All Questions ⁺⁰231021 Questions

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hey guys

I run a book club with z people, not including myself. Every day, for 400 days, I invite 5 members in the club to review a book. What is the smallest positive integer z so that I can avoid ever having the exact same group of 5 members over all 400 days read more ..

fjeihqo0 Mar 30, 2024

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+52

How are linear velocity and angular velocity related?

How are linear velocity and angular velocity related?
Drag a word, phrase, or equation into each box to correctly complete the statements.
Angular velocity is the change in distance over time, where distance is _____.
Angular read more ..

xXValeXx Mar 30, 2024

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+987

help with triangle

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If $PQ = 36$, $PM read more ..

Akhain1 Mar 30, 2024

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+1050

Sequence

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

kittykat Mar 30, 2024

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+1050

Algebra

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

kittykat Mar 30, 2024

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+1050

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

kittykat Mar 30, 2024

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+1050

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

kittykat Mar 30, 2024

Mar 29, 2024

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+987

Polynomials

Let $f(x) = x^3 + 3x^2 + 4x - 7$ and $g(x) = 2x^8 - 8x^7 + 4x^6 - x^5$. What is the coefficient of $x^2$ in the sum $f(x) + g(x)$?

Akhain1 Mar 29, 2024

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+987

Polynomials

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 $g(x) = x^15 - 3x^14 - 2x^13 - 6x^12 + 14x - 10$?

Akhain1 Mar 29, 2024

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+987

Algebra

Let $f$ be a cubic polynomial such that $f(0) = 0$, $f(1) = 0$, $f(2) = 0$, and $f(3)=0$. What is the sum of the coefficients of $f$?

Akhain1 Mar 29, 2024

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+987

Polynomials

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

Akhain1 Mar 29, 2024

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+987

Triangle

Altitudes $\overline{AP}$ and $\overline{BQ}$ of an acute triangle $\triangle ABC$ intersect at point $H$. What is the area of triangle $ABC$?

Akhain1 Mar 29, 2024

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+987

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 ..

Akhain1 Mar 29, 2024

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+64

Geometric Sequence

A geometric sequence has 400 terms. The first term is 1000 and the common ratio is -1/3 How many terms of this sequence are greater than 1?

SilviaJendeukie Mar 29, 2024

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+4

Help Please

The equation has exactly two different complex solutions. Find all possible complex values for .
Basically I expanded it and stuff and then made a quadratic and used the discriminant to get . So . But the problem wants all complex read more ..

somebodyrandom Mar 29, 2024

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+987

help angles

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 ..

Akhain1 Mar 29, 2024

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+987

Geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

Akhain1 Mar 29, 2024

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+987

Angles

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?

Akhain1 Mar 29, 2024

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+987

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 $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$,
<read more ..

Akhain1 Mar 29, 2024

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+987

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 ..

Akhain1 Mar 29, 2024

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+987

help coordinates

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

Akhain1 Mar 29, 2024

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