt{5}, where a and b are integers. Compute a^2 - 5b^2.

There are integers b, c for which both roots of the polynomial x^2 - x - 3$ are also roots of the polynomial x^3 - bx^2 - c. Determine the ordered pair (b,c).

bIueb3rry Feb 22, 2025

0

4

1

+458

Algebra

Find a monic quartic polynomial f(x) with rational coefficients whose roots include x = 1 + \sqrt{5} - 7 + \sqrt{3}. Give your answer in expanded form.

bIueb3rry Feb 21, 2025

0

12

0

+458

Algebra

bIueb3rry Feb 21, 2025

0

4

1

+6

Man im stuck pretty bad

Man im stuck pretty bad
log(y)+log(2) = log(a^(-x)+a^x) solve for x
mymilestonecard

Suppose P(x) is a polynomial of smallest possible degree such that:
* P(x) has rational coefficients.
* P(-2) = P(\sqrt{5}) = P(\sqrt{7}) = P(\sqrt{17}) = 0.
* P(-1) = 13.
Determine the value of P(0).

mymilestonecc Feb 21, 2025

0

9

0

+1729

Algebra

parmen Feb 21, 2025

0

8

0

+1729

Algebra

Find a monic quartic polynomial f(x) with rational coefficients whose roots include x = 2 - i \sqrt[3]{3}$. Give your answer in expanded form.

parmen Feb 21, 2025

0

8

1

+1729

Algebra

Let f(x) = x^3 + bx + c, where b and c are integers. If f(\sqrt{5}) = 0, determine b + c.

Find a monic quartic polynomial f(x) with rational coefficients whose roots include x = 1 - \sqrt{2} and x = 2 and x = 7. Give your answer in expanded form.

parmen Feb 21, 2025

0

9

1

+1729

Algebra

Find all roots of the polynomial
f(x) = x^4 - 5x^3 + 5x^2 + 17x - 42 + 4x^4 + 10x^3 - 18x^2 + 2x - 5.

parmen Feb 21, 2025

0

9

1

+1729

Algebra

Let p(x) be a cubic polynomial. If p(0) = 0, p(1) = 1, p(2) = 2, and p(3) = 3, then compute p(4).

parmen Feb 21, 2025

0

5

1

+1729

Algebra

Let p(x) be a polynomial with integer coefficients. Suppose p(4) = 5 and p(-2) = 3. If p(x) has an integer root r, then find all possible values of r.

parmen Feb 20, 2025

0

3

0

+1729

Algebra

parmen Feb 20, 2025

0

4

1

+1729

Algebra

Let f(x) = x^3 + ax^2 + bx + c be a polynomial. All the roots of f(x) are negative integers. If a + b + c = 10, then find the roots of f(x).

Let f(x) = x^3 + ax^2 + bx + c be a polynomial. All the roots are negative integers. If a + b + c = 10, then find c.

parmen Feb 20, 2025

0

9

0

+1729

Algebra

parmen Feb 20, 2025

0

2

1

+1729

Algebra

Find all positive integers n for which n^2 - 19n + 59 + n^2 + 4n - 31 is a perfect square.

Let f(x) be a polynomial with integer coefficients. There exist distinct integers p, q, r, s, t such that
f(p) = f(q) = f(r) = f(s) = 18
and f(t) > 18. What is the smallest possible value of f(t)?

parmen Feb 20, 2025

0

7

0

+1729

Algebra

parmen Feb 20, 2025

0

9

0

+1729

Algebra

If f is a polynomial of degree 4 such that
f(0) = 1, f(1) = 2, f(2) = -7, f(3) = 0, f(4) = 3,
then determine f(5).

parmen Feb 20, 2025

0

8

1

+1729

Algebra

The polynomial
g(x) = x^3 - 14x^2 - 67x - 90 + 5x^3 - 20x^2 + 7x - 135
has one integer root. What is it?

What is the remainder when the polynomial
g(x) = x^3 - 14x^2 - 67x - 90 + 5x^3 - 20x^2 + 7x - 135
is divided by x - 1?

parmen Feb 20, 2025

0

15

0

+1729

Algebra

parmen Feb 20, 2025

0

15

0

+1729

Algebra

Find all integers x for which x^3 = (x - 1)^3 + (x - 2)^3 + (x - 3)^3 + (x - 4)^3 + (x - 5)^3 + (x - 6)^3 + (x - 7)^3.

parmen Feb 20, 2025

0

10

0

+921

Algebra

Find all roots of the polynomial f(x) = 12x^3 - 28x^2 - 9x + 10 + 4x^3 - 40x^2 + 16x + 15.

booboo44 Feb 20, 2025

0

7

1

+921

Algebra

Find all roots of the polynomial f(x) = 3x^3 - 7x^2 - 10x + 4 + 4x^3 - 5x^2 + 18x + 28.

Find all roots of the polynomial p(x) = 12x^3 - 28x^2 - 9x + 10 + 4x^3 - 40x^2 + 16x + 15.

booboo44 Feb 20, 2025

0

8

0

+921

Algebra

booboo44 Feb 20, 2025

0

7

0

+921

Algebra

Find all roots of the polynomial p(x) = 3x^3 - 7x^2 - 10x + 4 + 4x^3 - 5x^2 + 18x + 28.

booboo44 Feb 20, 2025

0

13

0

+921

Algebra

Find all roots of the polynomial p(x) = 2x^3 - 5x^2 - 2x + 2 - 8x^3 + 11x^2 - 17x + 8.

booboo44 Feb 20, 2025

0

8

0

+921

Algebra

The polynomial
f(x) = x^3 + 10x^2 + 21x + 10 + 4x^3 - 17x^2 + 8x - 66
has one integer root. What is it?

booboo44 Feb 20, 2025

0

15

0

+458

Algebra

Find a polynomial f(x) of degree 5 such that both of these properties hold:
* f(x) is divisible by x^3.
* f(x) is divisible by (x+1)^3.
Write your answer in expanded form. read more ..

bIueb3rry Feb 20, 2025

0

12

0

+458

Algebra

Suppose the polynomial f(x) is of degree 3 and satisfies f(3) = 2, f(4) = -4, f(5) = 6, and f(8) = 8.
Determine the value of f(0).

bIueb3rry Feb 20, 2025

0

7

1

+290

Algebra

Find the range of the function
h(x) = \frac{5x^2 + 20x + 33}{x^2 + 4x - 7}.
Enter your answer in interval notation.

Find all integers n for which \frac{n^2 + n + 1}{n - 2 + n^3} is an integer.

AUnVerifedTaxPayer Feb 20, 2025

0

15

0

+290

Algebra

AUnVerifedTaxPayer Feb 20, 2025

0

12

0

+290

Algebra

Let f(x) = x^{10}+5x^9-8x^8+4x^7-x^6-33x^5+4x^4-22x^3+8x^2-3x-5.
Without using long division (which would be horribly nasty!), find the remainder when f(x) is divided by x^2 - 4.

AUnVerifedTaxPayer Feb 20, 2025

0

18

0

+290

Algebra

Let f(x) be a polynomial such that f(0) = 4, f(1) = 8, and f(2) = -6. Find the remainder when f(x) is divided by x.

AUnVerifedTaxPayer Feb 20, 2025

0

14

0

+290

Algebra

Let f(x) be a polynomial such that f(0) = 4, f(1) = 6, and f(2) = -2. Find the remainder when f(x) is divided by x.

AUnVerifedTaxPayer Feb 20, 2025

0

5

1

+290

Algebra

The polynomial
g(x) = x^3 - x^2 - (m^2 + m + 18) x + 2m^2 - 14m - 6
is divisible by x - 5 and all of its zeroes are integers. Find all possible values of m.

Find the remainder when p(x) is divided by q(x), where p(x) = x^5 + 1 and q(x) = x^2 + x + 2.

AUnVerifedTaxPayer Feb 20, 2025

0

15

0

+290

Algebra

AUnVerifedTaxPayer Feb 20, 2025

0

12

0

+290

Algebra

Given that x = 2 is a root of p(x) = x^4 - 3x^3 + 11x^2 - 25x + k for some constant k, find all the roots of p(x) (real and nonreal).
Enter your answer as a list of numbers separated by commas.

