All Questions ⁺⁰235546 Questions

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please help me!!

An expression is well-defined if you can compute its value without any illegal operations. Examples of expressions that are not well-defined include and . For what values of is the expression
well-defined? read more ..

ABJelly Apr 2, 2024

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22

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+1234

Geometry

Can you solve this?
Points $X$, $Y$, and $Z$ are on the sides $\overline{QR}$, $\overline{PR}$, and $\overline{PQ}$, respectively, of right triangle $PQR$ such that $PZXY$ is a square. If $PQ = 6$ and $PR = 6$, then what is the side read more ..

Akhain1 Apr 2, 2024

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Triangle

Can you solve this?
In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $AF = 1$ and $DF = 2$, then read more ..

Akhain1 Apr 2, 2024

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Triangles

Can you solve this?
In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 18$, $BC = 18$, $CE = 6$, $AC = 14$ and $AB = 10$, then what is $DE$ read more ..

Akhain1 Apr 2, 2024

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Circles

Can you do these difficult geometry questions?
1.

2.
<#> read more ..

Akhaim1 Apr 2, 2024

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Counting

How many solutions are there to the equation
u + v + w + x + y + z = 2,
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $1?$

kittykat Apr 2, 2024

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Counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly $7$ chocolates?

kittykat Apr 2, 2024

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Counting

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends, if every friend gets at least one sticker.

kittykat Apr 2, 2024

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15

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+1431

Counting

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends. (Not everyone has to get a sticker.)

kittykat Apr 2, 2024

+1

14

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+1839

help algebra

What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates read more ..

ABJeIIy Apr 2, 2024

Apr 1, 2024

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plz help me

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

ABJeIIy Apr 1, 2024

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need help

Find all points (x,y) that are 5 units away from the point (2,7) and that lie on the line x + y = 13.

ABJeIIy Apr 1, 2024

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20

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+1839

help with algebra

Let a and b be the solutions to 7x^2 + x - 5 = 6x^2 - 4x + 5. Compute (a - 4b)(b - 4a).

ABJeIIy Apr 1, 2024

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Roots

Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = x^2 - 14x + 2. Compute a^3/b^3 + b^3/a^3.

ABJeIIy Apr 1, 2024

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help I need help

One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 48$ and $a^2 = 24$. What is the value of $b$ in this ordered pair?

ABJeIIy Apr 1, 2024

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help me help me

Seven years ago, Grogg's dad was $9$ times as old as Grogg. Four years ago, Grogg's dad was $6$ times as old as Grogg. How old is Grogg's dad currently?

ABJeIIy Apr 1, 2024

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+1234

Polygon

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.
An equilateral triangle, a regular dodecagon, a square, and a regular n-gon, all with the same side length, also read more ..

Akhain1 Apr 1, 2024

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Polygon

The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $3$ sides, then find the smallest angle, in degrees.

Akhain1 Apr 1, 2024

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help with algebra help

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far read more ..

ABJeIIy Apr 1, 2024

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i need help now

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $4$ days earlier. If the job needs to be completed $20$ days earlier, how many additional workers should be hired?

ABJeIIy Apr 1, 2024

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help me plz

(1) Let a1, a2, a3 be real numbers such that
|a_1 - a_2| + 2 |a_2 - a_3| + 3 |a_3 - a_1| = 1.
What is the largest possible value of |a_1 - a_2|?

(2) Let a1, a2, a3, \dots, a{10} be real numbers such that read more ..

ABJeIIy Apr 1, 2024

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help with algebra now

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 $f$.)

ABJeIIy Apr 1, 2024

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help me help

Find constants A and B such that
\frac{2x + 11 - 5x + 17}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}
for all $x$ such that $x\neq -1$ and $x\neq 2$.

ABJeIIy Apr 1, 2024

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help me fast

One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?
x^2 - 2x + 1
x^2 - 4x - 4
x^2 + 6x - 9 read more ..

ABJeIIy Apr 1, 2024

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really need help

Let $a$ and $b$ be the roots of $x^2 + 7x - 4 = -x^2 + 9x + 6$. Find $(a + 3) + (b + 3).$

ABJeIIy Apr 1, 2024

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