All Questions ⁺⁰235489 Questions

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+195

Algebra

Expand (sqrt(x) + 3x)*4 + (sqrt(x) - 3x)*4.

BRAlNBOLT Oct 23, 2024

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+195

Algebra

Fill in the blanks with positive integers:
(3 + sqrt(6))*3 = ___ + ___ * sqrt(6)

BRAlNBOLT Oct 23, 2024

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+330

Number Theory

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.

Stanry Oct 23, 2024

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+330

Number Theory

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$.

Stanry Oct 23, 2024

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+330

Number Theory

When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
0.\overline{0121}_3 = 0.01210121 \dots,
which is repeating.
When read more ..

Stanry Oct 23, 2024

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+330

Number Theory

You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $52$ pieces of candy per scoop to the vat, and another machine that can remove exactly $39$ pieces of candy with a different scoop from read more ..

Stanry Oct 23, 2024

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+1415

Geometry

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR

blackpanther Oct 23, 2024

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+1415

Geometry

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

blackpanther Oct 23, 2024

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+1415

Geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, read more ..

blackpanther Oct 23, 2024

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+36

Help

Given a sequence which contains the numbers $1$ through $8,$ a move consists of moving one of the numbers to the front of the sequence. For example, for the sequence $(1, 5, 8, 3, 6, 2, 7, 4),$ we can move the number $6$ to the front, which results in the read more ..

HelpIneedHelp Oct 23, 2024

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+830

Geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

magenta Oct 23, 2024

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+830

Geometry

In the diagram, ABCD is a square. Find PR.
L, M, N, O, are midpoints of sides.
Side AB = 12

magenta Oct 23, 2024

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+830

Geometry

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

magenta Oct 23, 2024

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+422

Algebra

Point $A$ is reflected over the line shown below to point $B$. Find the coordinates of $B$.
Write your answer as an ordered pair $(x,y)$.
The line is y = 3x - 2, and A = (-5,6).

onyuIee Oct 23, 2024

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+422

Algebra

The graph of the equation
4x^2 - 12x + 4y^2 + 16y + 17 = -4x + 2y + 5
is a circle. Find the radius of the circle.

onyuIee Oct 23, 2024

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+271

Geometry

Altitudes AD and BE of triangle ABC intersect at H . If angle AHB = 120 degrees and angle BAC = 52 degrees, then what is angle AHC?

MeIdHunter Oct 23, 2024

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+271

Geometry

Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle ADT if [DET] = 14.

MeIdHunter Oct 23, 2024

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+271

Geometry

In trapezoid $EFGH,$ $\overline{EF} \parallel \overline{GH},$ and $P$ is the midpoint of side $\overline{EH}$. If the area of triangle $PEF$ is $18$, and the area of triangle $PGH$ is $36$, then find the area of trapezoid $EFGH$.

MeIdHunter Oct 23, 2024

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+271

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $4,$ and the area of triangle $PSR$ is $8.$ Find the area of trapezoid read more ..

MeIdHunter Oct 23, 2024

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+63

Polynomials!!

Given that is expressible as a polynomial in with real coefficients only if n is an odd positive integer, find P(z) so that

MeldHunter Oct 23, 2024

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+834

Geometry

Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle. Find the area of ABCD.
PQDC is a square.

eramsby1O1O Oct 23, 2024

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+834

Geometry

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

eramsby1O1O Oct 23, 2024

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