AUnVerifedTaxPayer Feb 20, 2025

0

13

0

+290

Algebra

Find an ordered pair of constants (a,b) such that the polynomial f(x)=x^3+ax^2+(b+2)x+1 is divisible by x^2-3.
Enter your answer as an ordered pair in the format $(a,b)$, where $a$ and $b$ are replaced by appropriate numbers. read more ..

AUnVerifedTaxPayer Feb 20, 2025

0

6

1

+290

Algebra

When g(x) is divided by x^2 - x - 6, the remainder is 2x + 7. What is the value of g(8)?

1. Explain/show how to find the amplitude of the function f(x)=-5 sin(x/3)-1.

2. Explain/show how to find the equation of the midline for the function f(x)=-5 sin(x/3)-1.
3. Explain/show how to find the frequency read more ..

AUnVerifedTaxPayer Feb 20, 2025

+1

6

+14

1. Explain/show how to find the amplitude of the function f(x)=-5 sin(x/3)-1.

●●●●●●

queenirene721 Feb 20, 2025

+1

8

5

+14

MATHEMATICS

1. Explain/show how to graph the function f(x)=sin(pix/3).

PLEASE HELP ME GRAPH IT TOO <33

2. In the function f(x)=cos x, f(x) is multiplied by a factor of 3, x is replaced with 4x and 5 is added to the function. read more ..

●●●●●

queenirene721 Feb 20, 2025

0

13

1

+290

Algebra

Find the quotient and remainder when p(x) is divided by q(x)$, where p(x) = x^4 - x^2 + 3x - 7 and q(x) = x^2 + 2x - 5.

Find the quotient and remainder when p(x) is divided by q(x), where p(x) = 9x^4 + x^3 - 12x + 21 and q(x) = x.

AUnVerifedTaxPayer Feb 20, 2025

0

9

1

+290

Algebra

Find the quotient and remainder when p(x) is divided by q(x), where p(x) = x^2 + 2 and q(x) = x^4 + 11x^2 - 7x + 10.

AUnVerifedTaxPayer Feb 20, 2025

0

9

1

+290

Algebra

An ellipse and a hyperbola have the same foci, $A$ and $B$, and intersect at four points. The ellipse has major axis $24,$ and minor axis $13.$ The distance between the vertices of the hyperbola is $5$. Let $P$ be one of the points of intersection read more ..

AUnVerifedTaxPayer Feb 20, 2025

0

7

1

+290

Algebra

Graph a sine function whose amplitude is 3, period is pi, midline is y=-2, and y-intercept (0,-2).

PLEASE HELP ME GRAPH IT <33

AUnVerifedTaxPayer Feb 20, 2025

-1

5

4

+14

Graph a sine function whose amplitude is 3, period is pi, midline is y=-2, and y-intercept (0,-2).

●●●●

queenirene721 Feb 20, 2025

0

5

1

+290

Algebra

Square ABCD has side length 6. An ellipse $\mathcal{E}$ is circumscribed about the square and there is a point $P$ on the ellipse such that $PC = PD = 8$. What is the area of ellipse $\mathcal{E}$? (You may assume the sides of the square are parallel to read more ..

Find the constant k so that the equation
4x^2 + 9y^2 - 8x + 54y + k = 2x^2 + 5y^2 - 12x + 34y
represents an ellipse which has an area of 6 \pi.

AUnVerifedTaxPayer Feb 20, 2025

0

9

1

+290

Algebra

Find the asymptote of the hyperbola from part (a) with positive slope.
Enter your answer as an equation of the form $y = mx + b$.
-4x^2 + y^2 - 2y = -3y^2 + 8x + 9y + 15

AUnVerifedTaxPayer Feb 19, 2025

0

15

0

+290

Algebra

AUnVerifedTaxPayer Feb 19, 2025

0

6

1

+290

Algebra

Find the vertices of the hyperbola from part (a).
-4x^2 + y^2 - 2y = -3y^2 + 8x + 9y + 15

Parts (a)-(c) refer to the graph of
-4x^2 + y^2 - 2y = -3y^2 + 8x + 9y + 15
which is a hyperbola.
Find the center of the hyperbola.

AUnVerifedTaxPayer Feb 19, 2025

0

9

1

+290

Algebra

Find the foci of the ellipse shown below.
Enter your answer as a list of ordered pairs separated by commas.
Points on the ellipse are (-4,9), (-7,2), (-5,2), (-7, 1)

AUnVerifedTaxPayer Feb 19, 2025

0

16

0

+290

Algebra

AUnVerifedTaxPayer Feb 19, 2025

0

14

0

+290

Algebra

Find the conic section represented by the equation
-x^2 + 2y^2 - 8x + 10y - 43 = 3y^2 - 17x + 14

AUnVerifedTaxPayer Feb 19, 2025

0

6

1

+290

Algebra

Find the conic section represented by the equation
4x^2 - 8y^2 - 28x + 49 = 4x^2 + 5x - 11y + 20

Find the conic section represented by the equation
5x^2 + y^2 + 10x - 4y + 17 = -4y^2 - 18x + 12y

AUnVerifedTaxPayer Feb 19, 2025

0

15

0

+290

Algebra

AUnVerifedTaxPayer Feb 19, 2025

0

9

0

+290

Algebra

Find the conic section represented by the equation
y^2 + 3x + 11y + 18 = -x^2 - 17y + 59

AUnVerifedTaxPayer Feb 19, 2025

0

9

1

+290

Algebra

Find the conic section represented by the equation
3x^2 + y^2 + 9x - 5y - 20 = 8x^2 + 6x + 47

Find the conic section represented by the equation
x^2 - 4x + y^2 = y^2 + 8x + 20

AUnVerifedTaxPayer Feb 19, 2025

0

16

0

+290

Algebra

AUnVerifedTaxPayer Feb 19, 2025

0

11

1

+1216

Number Theory

Let p be a prime. What are the possible remainders when p is divided by 11? Select all that apply.

The real numbers x and y satisfy
x^2 + y^2 - 8x + 6y + 23 = 0.
Find the largest possible value of x + y.

AnswerscorrectIy Feb 19, 2025

0

5

1

+1216

Algebra

Determine the sum of all real numbers x satisfying
(x^2 - 6x + 4)(x^2 - 8x + 5) = 1.

AnswerscorrectIy Feb 19, 2025

0

12

0

+1216

Algebra

AnswerscorrectIy Feb 19, 2025

0

6

1

+1518

Graphing question

I need help!
What is the smallest distance between the origin and a point on the graph of y = \frac{1}{\sqrt{3}} (x^2 - 7 + 2x)?

The graph of the equation
4x^2 - 12x + 4y^2 + 16y - 15 = 10x + 25y + 28
is a circle. Find the radius of the circle.

learnmgcat Feb 19, 2025

0

6

0

+958

Algebra

gnistory Feb 19, 2025

0

3

1

+958

Algebra

Find the unique pair of real numbers (x,y) satisfying
(6x^2 - 18x + 17) + (3y^2 + 6y + 11) = 28
and x + y = 20.

Enter your answer as an ordered pair in the format $(x,y)$, where $x$ and $y$ are replaced by appropriate numbers read more ..

Write a recursive rule for the explicit rule.
$a_n=(-5)^{_{n-1}}$

gnistory Feb 19, 2025

+1

10

1

+5

Write a recursive rule for the explicit rule. $a_n=(-5)^{_{n-1}}$

Determine the set of all real x satisfying
(x^2 - 5x + 3)^2 < 9 + 6x + x^2
Enter your answer in interval notation.

Graysong6 Feb 19, 2025

0

5

0

+958

Alebra

gnistory Feb 19, 2025

0

8

0

+958

Algebra

Determine the set of all real x satisfying
x^3 - 2x^2 - 3x < -25x^2 + 17x.
Enter your answer in interval notation.

gnistory Feb 19, 2025

0

8

0

+958

Algebra

Determine the set of all real x satisfying
x^2 + 3x >= -2 - 5x^2 + 10x - 13.
Enter your answer in interval notation.

gnistory Feb 19, 2025

0

10

0

+958

Algebra

Determine the range of the function g(x) = 5x^2 - 2x + 1 + 3x^2 + 20x + 18. Enter your answer in interval notation.

gnistory Feb 19, 2025

0

5

1

+958

Algebra

Determine the range of the function $(x) = -4x^2-8x-6 + 3x^2 - 17x + 10. Enter your answer in interval notation.

