tomtom

509 Questions
22 Answers

0

6

0

+1926

Geometry

Triangle PQR is equilateral. Find AQ.

tomtom 01.01.2025

0

5

1

+1926

Geometry

In triangle ABC, \cos \angle A = \frac{1}{8}. Find the length of angle bisector \overline{AD}.

tomtom 01.01.2025

0

10

0

+1926

Geometry

In the diagram below, \angle XOY = 30^\circ and OA=15. Let B and C be points on rays \overrightarrow{OY}$ and $\overrightarrow{OX}, respectively. Find the area of triangle ABC if OB = 10 and OC = 12.
Triangle ABC is dilated to triangle mehr ..

tomtom 01.01.2025

0

7

2

+1926

Geometry

Find \sin C, to two decimal places.

tomtom 01.01.2025

0

16

0

+1926

Algebra

For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are 1 + 2x + 3x^2 + 4x^3 + ... Find c.

tomtom 29.09.2024

0

10

1

+1926

Algebra

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

tomtom 29.09.2024

0

16

0

+1926

Algebra

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

tomtom 29.09.2024

0

19

0

+1926

Algebra

For what values of $j$ does the equation $(2x + 7)(x - 4) = -31 + jx$ have exactly one real solution? Express your answer as a list of numbers, separated by commas.

tomtom 29.09.2024

0

13

1

+1926

Algebra

Find the value of $v$ such that $\frac{-21-\sqrt{201}}{10}$ a root of $5x^2+21x+v = 0$.

tomtom 29.09.2024

0

9

1

+1926

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. mehr ..

tomtom 29.09.2024

0

19

2

+1926

help counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $2000,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

tomtom 18.08.2024

0

13

1

+1926

Algebra

Let a1, a2, a3, ... be an arithmetic sequence. Let Sn denote the sum of the first n terms. If S_5 = 1/5 and S_10 = 1/10, then find S_15.

tomtom 10.08.2024

0

10

1

+1926

Geometry

Let k be a positive real number. The line x + y = 3k and the circle x^2 + y^2 = k - 4x - 6y are drawn. Find $k$ so that the line is tangent to the circle.

tomtom 10.08.2024

0

17

1

+1926

help with geometry

Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.

tomtom 09.08.2024

0

24

0

+1926

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid mehr ..

tomtom 16.07.2024

0

14

1

+1926

Geometry

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

tomtom 16.07.2024

0

18

0

+1926

Geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 15$, and $PR = 20$, mehr ..

tomtom 16.07.2024

0

15

1

+1926

Number Theory

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$

NotThatSmart ●

tomtom 17.06.2024

0

19

1

+1926

Number Theory

When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
\[0.\overline{0121}_3 = 0.01210121 \dots,\]
which is repeating.
When mehr ..

tomtom 17.06.2024

+1926

0

The answer is g(x) = -5x^2 + 7x + 4.

tomtom18.09.2024

+1926

0

The answer is g(x) = -5x^2 + 7x + 4.

tomtom18.09.2024