All Questions ⁺⁰237784 Questions

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Algebra

A line and a circle intersect at A and B. Find the coordinates of the midpoint of \overline{AB}.
The ilne is y = 3x - 2, and the circle is (x - 4)^4 + (y - 5)^2 = 68.

crimefightingvigiI Nov 22, 2024

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24

1

+4

help plz

You are given the $4 \times 4$ grid below. Find the number of ways of placing $8$ counters in the squares (at most one counter per square), so that each row contains exactly two counters, and each column contains exactly two counters.

Ning2020 Nov 22, 2024

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35

1

+823

Number Theory

What is the smallest prime divisor of 5^{19} + 7^{13} + 23?

crimefightingvigiI Nov 22, 2024

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41

1

+823

Number Theory

Find the greatest prime divisor of the value of the arithmetic series
1 + 2 + 3 + \dots + 200

crimefightingvigiI Nov 22, 2024

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47

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+823

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 ..

crimefightingvigiI Nov 22, 2024

Nov 21, 2024

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42

2

+972

Algebra

Seven years ago, Grogg's dad was 9 times as old as Grogg. Four years ago, Grogg's dad was 5 times as old as Grogg. How old is Grogg's dad currently?

Rangcr897 Nov 21, 2024

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49

0

+972

Algebra

Sophie's favorite (positive) number is a two-digit number. If she reverses the digits, the result is 14 less than her favorite number. Also, one digit is less than double the other digit. What is Sophie's favorite number?

Rangcr897 Nov 21, 2024

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45

0

+972

Algebra

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{3}.

Rangcr897 Nov 21, 2024

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51

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+498

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$

MeIdHunter Nov 21, 2024

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50

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+498

Geometry

In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

MeIdHunter Nov 21, 2024

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51

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+498

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.

MeIdHunter Nov 21, 2024

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47

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+1540

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

learnmgcat Nov 21, 2024

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52

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+823

Geometry

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 = x + 3, and A = (7,1).

crimefightingvigiI Nov 21, 2024

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39

2

+823

Geometry

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

crimefightingvigiI Nov 21, 2024

+1

45

1

+823

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 ..

crimefightingvigiI Nov 21, 2024

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48

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+823

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

crimefightingvigiI Nov 21, 2024

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51

0

+823

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 $PQ = 36$, $PM read more ..

crimefightingvigiI Nov 21, 2024

Nov 20, 2024

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54

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+898

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row?

cooIcooIcooI17 Nov 20, 2024

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