Suppose f(x) is a quadratic function such that f(1) = -24, f(4) = 10, and f(3) = 60.
Determine the value of f(-1).

gnistory Feb 19, 2025

0

10

1

+921

Algebra

Find all solutions $x$ to the equation
5(2x + 1) + 5*2 = 5*x + 5(x + 3).

booboo44 Feb 19, 2025

0

3

1

+921

Algebra

Find all complex solutions to the equation z^8 + 16 = 17z^4 - 8z^6 - 8z^2.

booboo44 Feb 19, 2025

0

1

+1800

Algebra

Find all complex solutions to the equation z^8 + 144 = 25z^4 + 10z^6 + 10z^2.

blackpanther Feb 19, 2025

0

15

0

+1800

Algebra

blackpanther Feb 19, 2025

0

4

1

+1800

Algebra

Find all complex solutions to the equation z^4 = -64 - 16z^2.
Enter all the solutions in the form $a + bi$, where $a$ and $b$ are real numbers.

Find the solutions x of the equation
2ix^2 + x + 15i = 7ix - 4

blackpanther Feb 19, 2025

0

15

0

+1800

Algebra

blackpanther Feb 19, 2025

0

12

0

+1800

Algebra

Find all nonzero constants $a$ such that
ax^2 + 7x + 2 = 5x^2 + 23x - 12
has only one distinct root.

blackpanther Feb 18, 2025

+1

6

1

+1800

Algebra

Find all solutions x to the equation
(x^4 + 2x^3 - 15x^2) - (4x^2 + 8x - 60) = x^4 + 10x^3 - 7x^2 - 5x - 3.

For what values of $x$ is $y = f(x)$ negative?
f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.
Enter your answer as an interval or a union of separated intervals.

blackpanther Feb 18, 2025

0

12

1

+829

Algebra

What are the $x$-coordinate(s) of all point(s) where the parabola $y = f(x)$ intersects the line $y = 0$?
f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.
Your answer should be a list of numbers and should not include variable read more ..

cooIcooIcooI17 Feb 18, 2025

+1

5

1

+829

Algebra

What is the equation of the line of symmetry of the parabola $y = f(x)$.
f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.

cooIcooIcooI17 Feb 18, 2025

+1

3

1

+829

Algebra

For parts (a) through (d), let f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7.
What is the vertex of the parabola y = f(x)?
Enter your answer as a coordinate pair, that is, as $(x,y)$ where $x$ and $y$ are replaced by read more ..

cooIcooIcooI17 Feb 18, 2025

0

11

0

+829

Algebra

cooIcooIcooI17 Feb 18, 2025

0

9

0

+829

Algebra

Complete the square: 3x^2 + 8x + 9 - 4x^2 + 25x + 19

cooIcooIcooI17 Feb 18, 2025

0

13

0

+829

Algebra

Complete the square: x^2 - 10x + 21 + 3x^2 - 2x + 8.

cooIcooIcooI17 Feb 18, 2025

0

10

0

+829

Algebra

Find all complex numbers z such that |z - 1| = |z + 3| + |z - 2i|.

cooIcooIcooI17 Feb 18, 2025

0

12

0

+829

Algebra

What is the area of the region of the complex plane defined by |z| < 3 + 2|z - 1|?

cooIcooIcooI17 Feb 18, 2025

0

13

0

+829

Algebra

Find all complex solutions to the equation z^3 = 8i - (15 + 2i)z^2 + (7 - 4i)z.

cooIcooIcooI17 Feb 18, 2025

0

9

0

+829

Algebra

Find all complex solutions to the equation z^2 = -55 - 48i + 40 + 63i.

cooIcooIcooI17 Feb 18, 2025

0

7

1

+829

Algebra

Simplify (i + 1)(100) - (i - 1)(100).

EggCHEK ●

cooIcooIcooI17 Feb 18, 2025

0

10

0

+829

Algebra

Compute (-5 + 4i) + (-5 - 4i).
Express your answer in the form $a+bi$, where $a$ and $b$ are real numbers.

cooIcooIcooI17 Feb 18, 2025

0

14

0

+829

Algebra

Find a complex number $z$ such that the real part and imaginary part of $z$ are both integers, and such that
z^2 + 2z = -53 + 8i.

cooIcooIcooI17 Feb 18, 2025

0

11

0

+829

Algebra

Find all complex numbers z satisfying the equation
\frac{z + 1}{z - 1} = 2 + i + \frac{-7 + 3z}{z}.

cooIcooIcooI17 Feb 18, 2025

0

14

0

+829

Algebra

Find all complex numbers $z$ satisfying the equation
\frac{z + 1}{z - 1} = 1 + i + \frac{5 + 2i}{z}.

cooIcooIcooI17 Feb 18, 2025

0

14

0

+829

Algebra

Express
\cfrac{1}{1 - \cfrac{1}{2 + \cfrac{1}{i}}}
in the form a+bi, where a and b are real numbers.

cooIcooIcooI17 Feb 18, 2025

0

12

0

+829

Algebra

Express (2 + i)(3 + i) in the form a + bi, where a and b a real numbers.

cooIcooIcooI17 Feb 18, 2025

0

12

0

+829

Algebra

Compute 1 + i + i^2 + i^3 + i^4 + \dots + i^{2000} + \dots + i^{2025}.

cooIcooIcooI17 Feb 18, 2025

0

8

1

+829

Algebra

Compute
(2 + 3i) + (2 - 3i) + (-2 + 3i) + (-2 - 3i).

Bosco ●

cooIcooIcooI17 Feb 18, 2025

0

12

0

+829

Algebra

Compute (-5 + 3i) + (-5 - 3i).
Express your answer in the form $a+bi$, where $a$ and $b$ are real numbers.

cooIcooIcooI17 Feb 18, 2025

0

18

0

+829

Algebra

Compute (2i-6) + (5+i), where i^2 = -1.

cooIcooIcooI17 Feb 18, 2025

0

12

0

+1729

Algebra

The function
f(x) = \frac{cx}{x - 1}
satisfies f(f(x)) = x for all real numbers x \neq 1. Find the value of c.

parmen Feb 18, 2025

0

7

0

+1729

Algebra

Functions that aren't invertible can be made invertible by restricting their domains. For example, the function $x^2$ is invertible if we restrict $x$ to the interval $[0,\infty)$, or to any subset of that interval. In that case, the inverse function is read more ..

parmen Feb 18, 2025

0

12

0

+1729

Algebra

Suppose f(x) = \frac{1}{\sqrt{x}} + x^2 for x > 0. Does f have an inverse? If so, find f^{-1}(2). If not, enter "undef".

parmen Feb 18, 2025

0

14

0

+1729

Algebra

Suppose f(x) = -3x^2 + 6x - 17 + 3x^2 + 2x - 14. Does f have an inverse function? If so, find f^{-1}(-41). If not, enter "undef".

parmen Feb 18, 2025

0

13

0

+1729

Algebra

Suppose f(x) = \frac{9}{5} x - 4 + x^2. Does f have an inverse? If so, find f^{-1}(0). If not, enter "undef".

parmen Feb 18, 2025

0

12

0

+1729

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(sqrt(x)/sqrt(-x)).
What is the domain of g?

parmen Feb 18, 2025

0

7

1

+1729

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f((x + 1)(x - 2)).
What is the domain of g?

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(2/x + x/2).
What is the domain of g?

parmen Feb 18, 2025

0

11

0

+1729

Algebra

parmen Feb 18, 2025

0

11

0

+1729

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = 5 - f(x) + f(5/x).
What is the domain of g?

parmen Feb 18, 2025

0

14

0

+1729

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(x - 4x^2)
What is the domain of g?

parmen Feb 18, 2025

0

14

0

+1729

Algebra

Suppose the domain of f is (-1,1). Define the function g by
g(x) = 5 - f(x) + f(5/x).
What is the domain of g?

parmen Feb 18, 2025

0

8

0

+1729

Function

Suppose the domain of f is (-1,1). Define the function g by
g(x) = f(x - 4x^2)
What is the domain of g?

parmen Feb 18, 2025

0

15

0

+1800

Algebra

Suppose f is a function such that f(f(x)) = x for all x in the domain of f, and suppose that f(-3) = 0. If f(x) = ax + b, then find a and b. Find all solutions to f(x) = 5.

blackpanther Feb 18, 2025

0

8

1

+1800

Algebra

Give an example of a quadratic function that has zeroes at x = 2 and x = -2, and that takes the value 0 when x = 2.

