All Questions ⁺⁰234657 Questions

0

18

0

+817

Counting

At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if each scientist must sit next to a mathematician? (Two seatings are considered equivalent read more ..

maximum Dec 14, 2023

0

20

1

+817

help plz

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

maximum Dec 14, 2023

0

16

1

+817

need help

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are read more ..

maximum Dec 14, 2023

0

6

1

+817

Counting

A speech class has $4$ freshmen and $3$ sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that all the freshmen are standing together?

maximum Dec 14, 2023

-1

34

0

+1756

help with geometry

Two rectangles overlap, as shown below. Find the area of the overlapping region (which is shaded) if $AB = BE = 3$ and $FB = BC = 3.$

bader Dec 14, 2023

0

20

0

+1756

Rectangle

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

bader Dec 14, 2023

0

28

1

+1756

Geometry

An equilateral triangle is constructed on each side of a square with side length $2,$ as shown below. The four outer vertices are then joined to form a large square. Find the area of the shaded region.

bader Dec 14, 2023

0

31

1

+1756

Geometry

Rectangle $ABCD$ contains a point $X$ such that $AX = 3$, $BX = 3$, and $CX = 3$. Find $DX$.

bader Dec 14, 2023

Dec 13, 2023

0

32

0

+1756

Rectangle

The perimeter of a rectangle is $40,$ and the length of one of its diagonals is $10 \sqrt{2}.$ Find the area of the rectangle.

bader Dec 13, 2023

0

24

1

+1756

Rhombus

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $90^\circ.$ Find the area of the rhombus.

bader Dec 13, 2023

0

17

1

+1756

Quadrilateral

In quadrilateral $PQRS$, $PQ = QR = RS = SP$, $PR = \sqrt{2}$, and $QS = \sqrt{2}$. Find the perimeter of $PQRS$.

bader Dec 13, 2023

-1

30

1

+1323

Triangles

As shown in the diagram $\angle BAC=90^\circ$. Let $X$ be the foot of the altitude from $A$ to $\overline {BC}$, $\overline{AY}$ be the bisector of $\angle BAC$, and $\overline{AZ}$ be the median of $\triangle ABC$. If $\angle BAY = 16^\circ$, then read more ..

blackpanther Dec 13, 2023

-1

34

0

+1323

Angle Bisectors

Angle bisectors $\overline{AX}$ and $\overline{BY}$ of triangle $ABC$ meet at point $I$. Find $\angle C,$ in degrees.

blackpanther Dec 13, 2023

+3

19

1

+180

In triangle ABC, cos A=sqrt frac (7/10) and cos B=sqrt (3/10) Find cos C

In triangle ABC, cos A=sqrt frac (7/10) and cos B=sqrt (3/10) Find cos C

itsash Dec 13, 2023

+2

15

1

+180

compute cos^2 1 +cos^2 2 +cos^2 3 ... +cos^2 89 (in degrees)

compute cos^2 1 +cos^2 2 +cos^2 3 ... +cos^2 89 (in degrees)

itsash Dec 13, 2023

+2

25

1

+180

compute tan 45/2 (degrees)

compute tan 45/2 (degrees)

itsash Dec 13, 2023

-1

23

1

+1323

Triangle

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BZ$.

blackpanther Dec 13, 2023

-1

32

1

+1323

Triangle

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BC$.

blackpanther Dec 13, 2023

-1

34

0

+1323

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If $PQ read more ..

blackpanther Dec 13, 2023

-1

37

0

+1323

Triangle

For the triangle below, let $x$ be the area of the circumcircle, and let $y$ be the area of the incircle. Compute $x - y.$

blackpanther Dec 13, 2023

0

15

1

+14

HELP MEEE

Find the greatest whole number that will satisfy this inequality: .

Ayobruh Dec 13, 2023

0

20

0

+1678

Integers

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

wiseowl Dec 13, 2023

0

28

0

+1678

Algebra

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

wiseowl Dec 13, 2023

0

30

0

+1678

help with quadratic

Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

wiseowl Dec 13, 2023

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