BRAlNBOLT

172 Questions
15 Answers

0

3

0

+207

Geometry

In triangle ABO, M is the midpoint of \overline{AB}. Points C, D, and N lie on line segments $\overline{AO},$ $\overline{BO},$ and $\overline{MO}$ extended, respectively, so that $DO = BO,$ $NO = MO,$ and $CO = AO.$ If $K$ is the area of triangle read more ..

BRAlNBOLT Oct 30, 2024

0

3

0

+207

Geometry

In the diagram below, ABCD is a square, DE = EF = FG = 2, GH = 1, HB = 5, and \angle DEF = \angle EFG = \angle FGH = \angle GHB = 60^\circ. Find the area of the shaded region.

BRAlNBOLT Oct 30, 2024

0

3

0

+207

Geometry

Unit square ABCD is divided into two triangles, which are congruent to each other, and two trapezoids, which are also congruent to each other. These pieces are then re-assembled into rectangle $PQRS,$ as shown below. Find the perimeter of rectangle read more ..

BRAlNBOLT Oct 30, 2024

-1

3

0

+207

Counting

Find the number of $7$-digit positive integers, where the sum of the digits is divisible by $3.$

BRAlNBOLT Oct 23, 2024

0

2

1

+207

Algebra

Expand (sqrt(x) + 3x)*4 + (sqrt(x) - 3x)*4.

BRAlNBOLT Oct 23, 2024

-1

2

1

+207

Algebra

Fill in the blanks with positive integers:
(3 + sqrt(6))*3 = ___ + ___ * sqrt(6)

BRAlNBOLT Oct 23, 2024

0

4

0

+207

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?

BRAlNBOLT Oct 14, 2024

0

5

0

+207

Number Theory

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

BRAlNBOLT Oct 14, 2024

0

4

0

+207

Number Theory

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

BRAlNBOLT Oct 14, 2024

0

6

0

+207

Algebra

Let $f(x)$ be a polynomial with integer coefficients. There exist distinct integers $p,$ $q,$ $r,$ $s,$ $t$ such that
f(p) = f(q) = f(r) = f(s) = 1
and $f(t) > 1.$ What is the smallest possible value of $f(t)?$

BRAlNBOLT Oct 1, 2024

0

11

0

+207

Algebra

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.

BRAlNBOLT Sep 11, 2024

0

3

0

+207

Algebra

Suppose $f(x)$ is a function defined for all real $x$, and suppose $f$ is invertible (that is, $f^{-1}(x)$ exists for all $x$ in the range of $f$). If the graphs of $y=f(x)$ and $y=f(1/x)$ are drawn, at how many points do they intersect?

BRAlNBOLT Sep 7, 2024