Find all values of t such that t - 1, t + 1, and 6 - t could be the lengths of the sides of a right triangle.

blackpanther Feb 18, 2025

0

13

0

+1800

Algebra

blackpanther Feb 18, 2025

0

13

0

+1800

Algebra

The domain of the function r(x) = (x^2 + 1)/(1 - x)^2 is (-infty,1) U (1,infty). What is the range?

blackpanther Feb 17, 2025

0

10

1

+1800

Algebra

The domain of the function q(x) = x^4 + 8x^2 + 7x^3 is (-infty,infty). What is the range?

The domain of the function p(x) = x^2 + 8x + 7x^3 is (-infty,infty). What is the range?

blackpanther Feb 17, 2025

0

15

0

+1800

Algebra

blackpanther Feb 17, 2025

0

12

0

+1800

Algebra

What is the range of the function g(x) = (6x + 7)(2x - 3)?

blackpanther Feb 17, 2025

0

13

0

+1800

Algebra

What is the domain of the function g(x) = (6x + 7)(2x - 3)?

blackpanther Feb 17, 2025

0

7

0

+1518

Algebra

What is the range of the function f(x) = sqrt(5 - 8x + x^2)?

learnmgcat Feb 17, 2025

0

3

0

+1518

Algebra

What is the domain of the function f(x) = sqrt(5 - 8x + x^2)?

learnmgcat Feb 17, 2025

0

8

0

+1518

Algebra

What is the domain of the function f(x) = sqrt(6x - 3 + x^2)?

learnmgcat Feb 17, 2025

0

5

0

+1518

Algebra

Find all values of x satisfying
sqrt(4x - 3) + 40/sqrt(4x - 3) = 12x + 14.

learnmgcat Feb 17, 2025

0

8

0

+1518

Algebra

Find all values of z such that z^4 - 4z^2 + 3 = 5z^2 + 11z^3 - 40.

learnmgcat Feb 17, 2025

0

4

0

+1518

Algebra

Given that
5a - 7b + 3c = 19
4a + 2b - 8c = 4
7a + 5b + 3c = -11 read more ..

learnmgcat Feb 17, 2025

0

7

0

+1518

Algebra

Solve the system of equations
5x + 3z = 1
-x + y - z = 0
2x - 3y + 7z = -4

learnmgcat Feb 17, 2025

0

11

0

+1518

Algebra

Solve the system of equations
x + y + 2z = 1
-2x - 4y + 2z = 7
10x - 17x + 13z = 8 read more ..

learnmgcat Feb 17, 2025

0

17

0

+1518

Algebra

The solutions to the equation
6x^2 + 10x = -2x^2 - 12x - 17
can be written in the form $x=\frac{P \pm \sqrt Q}{R}$, where $P$ and $R$ are relatively prime integers and $R > 0$.

learnmgcat Feb 17, 2025

0

14

0

+1518

Algebra

What are all solutions to the equation x^2 + 3x - 10 = 18x - 15?

learnmgcat Feb 17, 2025

+1

8

2

+1518

Geometry

In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.

CocoOwen ●●

learnmgcat Feb 17, 2025

+1

5

1

+5

help

A four by four grid of unit squares contains squares of various sizes (1 by 1 through 4 by 4), each of which are formed entirely from squares in the grid. In each of the 16 unit squares, write the number of squares that contain it. For instance, the middle read more ..

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

flybirdeee Feb 16, 2025

+1

6

1

+1518

Counting

Alex chooses a number at random from the set {1, 2, 3, 4, 5}. Winnie also chooses a number at random from the same set. (They can choose the same number.) What is the probability that the product of their numbers is at least 4? read more ..

learnmgcat Feb 16, 2025

0

6

1

+1518

Counting

The following cards are split into three piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
Ace of spades
Ace of hearts
Ace of diamonds read more ..

learnmgcat Feb 16, 2025

0

8

1

+1518

Counting

Let N be a positive integer. The number N has three digits when expressed in base 7. When the number N is expressed in base 18, it has the same three digits, in reverse order. What is N? (Express your answer in decimal read more ..

learnmgcat Feb 16, 2025

0

8

0

+357

Number Theory

cwimie Feb 16, 2025

0

17

0

+357

Number Theory

What is 100000_{16} * E21A8_{16} in base 16?

cwimie Feb 16, 2025

0

12

0

+357

Number Theory

Let $m$ and $n$ be positive integers. If $m$ has exactly $7$ positive divisors, $n$ has exactly $15$ positive divisors, and $mn$ has exactly $14$ positive divisors, then how many divisors does $m^2 n^2$ have?

cwimie Feb 16, 2025

0

9

1

+806

Algebra

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

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

crimefightingvigiI Feb 16, 2025

0

9

1

+806

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 $k?$

crimefightingvigiI Feb 16, 2025

0

19

0

+806

Algebra

crimefightingvigiI Feb 16, 2025

0

17

0

+806

Algebra

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

crimefightingvigiI Feb 16, 2025

0

9

0

+456

Algebra

For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.

Jasmo Feb 16, 2025

0

12

0

+456

Help algebra

Find all ordered pairs x, y of real numbers such that x+y=10 and x^3+y^3=300.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

Jasmo Feb 16, 2025

0

15

0

+456

Algebra question

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

Jasmo Feb 16, 2025

+1

6

2

+31

Trig question, help appreciated! :)

Let be an acute angle. If then what is Please use an exact answer. Thank you!

asinus ●●

Jasino Feb 15, 2025

0

15

0

+456

Algebra

Let $k$ be a positive real number. The line $x + y = 3 + k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.

Jasmo Feb 15, 2025

0

11

1

+456

Algebra

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The line is x = 4, and the equation of the circle is x^2 + y^2 = 25.

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 3 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 30 miles per hour, the trip takes 3 hours and 45 read more ..

Jasmo Feb 15, 2025

+1

9

2

+456

Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$

Jasmo Feb 14, 2025

0

7

1

+456

Algebra

mymilestonecc ●

Jasmo Feb 14, 2025

0

7

0

+456

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 ..

Jasmo Feb 14, 2025

+1

9

1

+456

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

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 $k?$

Jasmo Feb 14, 2025

0

17

0

+456

Algebra

Jasmo Feb 13, 2025

+1

11

0

+456

Number Theory

Let N be a positive integer. The number N has three digits when expressed in base 7. When the number N is expressed in base 18, it has the same three digits, in reverse order. What is N? (Express your answer in decimal read more ..

Jasmo Feb 13, 2025

0

15

0

+456

Number Theory

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.

Jasmo Feb 13, 2025

+1

12

1

+10

HELP!!!

This histogram shows the numbers of students who received each score on a 20 - point quiz. What was the mean quiz score? Express your answer as a decimal to the nearest tenth.

All members of our painting team paint at the same rate. If $10$ members can paint a $100$ square foot wall in $10$ minutes, then how long would it take the $15$ members to paint a $100$ square foot wall, in minutes?

Chiccen Feb 13, 2025

0

15

1

+456

Algebra

Seven years ago, Grogg's dad was $9$ times as old as Grogg. Four years ago, Grogg's dad was $6$ times as old as Grogg. How old is Grogg's dad currently?

Jasmo Feb 13, 2025

0

14

1

+456

Algebra

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/9 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

Jasmo Feb 13, 2025

0

12

1

+456

Algebra

The solutions to
2x^2 - 10x + 13 = -6x^2 - 18x - 15
are a+bi and a-bi, where a and b are positive. What is a\cdot b?

Jasmo Feb 13, 2025

0

10

1

+456

Algebra

I have been stumped with these question so any help will be appreciated. Thank You.
1. Link To Question 1
2. Link To Question 2
3. Link to Question 3 read more ..

Jasmo Feb 13, 2025

0

14

0

+6

Please Help, Geometry

hellohi689 Feb 13, 2025

+3

12

1

+113

algebra

what is the answer to 72x-86y=-75

Kromy ●

thatgirlaj Feb 12, 2025

0

6

1

+456

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 ..

