All Questions ⁺⁰234620 Questions

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+1694

Algebra

A mathematician works for t hours per day and solves p problems per hour, where and are positive integers. One day, the mathematician drinks some coffee and discovers that he can now solve 4p+5 problems per hour. In fact, he only works read more ..

ABJeIIy Jul 24, 2024

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4

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+1694

Algebra

Real numbers A and B satisfy: a + ab^2 = 250b, a - ab^2 = -240b enter all values of a, separated by commas.

ABJeIIy Jul 24, 2024

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5

2

+1694

Algebra

All members of our painting team paint at the same rate. If 20 members can paint a 2000 square foot wall in 40 minutes, then how long would it take the 20 members to paint a 6000 square foot wall, in minutes?

ABJeIIy Jul 24, 2024

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3

+1341

Number Theory

Find the remainder when $100^{100}$ is divided by $18$.

kittykat Jul 24, 2024

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+1341

Number Theory

Let $a$ be an integer such that $0 \le a \le 10$ and $a^2 \equiv a \pmod{11}$. If $a \neq 0,$ then find the value of $a$.

kittykat Jul 24, 2024

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+1341

Number Theory

Let $a$ be an integer such that $a \equiv 5 \pmod{7}$. Find the value of $a + 1 \pmod{7}$. Express your answer as a residue between $0$ and the modulus.

kittykat Jul 24, 2024

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+1341

Number Theory

Which of the residues $0,$ $1,$ $2,$ $3,$ $4$ satisfy the congruence $3x \equiv 0 \pmod{5}?$
Give your answer as a list, separated by commas, in order from least to greatest.

kittykat Jul 24, 2024

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+617

Number Theory

John and Ling start their new jobs on the same day. John's schedule is six workdays followed by one day off. Ling's schedule is seven workdays followed by one day off. On how many days during their first year of work ($365$ days) read more ..

AnswerscorrectIy Jul 24, 2024

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7

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+617

Number Theory

When $N$ is divided by $10$, the remainder is $a$. When $N$ is divided by $2$, the remainder is $b$. What is $N$ modulo $20$, in terms of $a$ and $b$?

AnswerscorrectIy Jul 24, 2024

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+4

Algebra

How many points of the form , where both coordinates are positive integers, lie below the graph of the hyperbola ?
Thanks in advance!

BioGrinder Jul 24, 2024

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+303

Number Theory

An eccentric baseball card collector wants to distribute her collection among her descendants. If she divided her cards among her $13$ great-great-grandchildren, there would be $8$ cards left over. If she divided her cards among her $10$ great-grandchildren, read more ..

onyuIee Jul 24, 2024

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+303

Number Theory

Carlos wants to send Cecil a message encrypted with RSA. Cecil has published his public encryption exponent $3$ and his public modulus $3$. When Carlos encrypts the number $3$ with this system, what is the result?

onyuIee Jul 24, 2024

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+303

Number Theory

The House of Lilliput is using RSA encryption to receive secret messages from all the realms. They have published their public encoding exponent $e = 8$ and their public modulus $M = pq = 6$.
Break the code: Find their secret decoding read more ..

onyuIee Jul 24, 2024

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+303

Algebra

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

NotThatSmart ●

onyuIee Jul 24, 2024

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6

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+303

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 $k?$

onyuIee Jul 24, 2024

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+303

Algebra

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

onyuIee Jul 24, 2024

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+303

Algebra

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

NotThatSmart ●

onyuIee Jul 24, 2024

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+303

Algebra

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 ..

NotThatSmart ●

onyuIee Jul 24, 2024

Jul 23, 2024

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+303

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?

NotThatSmart ●

onyuIee Jul 23, 2024

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+303

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 $(a,b)$.

onyuIee Jul 23, 2024

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