All Questions ⁺⁰236282 Questions

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Geometry

In rectangle ABCD, E is the midpoint of \overline{BC}, and $F$ is the midpoint of $\overline{CD}.$ Let $G$ be the intersection of $\overline{AE}$ and $\overline{BF}.$ Find $DG.$

siIviajendeukie Jan 1, 2025

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Algebra

A line bisects the area of the square below. The slope of the line is 3, and its y-intercept is (0,b). Find $b.$
The vertices of the square are (-4,-4), (-4,4), (4,4), and (4,-4).

nathanl6656 Jan 1, 2025

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Algebra

Find the coordinates of the intersection of the diagonals of quadrilateral ABCD, where:
A(3, 6), B(9, 6), C(7, 3), and D(1, 1).

nathanl6656 Jan 1, 2025

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Algebra

The graph x^2+y^2=121 intersects y=8x+10 at two points P and Q. Find PQ.

nathanl6656 Jan 1, 2025

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Algebra

The line 3x-4y=5 intersects the $x$-axis and $y$-axis at points $A$ and $B,$ respectively. Find the distance $AB.$

nathanl6656 Jan 1, 2025

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+364

Algebra

Let x, y, and z be nonzero real numbers. Find all possible values of
(x + y + z)/(|x| + |y| + |z|).

MEMEG0D Jan 1, 2025

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Number Theory

Find the number of bases n \ge 2 such that 100_n + 1_n is prime.

MEMEG0D Jan 1, 2025

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+36

Math

Suresh used 2/5 of his money to buy 4 pens and 9 rulers. The cost of 2 pens was the same as that of 3 rulers. What was the greatest number of rulers that Suresh could buy with the money he had left?
1) 15
2) 21
3) 22 read more ..

AskQuestonsInNewYear Jan 1, 2025

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Math

Ali ears a fixed monthly salary. In June, he spent 1/3 of his salary on a table and 5/6 of his remaining salary on a television.
(a) What fraction of Ali's salary was spend on the television?
(b) After buying the table and television, Ali read more ..

AskQuestonsInNewYear Jan 1, 2025

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Math

Ahmad baked some chocolate and strawberry cupcakes in the ratio of 2:7. He sold 1/2 of the strawbery cupcakes in the moming. After that, he had 285 more strawberry cupcakes than chocolate cupcakes left. How many cupcakes did Ahmad bake in total? read more ..

AskQuestonsInNewYear Jan 1, 2025

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Math

Ali, Bala and Charles had 60 marbles altogether. Ali gave 3/10 of his marbles to Bala and 1/5 of his marbles to Charles. In the end, all 3 boys had the same number of marbles.
(a) Who had more marbles at first, Bala or Charles? How many read more ..

AskQuestonsInNewYear Jan 1, 2025

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Math

Andrew, Chris, Jeremy and Glen sold some funfair tickets. Both Andrew and Glen sold 1/5 of the tickets each. Chris sold 12 tickets more than Andrew and Jeremy sold 30 tickets. How many tickets did they sell altogether?

AskQuestonsInNewYear Jan 1, 2025

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Math

David had two bags of marbles. After he sold 44 marbles from bag X to his friend, the number of marbles in bag Y was 5/7 of the marbles in bag X. Given that there were 2/5 as many marbles in bag Y as in bag X originally, how many marbles were there in bag read more ..

AskQuestonsInNewYear Jan 1, 2025

Dec 31, 2024

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+505

Geometry

Triangle ABC is dilated to triangle A'B'C', so that the distance between corresponding sides is $1.$ Given that triangle $ABC$ has perimeter $100$, find the scale factor of the dilation.

crimefightingvigiI Dec 31, 2024

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Geometry

In the diagram below, \angle XOY = 30^\circ and OA=15. Let B and C be points on rays \overrightarrow{OY}$ and $\overrightarrow{OX}, respectively. Find the area of triangle ABC if OB = 10 and OC = 12.

crimefightingvigiI Dec 31, 2024

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Geometry

In triangle XYZ, X_1, Y_1, and Z_1 are the midpoints of $\overline{YZ},$ $\overline{XZ},$ and $\overline{XY},$ respectively. A dilation maps $X$ to $Y$ with scale factor 3. A second dilation maps $Y$ to $Z_1$ with scale factor 5. When both dilations read more ..

crimefightingvigiI Dec 31, 2024

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Geometry

When a square with area 16 is dilated by a scale factor of k, we obtain a square with area 25. If the side length of the second square is 5, then find the side length of the first square.

crimefightingvigiI Dec 31, 2024

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Geometry

We cut a regular octagon ABCDEFGH out of a piece of cardboard. If $AB = 1$, then what is the area of the octagon?

CPhill ●●●

magenta Dec 31, 2024

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Geometry

David wants to add one more dot to the diagram below so that the four dots form the four vertices of a parallelogram. If A = (3,4), B = (4,-1), C = (6,8), then where should D be to form parallelogram ABCD?

magenta Dec 31, 2024

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+911

Geometry

A circle with radius 4 is translated 2 units. What is the area of the region swept out by the circle?

magenta Dec 31, 2024

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Geometry

Equilateral triangle ABC is inscribed in a circle. Let P be a point on arc BC. Given that $PB = 18$ and $PC = 18,$ find $PA.$

magenta Dec 31, 2024

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+1504

Geometry

In the diagram below, Point A is \sqrt 3 units above O. Whenever Tasha moves a point, she translates the point $\sqrt 2$ units to the right. Whenever Richard moves a point, he rotates the point clockwise about point $O$ by $60^\circ.$
In read more ..

kittykat Dec 31, 2024

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Geometry

As shown in the diagram, a 7 \times 2 rectangle (in black) is rotated $90^\circ$ counterclockwise around its center (i.e. the intersection of its diagonals) to reach its new position (in red). Find $\angle XYZ$ in degrees.

kittykat Dec 31, 2024

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Geometry

Jessica wants to add one more dot to the diagram below so that the four dots form the four vertices of a parallelogram. If A = (3,4), B = (4,-1), C = (6,8), then where should D be to form parallelogram ABCD?

kittykat Dec 31, 2024

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