Bosco ●

Jasmo Feb 12, 2025

0

7

2

+456

Algebra

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

Bosco ●●

Jasmo Feb 12, 2025

+1

8

1

+9

A9 multiply by b9 = 2001 .

A9 multiply by b9 = 2001 .
Find the value of A and B? A and B are single digit number.
Anyone can help?

Bosco ●

Kstartmaths Feb 12, 2025

0

10

1

+456

Algebra

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

Bosco ●

Jasmo Feb 12, 2025

0

12

1

+456

Algebra

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

The parabola $y = ax^2 + bx + c$ is graphed below. Find $a \cdot b \cdot c.$ (The grid lines are one unit apart.) read more ..

Jasmo Feb 11, 2025

0

13

1

+456

Algebra

Let $A$, $B$, and $C$ be constants so that
\frac{1}{x^3-2x^2-5x+9}=\frac{A}{x+5}+\frac{B}{x-3} + \frac{C}{(x - 3)^2}
holds for all real numbers $x$ other than $-5$ and $3.$ What is $A$?

Jasmo Feb 11, 2025

0

16

0

+456

Algebra

Jasmo Feb 11, 2025

0

15

0

+456

Algebra

Suppose $f(x)$ is a function defined for all real $x$, and suppose $f$ is invertible (that is, $f^{-1}(x)$ exists for all $x$ in the range of $f$). If the graphs of $y=f(x)$ and $y=f(x^3)$ are drawn, at how many points do they intersect?

Jasmo Feb 11, 2025

0

10

2

+456

Number Theory

How many positive four-digit integers $N$ have the property that the three-digit number obtained by removing the leftmost digit is equal to $\frac{N}{24}?$

Find the largest positive integer n such that
\frac{(n + 1)^2}{n + 2}
is an integer.

Jasmo Feb 10, 2025

0

12

1

+456

Number Theory

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.

Jasmo Feb 10, 2025

0

19

0

+456

Number Theory

Jasmo Feb 10, 2025

0

11

1

+9

Multiplication

(A9)*(b9)=2001
Find value of a and b . A and b is single digit number.

Involving the following equation: 2K + Cl2 → 2KCl
How many moles of KCl can be produced from 6 moles K?

Kstartmaths Feb 10, 2025

0

20

1

+4

Stoichiometry

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

SweetPotato Feb 9, 2025

+1

6

1

+456

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 $XY.$

Jasmo Feb 9, 2025

-2

8

1

+456

Geometry

Let ABCD be a trapezoid with bases AB and CD. Let P be a point on side CD, and let X, Y be the feet of the altitudes from P to AD, BC respectively. Prove that if AD = 5, BC = 7, AB = 6, CD = 12, and CP/PD = 1, then PX = 12*sqrt(6)/5 and PY = read more ..

Jasmo Feb 9, 2025

0

14

1

+456

Geometry

A terminal zero is a $0$ that appears at the end of a number. For example, the number $3,800$ has two terminal zeros.
How many terminal zeroes does $40 \cdot 6 \cdot 75 \cdot 12$ have?

Jasmo Feb 9, 2025

0

8

2

+456

Number Theory

The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$
What is the smallest positive integer that has exactly $2$ perfect square divisors?

Jasmo Feb 8, 2025

0

12

2

+456

Number Theory

A positive integer is called nice if it is a multiple of $6.$
A certain nice positive integer $n$ has exactly $8$ positive divisors. What is the smallest possible value of $n$?

Jasmo Feb 8, 2025

0

12

1

+456

Number Theory

A positive integer is called nice if it is a multiple of $6.$
A certain nice positive integer $n$ has exactly $8$ positive divisors. How many prime numbers are divisors of $n?$

Jasmo Feb 8, 2025

0

15

2

+456

Number Theory

A positive integer is called terrific if it has exactly 5 positive divisors. What is the smallest terrific positive integer?

Jasmo Feb 8, 2025

0

6

1

+456

Number Theory

A positive integer is called terrific if it has exactly 5 positive divisors. What is the largest number of primes that could divide a terrific positive integer?

Jasmo Feb 8, 2025

0

13

1

+456

Number Theory

A positive integer is called terrific if it has exactly 5 positive divisors. What is the smallest number of primes that could divide a terrific positive integer?

Jasmo Feb 8, 2025

0

11

1

+456

Number Theory

A new car is purchased for 25000 dollars. The value of the car depreciates at 8.25% per year. What will the value of the car be, to the nearest cent, after 15 years?

Jasmo Feb 8, 2025

+1

4

2

+5

Help

CPhill ●●

Coolpuppet390 Feb 7, 2025

0

13

1

+456

Counting

Starting with the A moving one letter at a time vertically, horizontally, or diagonally, how many different paths spell ARCH?
A
RRR
CCCCC read more ..

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?

Jasmo Feb 7, 2025

0

13

0

+456

Counting

Jasmo Feb 7, 2025

0

15

0

+456

Counting

In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving at least four pieces each?

Jasmo Feb 6, 2025

0

9

1

+456

Counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $6,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

A baking club wants to form an executive committee. There are $15$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people, not including Mark?

Jasmo Feb 6, 2025

0

17

0

+456

Counting

Jasmo Feb 6, 2025

0

14

1

+456

Algebra

Real numbers a and b satisfy
a + ab = 250
a - ab = -240
Enter all possible values of a, separated by commas.

Bosco ●

Jasmo Feb 6, 2025

0

7

1

+456

Algebra

Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

Find the largest integer k such that the equation 5x^2 - kx + 8 - 2x^2 + 25 =0 has no real solutions

Jasmo Feb 6, 2025

0

7

1

+456

Algebra

Bosco ●

Jasmo Feb 5, 2025

+1

10

2

+456

Algebra

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2.

The roots of Ax^2+Bx+1 are the same as the roots of x^2- 3x + 5 + x^2 - 2x + 1. What is A+B?

Jasmo Feb 5, 2025

0

9

1

+456

Algebra

what is the answer to 2x+86y+17=-4

Jasmo Feb 5, 2025

+3

11

1

+113

algebra

In triangle $ABC,$ $BC = 32,$ $\tan B = \frac{3}{5},$ and $\tan C = \frac{1}{4}.$ Find the area of the triangle.

thatgirlaj Feb 4, 2025

0

12

1

+1800

Geometry

In the diagram below, we have $AB = 24$ and $\angle ADB =90^\circ$. If $\sin A = \frac13$ and $\sin C = \frac12$, then what is $BC$?

blackpanther Feb 4, 2025

0

13

1

+1800

Geometry

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

blackpanther Feb 4, 2025

0

10

1

+1800

Geometry

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

blackpanther Feb 4, 2025

0

6

1

+456

Algebra

Bosco ●

Jasmo Feb 4, 2025

0

9

1

+456

Algebra

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{12}.

The system of equations \frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 1 has exactly one solution. What is $z$ in this solution?

Jasmo Feb 4, 2025

0

5

1

+456

Algebra

For what values of $j$ does the equation $(2x + 7)(x - 4) = -31 + jx$ have exactly one real solution? Express your answer as a list of numbers, separated by commas.

Jasmo Feb 4, 2025

0

8

1

+456

Algebra

Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-3x+8$.

Jasmo Feb 3, 2025

0

14

1

+456

Algebra

Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.

Jasmo Feb 3, 2025

0

7

1

+456

Algebra

Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$

Jasmo Feb 3, 2025

0

11

1

+456

Algebra

Let $x$ and $y$ be real numbers. If $x^2 + 3y^2 = 18$, then find the maximum value of $x + y$.

Jasmo Feb 3, 2025

0

12

1

+456

Algebra

Let $c$ be a real number. What is the maximum value of $c$ such that the graph of the parabola $y = -6x^2$ has at most one point of intersection with the line $y = 5x+c?$

Jasmo Feb 2, 2025

0

13

1

+456

Algebra

Find all real values of $p$ such that
(x+1)(x-2p)
has a minimum value of 0 over all real values of $x$.

Jasmo Feb 2, 2025

0

5

1

+456

Algebra

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

Jasmo Feb 2, 2025

0

20

1

+456

Algebra

Find all ordered pairs x, y of real numbers such that x+y=10 and x^2+y^2=64.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

Jasmo Feb 2, 2025

0

13

1

+456

Algebra

Simplify \dfrac{1}{\sqrt2+sqrt3}+\dfrac{1}{\sqrt2-sqrt3}.

