All Questions ⁺⁰238436 Questions

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trapezoid

Trapezoid $ABCD$ has bases $\overline{AB}$ and $\overline{CD}$. Line segment $\overline{EF},$ which is parallel to the bases, divides trapezoid $ABCD$ into two trapezoids of equal area. Find the length $EF.$ read more ..

parmen Dec 29, 2023

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106

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+1757

Triangle

Find sin \angle ACB.

parmen Dec 29, 2023

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111

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Question on Polygons

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.
An equilateral triangle, another equilateral triangle, a square, and a regular n-gon, all with the same side read more ..

parmen Dec 29, 2023

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113

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Inequality

Solve the inequality (x - 2)(x + 6) \le (x - 2)(x + 5). Write your answer in interval notation.

kittykat Dec 29, 2023

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129

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Inequality

Solve the inequality x(x + 6) > 16 - x + 14 + x^2. Write your answer in interval notation.

kittykat Dec 29, 2023

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113

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Inequality

Solve the inequality 4t^2 \le -9t + 12 - 4t + 23 + (2t - 1)(2t + 1). Write your answer in interval notation.

kittykat Dec 29, 2023

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112

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+1661

Inequality

Solve the inequality
\frac{3-z}{z+1} \ge 2(z + 4).
Write your answer in interval notation.

kittykat Dec 29, 2023

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145

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+1776

counting

North High School has a math club and a science club. There are a students in the math club and b students who are members of both clubs. The total number of students is c. Find an expression for the total number of students read more ..

bader Dec 29, 2023

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120

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counting

North High School has a math club and a science club. There are a students in the math club and b students who are members of both clubs. The total number of students is c. Find an expression for the total number of students read more ..

bader Dec 29, 2023

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88

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Completing the Square: Circle

The radius of a circle inscribed within three mutually externally tangent circles of radii , , and is given by

What is the value of when , and ?
read more ..

alibaba Dec 29, 2023

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114

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+1844

Circle

In the diagram below, $O$ is the center of the circle, and $\overline{UV}$ is a diameter. Find $\angle XYZ$, in degrees.

blackpanther Dec 29, 2023

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63

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+1844

Circle

In the figure, if the measure of arc $FG$ is $118^\circ$, the measure of arc $FQ$ is $25^\circ$, and $FR = FQ,$ then what is $\angle RPG$, in degrees?

blackpanther Dec 29, 2023

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126

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Circle

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

blackpanther Dec 29, 2023

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140

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+1844

Cyclic quadrilaterals

In cyclic quadrilateral $PQRS,$
angle P = angle Q = angle R
Find the largest angle in quadrilateral $PQRS,$ in degrees.

blackpanther Dec 29, 2023

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116

2

+157

Help

Tommy has 30 marbles in a bag. If 1/2 are blue, 1/3 are red, and 1/6 are yellow and he draws out a marble, records the color, returns it to the bag and repeats the process 10 times,
a) approximately how many times should he expect to draw a read more ..

sugabreaddoughman Dec 29, 2023

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105

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+157

Anyone can help

The ratio of the volumes of the water in two jugs. M and N, is 2:3 respectively. If the water in M is increased by 65%, by what percentage must the water in jug N be increased so that the volumes of the water in both jugs will be the same?

sugabreaddoughman Dec 29, 2023

-1

108

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+1844

tangents

Lines $XQ$ and $XR$ are tangent to a circle, as shown below. If $\angle QXR = 60^\circ$, then find $\angle TAU$.

blackpanther Dec 29, 2023

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131

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Polygons

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

blackpanther Dec 29, 2023

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78

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Quadrilateral

In the diagram below, each side of convex quadrilateral $ABCD$ is trisected. (For example, $AP = PQ = QB.$) The area of convex quadrilateral $ABCD$ is $180.$ Find the area of the shaded region. read more ..

blackpanther Dec 29, 2023

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91

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+1944

Counting

Determine the number of ways of choosing three points from the grid below, so that they form an isosceles right triangle.

●●●●●

tomtom Dec 29, 2023

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Counting question

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are read more ..

tomtom Dec 29, 2023

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104

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+1944

help plz

Syd chooses two different primes, and multiplies them. If both primes are greater than $20$, and the resulting product is less than $2000$, then how many different products could Syd have ended up with?

tomtom Dec 29, 2023

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