All Questions ⁺⁰230829 Questions

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Counting

A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile read more ..

bader Apr 18, 2024

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+866

Counting

At a meeting, 4 mathematicians, 3 scientists, and 2 journalists are to be seated around a circular table. How many different arrangements are possible if every mathematician must sit next to a scientist? (Two seatings are considered equivalent if one read more ..

ABJeIIy Apr 18, 2024

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+1588

Algebra

In Linguistics $101,$ the ratio of the number of juniors to the number of seniors is $3:2$. When $6$ more juniors join the class, and $1$ senior drops the class, the ratio of the number of juniors to the number of seniors becomes $18:7$. How read more ..

bader Apr 18, 2024

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+866

Geometry

A line and a circle intersect at and as shown below. Find the distance between and .
The circle is x^2 + y^2 = 20.
The line is y = -4.

ABJeIIy Apr 18, 2024

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+866

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

ABJeIIy Apr 18, 2024

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3

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+866

Geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

ABJeIIy Apr 18, 2024

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2

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+866

Geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

ABJeIIy Apr 18, 2024

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+866

Geometry

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

ABJeIIy Apr 18, 2024

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+359

Inequality

Solve the inequality -4(x + 4) > x + 7 + 8x + 21.

ChiIIBill Apr 18, 2024

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+359

Inequality

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $500$ pounds more than each of her trucks, but no more than $\frac{1}{4}$ of the total load her four trucks combined can carry. read more ..

ChiIIBill Apr 18, 2024

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+359

Inequality

Solve the inequality 2x - 5 <= -x + 12 - 7x + 18.

ChiIIBill Apr 18, 2024

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+6

Hard Math geometry problem

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 ,
If ,and , then find the constant K.
This is hard but please give me an answer read more ..

TX4181941 Apr 18, 2024

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+1588

Algebra

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $7$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $2$ times as much money as read more ..

bader Apr 18, 2024

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+1588

Algebra

One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 48$ and $a^2 = 24$. What is the value of $b$ in this ordered pair?

bader Apr 18, 2024

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+1588

Algebra

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

bader Apr 18, 2024

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+1588

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?

bader Apr 18, 2024

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+359

Algebra

Let $a$ and $b$ be the roots of the quadratic equation $2x^2 - 7x + 2 = -x^2 + 4x + 9.$ Find $\frac{1}{a-1}+\frac{1}{b-1}.$

ChiIIBill Apr 18, 2024

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+359

Algebra

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

ChiIIBill Apr 18, 2024

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+359

Algebra

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $8$ days earlier. If the job needs to completed $28$ days earlier, how many additional workers should be hired?

ChiIIBill Apr 18, 2024

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3

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+1588

Geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

bader Apr 18, 2024

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3

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+1588

Geometry

In the diagram, $\overline{CX}$ bisects $\angle ACB$. Find the ratio of the area of triangle $BCX$ to the area of triangle $ACX$. Express your answer as a common fraction. read more ..

bader Apr 18, 2024

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+1588

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

bader Apr 18, 2024

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+16

Algebra

For every integer n≥1, let P(n) denote the product of the first n odd numbers:
P(n)=1×3×5×⋯×(2n−1)
Prove that for all integers n≥1, P(n)=(2n)!/2^n×n!.

Sxchen1110 Apr 18, 2024

Apr 17, 2024

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+359

Algebra

All members of our painting team paint at the same rate. If $50$ members can paint a $3600$ square foot wall in $20$ minutes, then how long would it take for $25$ members to paint a $4000$ square foot wall, in minutes?

ChiIIBill Apr 17, 2024

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+359

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 ..

ChiIIBill Apr 17, 2024

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