Jasmo Feb 2, 2025

0

6

1

+456

Algebra

What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates read more ..

Jasmo Feb 2, 2025

0

11

2

+456

Algebra

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

Jasmo Feb 2, 2025

0

16

1

+456

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

Jasmo Feb 2, 2025

0

19

1

+456

Geometry

How many numbers between $1000$ and $2000$ leave a remainder of $3$ when divided by $47?$

Jasmo Feb 2, 2025

0

11

0

+456

Number Theory

Jasmo Feb 2, 2025

0

13

1

+456

Number Theory

For a positive integer n, \phi(n) denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$. What is $\phi(2835)$?

Fill in the blanks with three distinct positive integers.
1/___ + 1/___ + 1/___ = \frac{13}{12}

Jasmo Feb 2, 2025

0

6

2

+456

Number Theory

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?

Jasmo Feb 2, 2025

0

14

1

+456

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 $IJKLMN$.

Jasmo Feb 1, 2025

0

19

1

+456

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.

Jasmo Feb 1, 2025

0

20

0

+456

Geometry

Jasmo Feb 1, 2025

0

21

0

+456

Geometry

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.

Jasmo Feb 1, 2025

0

11

1

+84

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

hemiiI8675 Feb 1, 2025

0

10

1

+84

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

hemiiI8675 Feb 1, 2025

0

7

1

+84

Algebra

When the polynomial is divided by the remainder is . When the polynomial is divided by the remainder is Let be the remainder when is divided by Find read more ..

hemiiI8675 Feb 1, 2025

+1

6

3

+7

Remainder Problem Help

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends, if every friend gets at least one sticker.

singlebl Feb 1, 2025

0

7

1

+806

Counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly $7$ chocolates?

crimefightingvigiI Feb 1, 2025

0

15

1

+806

Counting

How many solutions are there to the equation
u + v + w + x + y + z = 2,
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $1?$

crimefightingvigiI Feb 1, 2025

0

13

0

+806

Counting

crimefightingvigiI Feb 1, 2025

0

19

0

+456

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

Jasmo Feb 1, 2025

0

16

1

+456

Geometry

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 66^\circ$, then what is $\angle HCA$ in degrees?

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$,
<read more ..

Jasmo Feb 1, 2025

0

18

0

+456

Geometry

Jasmo Feb 1, 2025

0

18

0

+456

Geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, read more ..

Jasmo Feb 1, 2025

+1

10

3

+31

I'm confused.

Let k be a positive real number. The line x + y = 3k and the circle x^2 + y^2 = k are drawn. Find k so that the line is tangent to the circle.
If someone could send help, it would be much appreciated! :)

Find the coordinates of the center of the circle.
The points on the circle are (22,15), (-25,0), (22,-29).

Jasino Feb 1, 2025

+1

14

1

+1216

Geometry

Determine the coordinates of the point $P$ on the line $y=-x+6$ such that $P$ is equidistant from the points $A(10,-12)$ and $O(2,8)$ (that is, so that $PA=PO$). Express your answer as an ordered pair $(a,b)$.

AnswerscorrectIy Feb 1, 2025

0

18

0

+1216

Geometry

AnswerscorrectIy Feb 1, 2025

0

18

0

+1216

Geometry

In the diagram, the four points have coordinates $A(0,1)$, $B(1,3)$, $C(5,2)$, and $D(4.5,0)$. What is the area of quadrilateral $ABCD$?

AnswerscorrectIy Feb 1, 2025

0

20

0

+1216

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

AnswerscorrectIy Feb 1, 2025

0

13

0

+1216

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

AnswerscorrectIy Feb 1, 2025

0

14

1

+216

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

At a meeting, four scientists, two mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if the mathematicians must sit next to each other? (Two seatings are considered equivalent if read more ..

BRAlNBOLT Jan 31, 2025

0

15

0

+216

Counting

BRAlNBOLT Jan 31, 2025

0

14

0

+216

Counting

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

BRAlNBOLT Jan 31, 2025

0

13

1

+806

Algebra

Let a1, a2, a3, ... be an arithmetic sequence. Let Sn denote the sum of the first n terms. If S_5 = 1/5 and S_10 = 1/10, then find S_15.

Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.

crimefightingvigiI Jan 31, 2025

0

10

1

+806

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

crimefightingvigiI Jan 31, 2025

0

14

0

+806

Algebra

crimefightingvigiI Jan 31, 2025

0

17

0

+806

Algebra

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

crimefightingvigiI Jan 31, 2025

0

20

1

+4

I NEED HELP!!!!

Can somone help me!

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

Ehaten Jan 31, 2025

0

17

0

+1216

Geometry

AnswerscorrectIy Jan 30, 2025

0

13

0

+1216

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

AnswerscorrectIy Jan 30, 2025

+1

6

2

+5

how to determine shape of conic equation?

from a general conic equation (ax^2+by^2+cx+dy+e), how would I determine whether it is a circle, ellipse, parabola, or hyperbola? i just want to know so i can solve a string of questions with varying equations.

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

taboo Jan 30, 2025

0

7

1

+448

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

MEMEG0D Jan 30, 2025

0

12

0

+448

Geometry

MEMEG0D Jan 30, 2025

0

17

0

+4

Algebra

(n(1) + n(0)) * 20.62625

dluc2 Jan 30, 2025

0

15

0

+1800

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

blackpanther Jan 30, 2025

0

13

1

+1800

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.

A circle is inscribed in a quarter-circle, as shown below. If the radius of the quarter-circle is $4,$ then find the radius of the circle.

blackpanther Jan 30, 2025

0

15

0

+1800

Geometry

blackpanther Jan 30, 2025

0

10

1

+977

Geometry

In triangle $ABC,$ $AB = 3,$ $AC = 5,$ $BC = 7,$ and $D$ lies on $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC.$ Find $\cos \angle BAD.$

In triangle $ABC,$ $BC = 32,$ $\tan B = \frac{3}{5},$ and $\tan C = \frac{1}{4}.$ Find the area of the triangle.

magenta Jan 30, 2025

0

10

1

+977

Geometry

For what value of $c$ will the circle with equation $x^2 - 10x + y^2 + 10y + c = 0$ have a radius of length 1?

magenta Jan 30, 2025

0

9

1

+977

Geometry

What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+2x-6y+3$?

magenta Jan 30, 2025

0

15

0

+977

Geometry

magenta Jan 30, 2025

0

14

0

+958

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 $XY = 15$ and $WY = 10,$ find $WX.$

gnistory Jan 30, 2025

0

11

1

+958

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 $IJKLMN$.

The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $3$ sides, then find the smallest angle, in degrees.

gnistory Jan 30, 2025

0

13

1

+958

Geometry

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 2 and QC = 3. Find sin angle PAQ.

gnistory Jan 30, 2025

0

9

1

+958

Geometry

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

gnistory Jan 29, 2025

0

14

1

+958

Geometry

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $4$ days earlier. If the job needs to be completed $20$ days earlier, how many additional workers should be hired?

gnistory Jan 29, 2025

0

16

1

+829

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 ..

cooIcooIcooI17 Jan 29, 2025

0

14

1

+829

Algebra

For a certain value of $k$, the system
x + y + 3z &= 10, \\
6x + 4y + z &= 18 - 5y - x, \\
kx + 7z &= 8 - 14y
has no solutions. What is this value of $k$?

cooIcooIcooI17 Jan 29, 2025

0

20

0

+829

Algebra

cooIcooIcooI17 Jan 29, 2025

0

19

0

+829

Algebra

Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a+2b+3c+4d+5e=47
2a+3b+4c+5d=15
3a+4b+5c=34 read more ..

cooIcooIcooI17 Jan 29, 2025

0

15

1

+806

Algebra

Assume that f(3) = 4. Name a point that must be on the graph of y= (5 + f(2x/3))/11$.

