All Questions ⁺⁰234646 Questions

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Arithmetic sequences

When the same constant is added to the numbers 60, 100 and 165 a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

ABJelly Apr 9, 2024

+1

25

2

+273

help me please!!

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

ABJelly Apr 9, 2024

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11

1

+273

please help

In a geometric sequence, the 23rd term is 26 and the 26th term is 12. What is the 32nd term?

ABJelly Apr 9, 2024

+1

12

1

+273

Arithmetic sequences

In an arithmetic sequence, the 23rd term is and the 35th term is . What is the 48th term?

ABJelly Apr 9, 2024

0

12

1

+251

Counting

A baking club wants to form an executive committee. There are $18$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people?
A baking club wants to form read more ..

fjeihqoO Apr 9, 2024

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17

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Counting

I run a book club with $n$ people, not including myself. Every day, for $100$ days, I invite $14$ members in the club to review a book. What is the smallest positive integer $n$ so that I can avoid ever having the exact same group of $14$ members read more ..

fjeihqoO Apr 9, 2024

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22

0

+251

Counting

In how many ways can $4$ balls be placed in $8$ boxes if the balls and boxes are both distinguishable?
In how many ways can $4$ balls be placed in $8$ boxes if neither the balls nor the boxes are distinguishable?
In read more ..

fjeihqoO Apr 9, 2024

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13

1

+251

Domain

Let
f(x) = \frac{2x + 3}{x^2 + 7}.
Find the domain of $f$. Give your answer using interval notation.

fjeihqoO Apr 9, 2024

Apr 8, 2024

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17

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+21

Combinatorics

Let S = {1, 2, . . . , 2021}, and let F denote the set of functions f : S → S. For a function f ∈ F, let Tf = f 2021(s) : s ∈ S , where f 2021(s) denotes f(f(· · ·(f(s))· · ·)) with 2021 copies of f. Compute the remainder when sigma notation f∈F read more ..

Sxchen1110 Apr 8, 2024

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8

2

+21

Geometry

Let ABTCD be a convex pentagon with area 22 such that AB = CD and the circumcircles of triangles TAB and TCD are internally tangent. Given that ∠ATD = 90◦ , ∠BTC = 120◦ , BT = 4, and CT = 5, compute the area of triangle TAD.

Sxchen1110 Apr 8, 2024

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23

2

+251

Geometry

In triangle $ABC,$ $AB = 15,$ $BC = 10,$ and $AC = 12.$ Find the length of the shortest altitude in this triangle.

fjeihqoO Apr 8, 2024

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12

3

+251

Geometry

Find the area of triangle $ABC$ if $AB = 6,$ $BC = 8,$ and $\angle ACB = 30^\circ$.

fjeihqoO Apr 8, 2024

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9

2

+251

Geometry

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

fjeihqoO Apr 8, 2024

+2

7

3

+35

Help Please

Problem 1
Arpit has 184756 penguins that waddle a unique lattice path from (0,0) to (10,10) on the coordinate plane (penguins only take unit length steps up or to the right). Arpit also has many penguin counters that read more ..

Mather459 Apr 8, 2024

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16

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+251

Algebra

Find the domain of the function $f(x)=\frac{2x-7}{\sqrt{x^2}} - \sqrt{5x+6-11}$.

fjeihqoO Apr 8, 2024

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7

2

+251

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?

fjeihqoO Apr 8, 2024

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14

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+251

Algebra

Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

fjeihqoO Apr 8, 2024

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34

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+1212

Geometry

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

Akhain1 Apr 8, 2024

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12

2

+51

conditions

Find the number of positive integers that satisfy both the following conditions:
Each digit is a 1 or a 3
The sum of the digits is 12
I got 3, its not correct. help is appreciated read more ..

hairyberry ●●

fjeihqo0 Apr 8, 2024

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12

1

+51

help plz

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row?
I got 36, its not right i cant figure out why

fjeihqo0 Apr 8, 2024

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19

2

+16

Cartesian plane question

Question:
Find the equation whose graph is shown below. Write your answer in standard form.
(Standard form is A (x) + B (y) =C, where A is positive, and A, B, and C are integers with the greatest common divisor 1.)
It read more ..

hairyberry ●●

Seraphspace Apr 8, 2024

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20

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+16

Cartesian plane question

Write the equation of the line below in the form A(x) + B(x) = C, where A, B, and C are integers with greatest common divisor 1, and A is positive.
The line consists of two known points: (-4, 2) and (1, -1)

Seraphspace Apr 8, 2024

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14

2

+16

Cartesian plane question

A line passes through the points A, B, and C. Find y.
A = (-3, 5)
B = (1, -2)
C = (6, y) read more ..

Seraphspace Apr 8, 2024

0

17

1

+16

Cartesian plane question

Question:
Find the equation whose graph is shown below. Write your answer in standard form.
(Standard form is A (x) + B (y) =C, where A is positive, and A, B, and C are integers with the greatest common divisor 1.) read more ..

Seraphspace Apr 8, 2024

0

16

1

+1212

Geometry

In triangle $ABC$, $AB = 10$ and $AC = 15$. Let $D$ be the foot of the perpendicular from $A$ to $BC$. If $BD:CD = 1:3$, then find $AD$.

Akhain1 Apr 8, 2024

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