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All Questions
^{+0}
234575 Questions
0
2
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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
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ABJeIIy
Jul 24, 2024
0
4
0
+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
0
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?
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ABJeIIy
Jul 24, 2024
0
1
3
+1341
Number Theory
Find the remainder when $100^{100}$ is divided by $18$.
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kittykat
Jul 24, 2024
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2
2
+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 $a$.
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kittykat
Jul 24, 2024
0
3
1
+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.
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kittykat
Jul 24, 2024
0
1
2
+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.
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kittykat
Jul 24, 2024
0
2
1
+601
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)
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AnswerscorrectIy
Jul 24, 2024
0
6
0
+601
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
0
1
4
+4
Algebra
How many points of the form , where both coordinates are positive integers, lie below the graph of the hyperbola ?
Thanks in advance!
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BioGrinder
Jul 24, 2024
0
7
0
+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,
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onyuIee
Jul 24, 2024
0
5
0
+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
0
7
0
+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
0
4
1
+303
Algebra
Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.
NotThatSmart
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onyuIee
Jul 24, 2024
0
5
0
+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
0
4
1
+303
Algebra
What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?
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onyuIee
Jul 24, 2024
0
2
1
+303
Algebra
Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5.
NotThatSmart
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onyuIee
Jul 24, 2024
0
1
1
+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
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onyuIee
Jul 24, 2024
Jul 23, 2024
0
3
1
+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
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onyuIee
Jul 23, 2024
0
1
1
+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 $(a,b)$.
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onyuIee
Jul 23, 2024
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