Find all points (x,y) that are 5 units away from the point (2,7) and that lie on the line x + y = 13.

crimefightingvigiI Jan 29, 2025

0

15

1

+806

Algebra

Let x \mathbin{\spadesuit} y = \frac{x^2}{y} for all x and y such that y\neq 0. Find all values of $a$ such that $a \mathbin{\spadesuit} (a + 1) = 9$. Write your answer as a list separated by commas.

crimefightingvigiI Jan 29, 2025

0

16

1

+806

Algebra

Suppose $a(x) = 2x + 5 - 3x^2 + x^3$ and $b(x) = 4 - x^2 + 4x^4$. Find $(a\circ b)(3) - (b\circ a)(3).$

crimefightingvigiI Jan 29, 2025

0

19

0

+806

Algebra

crimefightingvigiI Jan 29, 2025

+1

10

1

+921

Algebra

Find the largest integer k such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.

Let b be a constant. What is the smallest possible degree of the polynomial f(x) + b \cdot g(x), where f(x) = 2x^5 - 6x^4 - 4x^3 + 12x^2 + 7x - 5 and g(x) = x^6 - 17x^5 + 2x^4 + 6x^3 + 11x^2 - 8x + 1.

booboo44 Jan 29, 2025

+1

13

0

+921

Algebra

booboo44 Jan 29, 2025

+1

12

0

+921

Algebra

Let f be a cubic polynomial such that f(0) = 5, f(2) = 8, f(3)=13, and f(7) = -5. What is the sum of the coefficients of f?

booboo44 Jan 29, 2025

0

8

2

+24

Hard Product Problem

Evaluate
Apparently this problem also asks to answer using square roots.

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

CocoOwen Jan 29, 2025

0

17

0

+448

Algebra

MEMEG0D Jan 29, 2025

0

7

1

+448

Algebra

Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.

Let a1, a2, a3, ... be an arithmetic sequence. Let Sn denote the sum of the first n terms. If S_5 = 1/5 and S_10 = 1/10, then find S_15.

MEMEG0D Jan 29, 2025

0

20

0

+448

Algebra

MEMEG0D Jan 29, 2025

0

18

0

+448

Algebra

Let
f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.
Find the inverse $f^{-1}(x)$.

MEMEG0D Jan 28, 2025

+1

14

1

+357

Geometry

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 62^\circ$ and $\angle STU = 29^\circ$, read more ..

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 20^\circ$, then what is $\angle ABH$ in degrees?

cwimie Jan 28, 2025

+1

13

1

+357

Geometry

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 13$, $SU = 14$, $TU = 4$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

cwimie Jan 28, 2025

+1

15

1

+357

Geometry

Determine all of the following for f(x) \cdot g(x), where f(x) = -7x^4-3x^2 + 2 and g(x) = 2x^8 - 3x^7 + 5x^6 + 3x^5 - 11x^4 + 3x^3 - 18x^2 + 17x - 5.
Leading term:
Leading coefficient:
Degree: read more ..

cwimie Jan 28, 2025

+1

13

0

+1216

Algebra

AnswerscorrectIy Jan 28, 2025

+1

16

1

+1216

Algebra

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

What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 4x^2 + 8x + 7)?

AnswerscorrectIy Jan 28, 2025

+1

15

1

+1216

Algebra

What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x + 7x + 1)?

AnswerscorrectIy Jan 28, 2025

+1

19

0

+1216

Algebra

AnswerscorrectIy Jan 28, 2025

0

17

0

+339

Geometry

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

jaekg Jan 28, 2025

0

16

0

+339

Geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$,
<read more ..

jaekg Jan 28, 2025

0

12

0

+339

Geometry

Let $ABC$ be a triangle. Let $D$ be a point on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 30^\circ$, $\angle C = 90^\circ$, and $AC = 12$, then find the area of triangle $ABD$. Give your answer in exact read more ..

jaekg Jan 28, 2025

0

11

1

+339

Geometry

Point $A$ is reflected over the line shown below to point $B$. Find the coordinates of $B$.
Write your answer as an ordered pair $(x,y)$.
The line is y = x + 3, and A = (7,1).

Compute
1 + \frac{3}{6} + \frac{5}{6^2}

jaekg Jan 28, 2025

0

13

0

+1556

Algebra

kittykat Jan 28, 2025

0

13

0

+1556

Algebra

Compute
\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 12}

kittykat Jan 28, 2025

0

15

0

+1556

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{36} + \sqrt{45}} + \frac{1}{\sqrt{39} +\sqrt{96}}

kittykat Jan 28, 2025

0

12

0

+1556

Algebra

The circles $x^2 + y^2 = 4$ and $(x - 5)^2 + (y - 8)^2 = 60$ intersect in two points $A$ and $B.$ Find the distance $AB$.

kittykat Jan 28, 2025

0

14

3

+4

GEOMETRY QUESTION

A square sheet of paper has area 15. The front side is white and the back side is black. A corner of the sheet is lifted and placed so that the crease is at a 45 degree angle. If the fold is such that the visible black area is equal to the visible read more ..

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

abc234 Jan 28, 2025

0

18

1

+1216

Algebra

The solutions to
2x^2 - 10x + 13 = -6x^2 - 18x - 15
are a+bi and a-bi, where a and b are positive. What is a\cdot b?

AnswerscorrectIy Jan 28, 2025

0

18

0

+1216

Algebra

AnswerscorrectIy Jan 28, 2025

0

10

2

+1216

Algebra

Find all the solutions to
\frac{x+4}{x+5} = \frac{x-3}{2} + \frac{x + 7}{5}

The roots of Ax^2+Bx+1 are the same as the roots of (x - 2)(x + 2). What is A+B?

AnswerscorrectIy Jan 28, 2025

0

16

1

+1216

Algebra

Iampanda ●

AnswerscorrectIy Jan 28, 2025

0

16

1

+1729

Geometry

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

parmen Jan 27, 2025

0

17

0

+1729

Geometry

parmen Jan 27, 2025

0

12

1

+1729

Geometry

In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

parmen Jan 27, 2025

0

18

0

+1729

Geometry

parmen Jan 27, 2025

+1

15

1

+448

Algebra

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

MEMEG0D Jan 27, 2025

+1

14

2

+448

Algebra

what is the answer 2x-49y+21x=-7

MEMEG0D Jan 27, 2025

+4

16

1

+113

algebra

Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
PA^2 + PB^2 + PC^2 = 3PQ^2 + k.
If $A = (7,-11),$ $B = (10,13),$ and $C = (18,-22)$, then find the constant read more ..

thatgirlaj Jan 27, 2025

0

18

0

+448

Algebra

MEMEG0D Jan 27, 2025

+1

10

1

+789

Algebra

The graph of the equation
4x^2 - 12x + 4y^2 + 16y + 17 = -4x + 2y + 5
is a circle. Find the radius of the circle.

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

bingboy Jan 27, 2025

+1

15

1

+789

Algebra

In a store window, there was a box of berries having a total weight of 200 kg. The berries were 98% water, by weight. After two days in the sun, the water content of the berries was only 95%, by weight. What was the total weight of the berries read more ..

bingboy Jan 27, 2025

+1

11

0

+789

Algebra

bingboy Jan 27, 2025

0

12

1

+458

Algebra

Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If $a_1 + a_3 = 5$ and $a_2 + a_4 = 6$, then find $a_1$.

When the same constant is added to the numbers $a,$ $b,$ and $c,$ a three-term geometric sequence arises. If $a = 60,$ $b = 100,$ and $c = 140,$ what is the common ratio of the resulting sequence?

bIueb3rry Jan 26, 2025

+1

21

0

+458

Algebra

bIueb3rry Jan 26, 2025

+1

17

0

+458

Algebra

My street hockey team plays three games each week. My team lost all $9$ games in the first three weeks. Then, my team won one game and lost two games in the fourth week, bringing our record to $1$ win and $11$ losses. Each week after that, my team read more ..

bIueb3rry Jan 26, 2025

+1

5

1

+5

help plsssss

The square below is dilated by a scale factor of 44. Find the perimeter of the dilated square. Figures are not necessarily drawn to scale. the area of the square is 100. the area is 100

Let
f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?

saanvi Jan 26, 2025

0

12

1

+972

Geometry

The function $f(x)$ is defined only on domain $[-1,2]$, and is defined on this domain by the formula
f(x) = 2x^2-8x+1.
What is the range of $f(x)$? Express your answer as an interval or as a union of intervals.

