All Questions ⁺⁰235753 Questions

0

22

0

+2669

Algebra

Let a and b be the solutions to 7x^2 + x - 5 = -3x^2 - 9x - 4. Compute (a - 4)/(b - 4) + (b - 4)/(a - 4).

LiIIiam0216 Mar 26, 2024

0

15

1

+2669

Quadratic

Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 + 11x - 6. Find u/v^2 + v/u^2.

LiIIiam0216 Mar 26, 2024

0

31

0

+2669

Quadratic

Let a and b be the solutions to 5x^2 - 11x + 4 = 4x^2 - 17x + 6. Find 1/a^3 + 1/b^3.

LiIIiam0216 Mar 26, 2024

0

25

1

+359

Quadratic

Fill in the blanks to make a quadratic whose roots are 5 and -5.
x^2 + ___ x + ___

falafronk Mar 26, 2024

0

15

1

+355

Solutions

Consider the quadratic equation ax^2 + bx + c = 0 with a, b, c integers from -4 to 4 and a is not 0. The solutions to this equation are in the form where D is square free . Determine the largest possible value of D.

Lilliam0216 Mar 26, 2024

0

20

1

+355

Area of a square

The area of a square, in square units, is 38 more than 10 times the length of a side of the square, in units.
Find all possible values for the side length of the square.

Lilliam0216 Mar 26, 2024

0

28

1

+359

Solid Geometry

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

falafronk Mar 26, 2024

0

30

0

+359

Pyramids

Let $ABCD$ be a regular tetrahedron. Let $E$, $F$, $G,$ $H$ be the centers of faces $BCD$, $ACD$, $ABD$, $ABC$, respectively. The volume of pyramid $DEFG$ is $18.$ Find the volume of pyramid $EFGH$

falafronk Mar 26, 2024

0

38

0

+359

help with geometry

Let $APQRS$ be a pyramid, where the base $PQRS$ is a square. The total surface area of pyramid $APQRS$ (including the base) is $800$. Let $W$, $X$, $Y$, and $Z$ be the midpoints of $\overline{AP}$, $\overline{AQ}$, $\overline{AR}$, and $\overline{AS}$, read more ..

falafronk Mar 26, 2024

0

16

1

+359

Circle

A circle lies inside a quarter-circle, as shown below. The circle is tangent to side AO and arc AB. Find the radius of the circle.

falafronk Mar 26, 2024

0

14

1

+1246

Minimum

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

Akhain1 Mar 26, 2024

0

23

1

+1246

help with floor

Let
f(x) = \left\lfloor\frac{3x - 5}{3x + 4}\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 $f$.)

Akhain1 Mar 26, 2024

0

17

0

+1246

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.

Akhain1 Mar 26, 2024

0

28

0

+1455

Counting problem

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?

kittykat Mar 26, 2024

0

29

0

+1455

Counting question

In how many ways can I arrange $3$ different math books and $4$ different history books on my bookshelf, if at least three of the history books are next to each other?

kittykat Mar 26, 2024

0

21

1

+359

help hard geometry

In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

falafronk Mar 26, 2024

0

35

0

+359

Semicircles

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

falafronk Mar 26, 2024

0

21

1

+743

Rectangle

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

bingboy Mar 26, 2024

0

21

1

+743

Geometry

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

bingboy Mar 26, 2024

0

16

1

+1768

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. read more ..

bader Mar 26, 2024

0

31

1

+1768

Algebra

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and read more ..

bader Mar 26, 2024

0

27

1

+1768

Rates

I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

bader Mar 26, 2024

0

30

0

+2669

Probability

Triangle XYZ is equilateral, with O as its center. A point P is chosen at random. Find the probability that P is closer to point O than to any of the side lengths.

LiIIiam0216 Mar 26, 2024

0

29

1

+2669

need help

The entries in a certain row of Pascal's triangle are
\[1, n, \dots, n, 1.\]
The average of the entries in this row is 2. Find $n$.

LiIIiam0216 Mar 26, 2024

0

20

1

+2669

counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

LiIIiam0216 Mar 26, 2024

2 Online Users