All Questions ⁺⁰236050 Questions

0

21

1

+862

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $AX = 5,$ and $CX = 5$. What is $BX$?

magenta Jun 3, 2024

0

14

1

+862

Geometry

In a certain regular polygon, the measure of each interior angle is $2$ times the measure of each exterior angle. Find the number of sides in this regular polygon.

NotThatSmart ●

magenta Jun 3, 2024

0

13

1

+862

Geometry

A regular hexagon has a perimeter of $p$ (in length units) and an area of $A$ (in square units). If $A = \frac{3}{2},$ then find the side length of the hexagon.

magenta Jun 3, 2024

-1

17

2

+1839

Counting

You are given the 4 x 4 grid below.
(a) Find the number of ways of placing 8 counters in the squares (at most one counter per square), so that each row contains exactly two counters.
(b) Find the number of ways read more ..

ABJeIIy Jun 3, 2024

-1

9

1

+1839

Counting

In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving at least four pieces each?

ABJeIIy Jun 3, 2024

-1

17

1

+1839

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

ABJeIIy Jun 3, 2024

-1

19

1

+1839

Counting

A coin is tossed $12$ times. How many different sequences of tosses could there have been, if the number of heads was at least $5?$

ABJeIIy Jun 3, 2024

-1

21

1

+1839

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.)

ABJeIIy Jun 3, 2024

-1

17

1

+1839

Counting

We call a number cozy if every digit in the number is either even or next to an even digit. For example, a number is cozy if every digit in the number is either a 2 or next to a 2. For example, the number 222, 72, 45, and 810 and read more ..

ABJeIIy Jun 3, 2024

-1

16

0

+1839

Counting

We call a number cozy if every digit in the number is either even or next to an even digit. For example, a number is cozy if every digit in the number is either a 2 or next to a 2. For example, the number 222, 72, 45, and 810 and read more ..

ABJeIIy Jun 3, 2024

0

17

1

+1310

Algebra

If $n$ is a positive integer, a $3$-partition of $n$ is a list of powers of $3$, arranged in order from greatest to least, whose sum is $n.$ For example, there are three $3$-partitions of $6,$ namely $3-3, 3-1-1-1$ and $1-1-1-1-1-1.$ How many different read more ..

learnmgcat Jun 3, 2024

0

9

3

+1310

Algebra

Consecutive positive even integers are sorted into $100$ groups. Group $1$ includes $2,$ $4$ and $6.$ Group $2$ includes $8,$ $10,$ $12$ and $14.$ Group $3$ includes $16,$ $18,$ $20,$ $22$ and $24.$ Each successive group has one additional number in it read more ..

NotThatSmart ●●●

learnmgcat Jun 3, 2024

0

14

1

+1310

Algebra

Amos counts out loud by six beginning with $0.$ Sarah counts out loud by three also beginning with $0.$ Between $0$ and $100$ inclusive, how many of the numbers do both Sarah and Amos say out loud?

learnmgcat Jun 3, 2024

0

14

1

+842

Geometry

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 66^\circ$, then what is $\angle HCA$ in degrees?

NotThatSmart ●

RedDragonl Jun 3, 2024

0

10

1

+1310

Algebra

If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?

learnmgcat Jun 3, 2024

0

7

1

+1310

Algebra

Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

learnmgcat Jun 3, 2024

0

15

0

+976

Geometry

In the diagram below, D is a point on segment CE such that segments AD and BE are parellel and point A is not on segment BC. Line segments AD and BC intersect at point P.
If angle CAD = 67 degrees, then what is angle read more ..

Hi6942O Jun 3, 2024

0

23

1

+976

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

Hi6942O Jun 3, 2024

0

18

1

+35

Trigonometry/geometry help

In triangle ABC, we know the following:
Find .

dplostthegame Jun 3, 2024

0

15

1

+976

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.

Hi6942O Jun 3, 2024

0

13

1

+976

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.

Hi6942O Jun 3, 2024

0

12

1

+842

Algebra

Find all $x$ such that both $2x$ and $3x-7$ are in the interval $(-1,12)$.

RedDragonl Jun 3, 2024

0

15

1

+842

Algebra

Find all $x$ such that $1-3x < x + 8 \le 7-x$. Give your answer in interval notation.

RedDragonl Jun 3, 2024

0

19

1

+842

Algebra

Find all $z$ such that neither $2+z-5z$ nor $2-z+8z$ is in the interval $(-7,13]$. Express your answer as an interval or as a union of intervals.

RedDragonl Jun 3, 2024

0

14

1

+842

Algebra

Find all $w$ so that neither $-2(6+2w)\le -16 + 7w$ nor $-3w\ge 18 - 5w + 3$.

RedDragonl Jun 3, 2024

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