Rangcr897 Jan 26, 2025

0

11

1

+972

Geometry

For certain values of k and m, the system
3a + 2b = 2
a + 2b = k - 8a - mb
has infinitely many solutions (a,b). What are k and m? read more ..

Rangcr897 Jan 26, 2025

0

11

1

+972

Geometry

Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$

Rangcr897 Jan 26, 2025

0

14

1

+972

Geometry

Let $ABC$ be a triangle. Let $X$ be a point on $\overline{AC}$ such that $\angle BXA = 90^\circ.$ If $\angle ABC = 90^\circ,$ $AX = 15,$ and $CX = 15,$ then what is $BX?$

Rangcr897 Jan 26, 2025

0

16

1

+448

Geometry

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

MEMEG0D Jan 26, 2025

0

19

1

+448

geometry

Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-3x+8$.

MEMEG0D Jan 26, 2025

0

17

1

+84

Algebra

Kromy ●

hemiiI8675 Jan 26, 2025

0

14

1

+84

Algebra

Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.

1. what is the anwer 5x+3y=12 And x-4y=7
2. what is the anwer 6x+2y=-12 And 4x3y=7
3. what is the anwer 4x-6y=26 And 5x-4y=8
4.what is the answer 5x+3y=13 And -7x-8y=16 read more ..

hemiiI8675 Jan 26, 2025

+3

11

1

+113

Algebra

For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are 1 - 12x + 54x^2 + cx^3 + ... Find c.

thatgirlaj Jan 26, 2025

0

22

1

+84

Algebra

The cost of 2 bottle of water(w) and 4 apples(a) is 4.50. The cost of 3 bottles of water and 5 apples is 7.50. Write a system of equations to model the situation. what is the answer ???

hemiiI8675 Jan 25, 2025

+2

16

1

+113

algebra

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

thatgirlaj Jan 25, 2025

0

7

1

+1518

Geometry

The perimeter of a rectangle is $40,$ and the length of one of its diagonals is $10 \sqrt{2}.$ Find the area of the rectangle.

learnmgcat Jan 25, 2025

0

15

1

+1518

Geometry

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $90^\circ.$ Find the area of the rhombus.

learnmgcat Jan 25, 2025

0

15

1

+1518

Geometry

In quadrilateral $PQRS$, $PQ = QR = RS = SP$, $PR = \sqrt{2}$, and $QS = \sqrt{2}$. Find the perimeter of $PQRS$.

learnmgcat Jan 25, 2025

0

12

1

+1518

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

learnmgcat Jan 25, 2025

0

12

1

+458

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

bIueb3rry Jan 25, 2025

0

12

0

+458

Geometry

bIueb3rry Jan 25, 2025

0

19

0

+458

Geometry

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

bIueb3rry Jan 25, 2025

+1

7

2

+31

Help please! :)

Let G be the center of equilateral triangle A dilation centered at G with scale factor -7/5 is applied to triangle XYZ to obtain triangle X'Y'Z' Let A be the area of the region that is contained inside both triangles XYZ and X'Y'Z Find read more ..

Triangle ABC is rotated completely around side BC, sweeping out a solid in space. Find the volume of the solid.
AB = 8, AC = 12, CB = 8

Jasino Jan 25, 2025

0

18

1

+806

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BZ$.

crimefightingvigiI Jan 25, 2025

0

16

0

+806

Geometry

crimefightingvigiI Jan 25, 2025

0

18

0

+806

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BC$.

crimefightingvigiI Jan 25, 2025

0

15

1

+806

Geometry

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

crimefightingvigiI Jan 25, 2025

0

16

2

+806

Geometry

A ski slope is 250 yards long with a vertical drop of 100 yardsfind the angle of depression of the slope?

crimefightingvigiI Jan 25, 2025

+2

13

2

+113

algebra

Let and . The function represents a reflection in the complex plane. Find the line that reflects over.
Give your answer simplified in the form where and . read more ..

thatgirlaj Jan 25, 2025

+1

10

1

+30

Complex Number Geometry I

gnistory ●

Chadly Jan 24, 2025

0

18

3

+81

math

If CPhill can dice 100 onions in 2.5 minutes, how many onions can he dice in the month of February 2028? (assume he is constantly dicing)

Find the inradius of triangle ABC.

nerdboy Jan 24, 2025

+1

16

1

+977

Geometry

Find the circumradius of triangle ABC.

magenta Jan 24, 2025

0

15

1

+977

Geometry

If you randomly threw the 26 letters of the alphabet into the air, how many times would you need to throw them before they landed in order A-Z?
And if you allowed 1 1/2 seconds between each throw, how many years would it take? I understand read more ..

magenta Jan 24, 2025

0

12

2

+4

question 26

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 14$, $AY = 14$, and $CY = 8$, find $BC$.

medonnieoscar Jan 24, 2025

0

17

1

+829

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 14$, $AY = 14$, and $CY = 8$, find $BZ$.

cooIcooIcooI17 Jan 24, 2025

0

14

1

+829

Geometry

Find the area of triangle $ABC$ if $AB = 6,$ $BC = 8,$ and $\angle ACB = 90^\circ$

cooIcooIcooI17 Jan 24, 2025

0

14

1

+829

Geometry

Find all real numbers a that satisfy \frac{1}{64a^3 + 7} - 7 = 0.

cooIcooIcooI17 Jan 24, 2025

0

11

1

+1271

Algebra

Find the coefficient of y^4 in the expansion of (2y-5+3y^2)^6.

Akhain1 Jan 24, 2025

0

9

1

+1271

Algebra

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab^2 = 4. What is the value of b in this ordered pair? (Note: you may have to use the Tab key to get your cursor into the middle answer box.)

Akhain1 Jan 24, 2025

0

8

2

+1271

Algebra

CPhill ●●

Akhain1 Jan 24, 2025

0

10

1

+4

Complex Analysis

follow the technique outlined in the text to find all solutions of the given equation $(z+1)^4 = (1-i)$
This is from Complex Variables by Stephen Fisher Question 24 from section 1.2. I am a bit unsure how to answer this if someone could help read more ..

Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3
q - 2r = -2 + q
p + r = 9 + p read more ..

laureltree Jan 24, 2025

0

9

3

+1271

Algebra

CPhill ●●●

Akhain1 Jan 24, 2025

+1

14

1

+750

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

Find the value of $v$ such that $\frac{-21-\sqrt{201}}{10}$ a root of $5x^2+21x+v = 0$.

siIviajendeukie Jan 23, 2025

0

14

1

+750

Algebra

Iampanda ●

siIviajendeukie Jan 23, 2025

0

10

1

+750

Algebra

For what values of $j$ does the equation $(2x + 7)(x - 4) = -31 + jx$ have exactly one real solution? Express your answer as a list of numbers, separated by commas.

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.

siIviajendeukie Jan 23, 2025

0

12

1

+750

Algebra

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

siIviajendeukie Jan 23, 2025

0

14

1

+750

Algebra

Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

siIviajendeukie Jan 23, 2025

0

13

1

+750

Algebra

At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if each scientist must sit next to a mathematician? (Two seatings are considered equivalent read more ..

siIviajendeukie Jan 23, 2025

0

18

0

+413

Counting

nathanl6656 Jan 23, 2025

0

19

0

+413

Counting

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

nathanl6656 Jan 23, 2025

0

12

1

+413

Counting

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are read more ..

What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates read more ..

nathanl6656 Jan 23, 2025

0

18

1

+608

Geometry

In triangle $ABC,$ $AB = 3,$ $AC = 5,$ $BC = 7,$ and $D$ lies on $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC.$ Find $\cos \angle BAD.$

onyuIee Jan 23, 2025

0

19

1

+608

Geometry

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

onyuIee Jan 23, 2025

0

5

1

+608

Geometry

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

onyuIee Jan 23, 2025

0

17

0

+608

Geometry

onyuIee Jan 23, 2025

0

16

1

+613

Geometry

In triangle $ABC,$ $BC = 32,$ $\tan B = \frac{3}{5},$ and $\tan C = \frac{1}{4}.$ Find the area of the triangle.

In the diagram below, we have $AB = 24$ and $\angle ADB =90^\circ$. If $\sin A = \frac13$ and $\sin C = \frac12$, then what is $BC$?

Pythagorearn Jan 23, 2025

0

16

1

+613

Geometry