All Questions ⁺⁰236027 Questions

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Help Fast!

Let x,y,z be nonzero real numbers, such that no two are equal, and

Find all possible numeric values of xyz
I got 1 as one of the answers.

MeldHunter Jul 23, 2024

+1

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+1938

Hi EP!

This is off-topic, but Hello EP! It's been a while!
I sound like an idiot right now, but I had an old account back in the days, and that account had MANY questions answered by EP!
Just sayin hello! Good to see you!
Also, read more ..

●●●●●●●●

NotThatSmart Jul 23, 2024

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14

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+510

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 $ABCD$?

onyuIee Jul 23, 2024

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23

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+510

Counting

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

onyuIee Jul 23, 2024

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20

1

+510

Number Theory

What is the fifth smallest prime number greater than 100?

NotThatSmart ●

onyuIee Jul 23, 2024

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15

3

+510

Number Theory

Jon teaches a fourth grade class at an elementary school where class sizes are always at least 10 students and at most 15. One day Jon decides that he wants to arrange the students in their desks in a rectangular grid with no gaps. Unfortunately read more ..

ElectricPavlov ●●●

onyuIee Jul 23, 2024

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20

0

+510

Number Theory

What are the first 5 digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{7}$ is written in base $16$?

onyuIee Jul 23, 2024

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18

1

+478

Number Theory

What is the largest positive integer $n$ such that $1457$, $1797$, $709$, $15$, $24$, $197$, $428$ all leave the same remainder when divided by $n$?

ChiIIBill Jul 23, 2024

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19

1

+478

Number Theory

If n \equiv 43 \pmod{165}, then what is the residue of $n$ modulo 2?

ChiIIBill Jul 23, 2024

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19

1

+478

Number Theory

A four-digit hexadecimal integer is written on a napkin such that the units digit is illegible. The first three digits are $7$, $D$, and $3$. If the integer is a multiple of $25_{10}$, what is the units digit?

ChiIIBill Jul 23, 2024

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12

1

+478

Number Theory

How many lattice points (points with integer coordinates) are on the line segment whose endpoints are $(3,17)$ and $(82,150)?$ (Include both endpoints in your count.)

NotThatSmart ●

ChiIIBill Jul 23, 2024

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+862

Algebra

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

magenta Jul 23, 2024

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+862

Algebra

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

magenta Jul 23, 2024

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16

1

+862

Algebra

Sophie's favorite (positive) number is a two-digit number. If she reverses the digits, the result is 72 less than her favorite number. Also, one digit is 1 less than double the other digit. What is Sophie's favorite number?

NotThatSmart ●

magenta Jul 23, 2024

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14

1

+862

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 ..

magenta Jul 23, 2024

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15

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+510

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 ..

onyuIee Jul 23, 2024

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20

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+510

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 ..

onyuIee Jul 23, 2024

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14

1

+510

Counting

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 ..

onyuIee Jul 23, 2024

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22

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+948

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest number of primes that could divide a terrific positive integer?

Rangcr897 Jul 23, 2024

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15

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+948

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest terrific positive integer?

Rangcr897 Jul 23, 2024

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1

+948

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 $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim read more ..

Rangcr897 Jul 23, 2024

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11

3

+54

Geometry

How many lattice points (points with integer coordinates) are on the line segment whose endpoints are (3, 17) and (81, 131) (Include both endpoints in your count.).
I know that the slope is 19/13, but what do I do next?

NotThatSmart ●●●

AUnVerifiedTaxPayer Jul 23, 2024

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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 ..

Hi6942O Jul 23, 2024

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10

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+976

Geometry

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

Hi6942O Jul 23, 2024

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14

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+976

Geometry

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

Hi6942O Jul 23, 2024

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