All Questions ⁺⁰237994 Questions

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In an equation of the form k^2=ax^2+bx+c, with a>0, the least possible value of k occurs at x=-b/(2a). In the equation , what is the least possible value for k?

UniCorns555 Feb 24, 2024

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109

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+1757

Triangle

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle PBA$, and $\angle ABC - \angle ACB = 24^\circ$. Find $\angle PBC$ in degrees.

parmen Feb 24, 2024

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55

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Help

Marian throws a dart that lands randomly on a dartboard shaped like an isosceles trapezoid with side lengths 12 inches, 12 inches, 12 inches and 24 inches. What is the probability that the dart is closer to the 24-inch side than it is to any of the other read more ..

UniCorns555 Feb 24, 2024

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96

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HELP

A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up three times in a row. What is the probability that the coin will be tossed more than 10 times? Express your answer as a common fraction.

UniCorns555 Feb 24, 2024

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105

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+1757

Circles

A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle? read more ..

parmen Feb 24, 2024

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67

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+1757

help with polygon

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

parmen Feb 24, 2024

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97

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+977

Circles

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.

magenta Feb 24, 2024

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82

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Circles

Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$. The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn. If the measure of arc $LM$ in circle $\omega_1$ is $90^\circ,$ and the radius of $\omega_1$ is 1, then find read more ..

magenta Feb 24, 2024

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75

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Trapezoid

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. read more ..

kittykat Feb 24, 2024

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93

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+1661

Similar Triangles

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

kittykat Feb 24, 2024

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71

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+1661

Triangle problem

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

kittykat Feb 24, 2024

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2

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+1776

Triangle problem

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, read more ..

bader Feb 24, 2024

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87

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+1776

Area of Strip

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

bader Feb 24, 2024

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1

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+1776

Angles

Points $T$ and $U$ lie on a circle centered at $O$, and point $P$ is outside the circle such that $\overline{PT}$ and $\overline{PU}$ are tangent to the circle. If $\angle TOP = 45^{\circ}$, then what is the measure of minor arc $TU$, in deg read more ..

bader Feb 24, 2024

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101

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+400

Coordinates

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

omgitsrne Feb 24, 2024

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101

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+400

Coordinates

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

omgitsrne Feb 24, 2024

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38

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+1124

Word sum

Good day friends,
long time no speak...

..This is for a grade 6 learner...My reason for asking assistance is because of the fact that this learner has not yet in his curriculum read more ..

juriemagic Feb 24, 2024

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93

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+1661

Triangles

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

kittykat Feb 24, 2024

Feb 23, 2024

-1

100

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+1661

Geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

kittykat Feb 23, 2024

-1

117

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+1661

Triangles

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 66^\circ$, then what is $\angle HCA$ in degrees?

kittykat Feb 23, 2024

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1

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+1661

Solid Geometry

In tetrahedron ABCO, angle AOB = angle AOC = angle BOC = 90^\circ. A cube is inscribed in the tetrahedron so that one of its vertices is at O, and the opposite vertex lies on face ABC. Let OA = 1, OB = 1, OC = 1. Show that the read more ..

kittykat Feb 23, 2024

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82

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+977

help with geometry

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

magenta Feb 23, 2024

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103

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+977

Geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, then read more ..

magenta Feb 23, 2024

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90

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+977

Triangles

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

magenta Feb 23, 2024

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