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Post New Question
All Questions
+0
236048 Questions
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40
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+1678
quadratic
Let $a$ and $b$ be the roots of $x^2 + 7x - 4 = -x^2 + 9x + 6$. Find $(a + 3) + (b + 3).$
wiseowl
Dec 18, 2023
0
43
1
+1678
Quadratic
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 ..
Bosco
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wiseowl
Dec 18, 2023
0
28
0
+816
Counting
We call a number cozy if every digit in the number is either even or next to an even digit. For example, a number is cozy if every digit in the number is either a 2 or next to a 2. For example, the number 222, 72, 45, and 810 and
read more ..
maximum
Dec 18, 2023
0
40
0
+816
Counting
We call a number cozy if every digit in the number is either even or next to an even digit. For example, a number is cozy if every digit in the number is either a 2 or next to a 2. For example, the number 222, 72, 45, and 810 and
read more ..
maximum
Dec 18, 2023
0
61
0
+1911
Polygon
In the diagram below, each side of convex quadrilateral $ABCD$ is trisected. (For example, $AP = PQ = QB.$) The area of convex quadrilateral $BQR$ is $180.$ Find the area of the shaded hexagon.
tomtom
Dec 18, 2023
0
44
0
+1911
Polygon
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 $\angle BDA,$ in degrees.
tomtom
Dec 18, 2023
0
23
1
+1911
Square
In the diagram, $ABCD$ is a square. Find $PR.$
The side length of the square is 10. L, M, N, O are midpoin
read more ..
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tomtom
Dec 18, 2023
0
43
1
+1911
Hexagon
Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.
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tomtom
Dec 18, 2023
0
31
1
+1911
Triangle
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.
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tomtom
Dec 18, 2023
0
30
2
+101
Geometry Question
A right rectangular prism has a total surface area of Also, the sum of all the edges of the prism is Find the length of the diagonal joining one corner of the prism to the opposite corner.
Thanks
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Vxritate
Dec 18, 2023
0
26
1
+1911
Polygons
Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.
An equilateral triangle, a square, and a regular $n$-gon, all with the same side length, also completely surround
read more ..
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tomtom
Dec 18, 2023
0
31
2
+1911
Diagonals
The number of diagonals in a certain regular polygon is equal to $2$ times the number of sides. How many sides does this polygon have?
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tomtom
Dec 18, 2023
0
23
1
+1911
Hexagon
A regular hexagon has a perimeter of $p$ (in length units) and an area of $A$ (in square units). If $A = \frac{3}{2},$ then find the side length of the hexagon.
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tomtom
Dec 18, 2023
0
23
2
+1911
Polygons
In a certain regular polygon, the measure of each interior angle is $2$ times the measure of each exterior angle. Find the number of sides in this regular polygon.
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tomtom
Dec 18, 2023
0
27
1
+101
3D Geometry Problem
In tetrahedron , . A cube is inscribed in the tetrahedron so that one of its vertices is at , and opposite vertex lies on face . Let and Show that the side length of the
read more ..
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Vxritate
Dec 18, 2023
Dec 17, 2023
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17
1
+1455
Trapezoid
Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. If $CD = 7$, $AD = 5$, and $BC = 2$, then find the radius of the semicircle.
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kittykat
Dec 17, 2023
0
27
1
+1455
Circle
In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.
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kittykat
Dec 17, 2023
0
29
1
+1455
Geometry
A semicircle is inscribed in triangle $XYZ$ so that its diameter lies on $\overline{YZ}$, and is tangent to the other two sides. If $XY = 10,$ $XZ = 10,$ and $YZ = 10,$ then find the area of the semicircle.
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kittykat
Dec 17, 2023
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