HumanBemg

35 Questions
3 Answers

-1

2

1

+146

Geometry

Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of triangle ABC?
A is at (0,0), B is at (1,0), and C is at (1,1).

HumanBemg 5 апр. 2025 г.

+1

1

1

+146

Geometry

In \triangle ABC, we have AB = AC = 4 and \angle BAC = 45^\circ. If M is the midpoint of BC, then find AM^2.

HumanBemg 5 апр. 2025 г.

+1

1

1

+146

Geometry

What is the equation of the reflection of the line y = 2x + 1 across the line y = 5x - 3? Give your answer in slope-intercept form.

HumanBemg 5 апр. 2025 г.

0

1

0

+146

Algebra

The function f : \mathbb{R} \rightarrow \mathbb{R} satisfies
xf(x) + f(1 - x)/x = x^3 + 3x^2 + 14x - 13
for all real x. Find f(x).

HumanBemg 1 апр. 2025 г.

0

1

0

+146

Algebra

Find all x such that
(2x)^{\log_{10} 2} = (9x)*{\log_{10} 9} + (5x)^{\log_{10} 9} + \log_x 243

HumanBemg 29 мар. 2025 г.

0

1

0

+146

Algebra

Let r_1, r_2, r_3, r_4, and r_5 be the complex roots of x^5 - 4x^2 + 7x - 1 = 0. Compute
(r_1^2 + r_1^6 + 2)(r_2^2 + r_2^6 + 2)(r_3^2 + r_3^6 + 2)(r_4^2 + r_4^6 + 2)(r_5^2 + r_5^6 + 2)

HumanBemg 29 мар. 2025 г.

0

2

0

+146

Algebra

Suppose f(x) is a rational function such that
3 f \left( \frac{1}{x} \right) - \frac{f(x)}{x} = x
for all $x \neq 0$. Find f(-2).

HumanBemg 27 мар. 2025 г.

0

3

0

+146

Algebra

Let F(x) be the real-valued function defined for all real x except for x = 1 and x = 2 and satisfying the functional equation
F(x) + F \left( \frac{2x - 3}{x - 1} \right) + F \left( \frac{1}{x} \right) = x.
Find the function F(x) satisfying прочитайте больше ..

HumanBemg 27 мар. 2025 г.

0

2

0

+146

Algebra

The function f(n) is defined for all integers n, such that
f(x) + f(y) = f(x + y) - 4xy - 1 + f(x^2) + f(y^2)
for all integers x and y, and f(1) = 1. Find f(n).

HumanBemg 27 мар. 2025 г.

0

2

0

+146

Algebra

The function f(n) takes the integers to the real numbers such that
f(m + n) + f(m - n) = 2f(m) + 2f(n) + mn
for all integers m and n, and f(1) = 2. Find f(n).

HumanBemg 27 мар. 2025 г.

0

2

0

+146

Algebra

Find the largest value of x where the plots of
f(x) = - \frac{2x + 5}{x + 3} and g(x) = \frac{12}{x - 1}
intersect.

HumanBemg 25 мар. 2025 г.

0

1

0

+146

Algebra

Fill in the blanks with constants, to make a true equation:
\frac{x^2 - 6x - 3}{x^3 - 4x} = ___/x + ___/(x - 2) + ___/(x + 2)

HumanBemg 25 мар. 2025 г.

0

3

0

+146

Algebra

Let (x,y,z) be the real solution to the system of equations
x + y = \sqrt{4z + 3}
y + z = \sqrt{4x - 1}
z + x = \sqrt{4y + 5}
Find x + y + z.

HumanBemg 25 мар. 2025 г.

0

3

0

+146

Algebra

Find all x such that
sqrt{3x^2 + 2x + 1} + sqrt{3x^2 + 2x - 3} = 20.

HumanBemg 25 мар. 2025 г.

0

3

0

+146

Algebra

Let f be a function such that
f(xy) + x = xf(y) + f(x) + xy^2
for all real numbers x and y. If f(-1) = 3, then compute f(100).

HumanBemg 21 мар. 2025 г.

+146

0

The range is [-5,infty).

HumanBemg21 мар. 2025 г.

+146

0

(A) k > 0 and a > 1

(B) k < 0 and a < 1

(C) k < 0 and a > 1

(D) k > 0 and a < 1

HumanBemg8 мар. 2025 г.