jaekg

50 Questions
17 Answers

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Algebra

Simplify (1 - 3i)(2 - i)(2 + i + 1 + 3i).

jaekg Oct 31, 2024

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2

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Algebra

Find the number of ordered pairs (m,n) of integers that satisfy
mn = 3m + 6n + 2m - 5n + 1.

jaekg Oct 31, 2024

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3

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Algebra

Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-3x+8$.

jaekg Oct 31, 2024

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2

1

+227

Algebra

Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.

jaekg Oct 31, 2024

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3

0

+227

Algebra

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

jaekg Oct 31, 2024

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

jaekg Oct 29, 2024

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Number Theory

Which of the residues $0,$ $1,$ $2,$ $\dots,$ $11$ satisfy the congruence $3x \equiv 8 \pmod{5}?$
Give your answer as a list, separated by commas, in order from least to greatest.

jaekg Oct 29, 2024

0

2

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+227

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + 2 + \frac{2}{5} + \frac{2}{5^3} + \frac{2}{5^4}

jaekg Oct 20, 2024

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2

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+227

Algebra

Let $x$ and $y$ be complex numbers. If $x + y = 2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

jaekg Oct 20, 2024

0

2

0

+227

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{39} + \sqrt{40}} + \frac{1}{\sqrt{40} +\sqrt{45}}

jaekg Oct 20, 2024