All Questions ⁺⁰238158 Questions

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119

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+1662

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

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113

1

+1662

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 ..

wiseowl Dec 18, 2023

0

95

0

+818

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

88

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+818

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

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113

1

+1944

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

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114

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+1944

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

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75

1

+1944

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 ..

tomtom Dec 18, 2023

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87

1

+1944

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 $IJKLMN$.

tomtom Dec 18, 2023

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81

1

+1944

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.

tomtom Dec 18, 2023

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80

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

Vxritate Dec 18, 2023

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43

1

+1944

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 ..

tomtom Dec 18, 2023

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91

2

+1944

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?

tomtom Dec 18, 2023

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33

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+1944

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.

tomtom Dec 18, 2023

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33

2

+1944

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.

tomtom Dec 18, 2023

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50

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 ..

Vxritate Dec 18, 2023

Dec 17, 2023

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87

1

+1661

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.

kittykat Dec 17, 2023

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102

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+1661

Circle

In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.

kittykat Dec 17, 2023

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113

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+1661

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.

kittykat Dec 17, 2023

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