All Questions ⁺⁰237789 Questions

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Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

learnmgcat Jun 8, 2024

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54

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+1524

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

learnmgcat Jun 8, 2024

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54

1

+1524

Algebra

Find all ordered pairs x, y of real numbers such that x+y=10 and x^2+y^2=64.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

learnmgcat Jun 8, 2024

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59

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+2730

Algebra

Simplify \dfrac{1}{\sqrt2+sqrt3}+\dfrac{1}{\sqrt2-sqrt3}.

LiIIiam0216 Jun 8, 2024

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79

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+2730

Algebra

Simplify \frac{4}{1 - \sqrt[3]{3}} + \sqrt[3]{9}.

LiIIiam0216 Jun 8, 2024

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58

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+2730

Algebra

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2ab - 12a + 3a + 3b - 8b - ab + ___

LiIIiam0216 Jun 8, 2024

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61

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+2730

Geometry

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 $a + b$.

LiIIiam0216 Jun 8, 2024

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24

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+363

Probability and Counting

1. There is a group of five children, where two of the children are twins. In how many ways can I distribute 8 identical pieces of candy to the children, if the twins must get an equal amount of candy?
2. In how many ways can you read more ..

Lilliam0216 Jun 8, 2024

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43

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+28

PieceWise Functions

wassyo Jun 8, 2024

+1

65

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+28

HELP

wassyo Jun 8, 2024

-2

69

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+224

Geometry

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 ..

BRAlNBOLT Jun 8, 2024

-2

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+224

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 ..

BRAlNBOLT Jun 8, 2024

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65

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+1761

Probability

Sam writes down the numbers $1,$ $2,$ $\dots,$ $315,$ $316,$ $317,$ $\dots,$ $248,$ $249,$ $250.$
(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down at random. What is the probability read more ..

parmen Jun 8, 2024

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59

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+1761

Probability

The six faces of a cube are painted black. The cube is then cut into $3^3$ smaller cubes, all the same size.
(a) How many of the smaller cubes have exactly one black face?
(b) How many of the smaller cubes do not have any read more ..

parmen Jun 8, 2024

+1

34

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+23

Algebra prob.

Find the largest prime factor of 1,005,010,010,005,001. (Without a computer of course).

Coolmonkey Jun 8, 2024

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60

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+1761

Geometry

Let $ABCDEFGH$ be a rectangular prism. Find the volume of pyramid $CFAH$.

parmen Jun 8, 2024

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60

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+1761

Geometry

Let $ABCD$ be a regular tetrahedron. Let $E$, $F$, $G,$ $H$ be the centers of faces $BCD$, $ACD$, $ABD$, $ABC$, respectively. The volume of pyramid $DEFG$ is $18.$ Find the volume of pyramid $EFGH$

parmen Jun 8, 2024

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72

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+1761

geometry

Let $APQRS$ be a pyramid, where the base $PQRS$ is a square. The total surface area of pyramid $APQRS$ (including the base) is $800$. Let $W$, $X$, $Y$, and $Z$ be the midpoints of $\overline{AP}$, $\overline{AQ}$, $\overline{AR}$, and $\overline{AS}$, read more ..

parmen Jun 8, 2024

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69

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+1761

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

NotThatSmart ●

parmen Jun 8, 2024

+2

53

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+282

Helps!

Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
x^2 + y^2 = 4x - 8y + 17x - 5y + 25,
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.

NotThatSmart ●

BRAINBOLT Jun 8, 2024

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61

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+1761

Geometry

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

parmen Jun 8, 2024

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67

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+1761

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

parmen Jun 8, 2024

+2

57

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+282

Algebra!

What is the sum of all positive common fractions (in simplest terms) less than $5$ whose denominator is 3?

BRAINBOLT Jun 8, 2024

+2

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+282

Logarithm! Help!

Compute \log_{1/2} (16*5*1/10).

BRAINBOLT Jun 8, 2024

+2

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+282

Geometry

All the sides of a triangle are integers. If the perimeter of the triangle is $5,$ then how many different possible triangles are there? (Assume that the triangle is non-degenerate. Two triangles are considered the same if they are co read more ..

BRAINBOLT Jun 8, 2024

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