All Questions ⁺⁰231042 Questions

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191

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Please Help I Don't Understand

1. Circle and circle , with radii 3 and 5, respectively, are both tangent to line at Enter all possible lengths of separated by commas.

2. Externally tangent circles read more ..

Guest Nov 29, 2022

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193

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help geometry

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area read more ..

Guest Nov 29, 2022

+1

216

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Tangent circles

The two circles below are externally tangent. A common external tangent intersects line PQ at R. Find QR.

Guest Nov 29, 2022

Nov 28, 2022

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106

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Counting problem

Six children are each offered a single scoop of any of 3 flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that each flavor of ice cream is selected by at least two children? read more ..

Guest Nov 28, 2022

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122

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Algebra

Carissa the chessplayer is a very, very slow walker. In fact, she walks at 100 meters per hour when walking uphill, 180 meters per hour when walking across flat ground, and 250 meters per hour when walking downhill. One day, Carissa walks read more ..

Guest Nov 28, 2022

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96

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Geometric series

For a real number r, let s(r) denote the set of real numbers that can be expressed in the form
a1 r + a2 r^2 + a3 r^3 + ...
with an infinite number of terms, where ai in {0,1}
(a) Show that 1/2 an element in S(1/4)
(b) Show that 1/5 read more ..

Guest Nov 28, 2022

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99

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Sydnee

Guest Nov 28, 2022

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108

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help algebra

Consider the two expressions (6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)/(2x + 3 - 7x - 11) and 4x^2 - 7 + 1/(2x + 3 - 7x - 11)
a) Show that the two expressions represent equal numbers when x = 10
b) Explain why these two expressions do read more ..

Guest Nov 28, 2022

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105

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triangles

Triangle ABC is a right triangle with angle BAC= 90 degrees and angle B > angle . Suppose AP is an altitude of the triangle, AQ is an angle bisector of the triangle, and AR is a median of the triangle, and angle PAQ = 18 degrees. If P read more ..

Guest Nov 28, 2022

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101

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need help

A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is 75% magical syrup by volume (and the rest is just water), and blue potion, which read more ..

Guest Nov 28, 2022

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207

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+656

Help would be helpful ;)

Let p and q be the two distinct solutions to the equation . If , what is the value of ?

Hint: Does not equal 7

●●●●●

Keihaku Nov 28, 2022

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102

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help probability

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. The read more ..

Guest Nov 28, 2022

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122

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Quadratic

Let r and s be the roots of 3x^2+4x-12=2x^2-6x+8. Find r^2 + s^2

Guest Nov 28, 2022

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102

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Function

Let F(x) be the real-valued function defined for all real x except for x = 1 and x = 2 and satisfying the functional equation
F(x) + F((2x - 3)/x) = x.
Find the function F(x) satisfying these conditions. Write F(x) as read more ..

Guest Nov 28, 2022

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130

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HALP ASAP!!!!! Sorry for latex

A base-10 integer $n$ can be represented as $32_a$ in one base and $23_b$ in another base, where $a$ and $b$ are any integer bases larger than 3. What is the smallest possible sum $a+b$?

Guest Nov 28, 2022

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124

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Infinite sequence question

The infinite sequence is defined by and for each integer . What is the remainder when is divided by ?

Guest Nov 28, 2022

+2

143

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+30

Off topic: Does anyone know what happened to cphill?

Title. Seriously, I've been using this site for like 2 years, Cphill used to answer literally all the questions around here in like 20 minutes. (My account is young because I finally gave in and made an account).

FirePhoenix Nov 28, 2022

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163

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The operation $\star$ is defined as $a \star b = a^2 \div b$. For how many integer values of $x$ will the value of $10 \star x$ be a positiv

The operation is defined as a \star b = a^2 \div b. For how many integer values of will the value of be a positive integer?

Guest Nov 28, 2022

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126

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base numbers Help ASAP

If and are non-zero distinct digits in base 6 such that , find in base 6.

Guest Nov 28, 2022

+1

122

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+30

I couldn't find answer

Sorry I didn't put this into text but the solutions are images and I don't like to make text explanations.

FirePhoenix Nov 28, 2022

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112

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algebra help

Let a and b be real numbers such that a + b = 4 and a^4 + b^4 = 16.
(a) Find all possible values of ab
(b) Find all possible values of a + b
(c) Find all possible values of a and b

Guest Nov 28, 2022

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100

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Counting

Find the number of positive integers that satisfy the following conditions:
* Each digit is a 1 or a 2 or a 3
* The sum of the digits is 10

Guest Nov 28, 2022

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100

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geometry

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area read more ..

Guest Nov 28, 2022

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