All Questions ⁺⁰237360 Questions

0

40

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+1855

Counting

At a meeting, $4$ scientists, $3$ mathematicians, and $2$ journalists are to be seated around a circular table. How many different arrangements are possible if every mathematician must sit next to a journalist? (Two seatings are considered read more ..

ABJeIIy Jun 22, 2024

0

27

1

+1855

Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all three mathematics textbooks must be together?

ABJeIIy Jun 22, 2024

0

26

1

+900

Counting

Starting with the A moving one letter at a time vertically, horizontally, or diagonally, how many different paths spell ARCH?
A
RRR
CCCCC read more ..

eramsby1O1O Jun 22, 2024

0

30

1

+900

Geometry

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

eramsby1O1O Jun 22, 2024

0

28

1

+900

Geometry

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

eramsby1O1O Jun 22, 2024

0

32

0

+900

Geometry

The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XY = 8$ and $WX = 8,$ find $XY.$

eramsby1O1O Jun 22, 2024

0

29

1

+900

Geometry

Let ABCD be a trapezoid with bases AB and CD. Let P be a point on side CD, and let X, Y be the feet of the altitudes from P to AD, BC respectively. Prove that if AD = 5, BC = 7, AB = 6, CD = 12, and CP/PD = 1, then PX = 12*sqrt(6)/5 and PY = read more ..

eramsby1O1O Jun 22, 2024

0

27

1

+2729

help me plz

In triangle $ABC$, $AB = 10$ and $AC = 15$. Let $D$ be the foot of the perpendicular from $A$ to $BC$. If $BD:CD = 1:3$, then find $AD$.

LiIIiam0216 Jun 22, 2024

0

36

1

+2729

need help

We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

LiIIiam0216 Jun 22, 2024

0

28

1

+2729

help with geometry

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point P on the edge of the table (as shown below) has a distance of 6 from one wall, and a distance of 6 from the other wall. Find the radius of the read more ..

LiIIiam0216 Jun 22, 2024

0

31

1

+2729

help geometry

In trapezoid EFGH, \overline{EF} \parallel \overline{GH}, and P is the point on \overline{EH} such that EP:PH = 1:2. If the area of triangle PEF is 6, and the area of triangle PGH is 6, then find the area of trapezoid EFGH.

LiIIiam0216 Jun 22, 2024

0

39

1

+972

Graph

Find the area of the region enclosed by the graph of x^2 + y^2 = 2x - 6y + 6 + 8x - 2y - 5x + 8y + 208.

Rangcr897 Jun 22, 2024

0

38

1

+972

Parabola

Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 + 6x^2 + 14x + 28.

Rangcr897 Jun 22, 2024

0

44

1

+972

Parabola

Find the vertex of the graph of the equation x - y^2 + 8y = 13 + 2y - 4x + 15y + 3y^2.

Rangcr897 Jun 22, 2024

0

26

1

+972

Parabola

The parabola $y = ax^2 + bx + c$ is graphed below. Find $a+b+c$. (The grid lines are one unit apart.)
The parabola goes through (-5,0), (0,3), and (4,0).

Rangcr897 Jun 22, 2024

0

28

0

+972

Help algebra

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

Rangcr897 Jun 22, 2024

0

50

0

+1000

Hard sum

Let
f(x) = \left\lfloor\frac{2 - 3x}{3x + 1}\right\rfloor.
Evaluate f(1)+f(2) + f(3) + \dots + f(999)+f(1000). (This sum has 1000 terms, one for the result when we input each integer from 1 to 1000 into f.)

Hi6942O Jun 22, 2024

0

45

0

+1000

Help algebra

Find all values of t such that floor(t) = 3t + 4 - t^2. If you find more than one value, then list the values you find in increasing order, separated by commas.

Hi6942O Jun 22, 2024

0

33

1

+1000

plz help

Find the minimum value of \frac{x^2}{x - 1 + x^3} for x > 1

Hi6942O Jun 22, 2024

0

21

1

+1000

Algebra problem

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does read more ..

Hi6942O Jun 22, 2024

0

32

1

+864

help geometry

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.

RedDragonl Jun 22, 2024

0

33

1

+864

Need help

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.

RedDragonl Jun 22, 2024

0

22

1

+864

Help geometry

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

RedDragonl Jun 22, 2024

0

21

1

+2729

Algebra

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab^2 = 4. What is the value of b in this ordered pair? (Note: you may have to use the Tab key to get your cursor into the middle answer box.)

LiIIiam0216 Jun 22, 2024

0

40

1

+2729

Algebra

Find all real numbers a that satisfy \frac{1}{64a^3 + 7} - 7 = 0.

LiIIiam0216 Jun 22, 2024

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