All Questions ⁺⁰237263 Questions

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Counting

Two different numbers are chosen at random from the set {1, 2, 3, ..., 5}. What is the probability that the product of the numbers is even?

kittykat Oct 28, 2024

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20

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+1556

Counting

Alex chooses a number at random from the set \{1, 2, 3, \dots, 5\}. Winnie also chooses a number at random from the same set. (They can choose the same number.) What is the probability that the product of their numbers is even?

kittykat Oct 28, 2024

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20

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+1556

Counting

The following cards are split into three piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
Ace of spades
Ace of hearts
Ace of diamonds read more ..

kittykat Oct 28, 2024

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22

1

+279

Algebra

One ordered pair $(a,b)$ satisfies the two equations ab^4 = 48 and ab = 24. What is the value of b in this ordered pair?

fjeihqoO Oct 28, 2024

Oct 27, 2024

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9

2

+279

Algebra

The roots of Ax^2+Bx+1 are the same as the roots of (x - 2)(x + 2). What is A+B?

fjeihqoO Oct 27, 2024

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21

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+279

Algebra

Find all the solutions to
\frac{x+4}{x+5} = \frac{x-3}{2} + \frac{x + 7}{5}

fjeihqoO Oct 27, 2024

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24

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+279

Algebra

The solutions to
2x^2 - 10x + 13 = -6x^2 - 18x - 15
are a+bi and a-bi, where a and b are positive. What is a\cdot b?

fjeihqoO Oct 27, 2024

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21

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+279

Algebra

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

fjeihqoO Oct 27, 2024

+1

24

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+5

help, diophantine equation!

Let P be the smallest prime such that there exist positive integers A and B satisfying
Find all possible values of A.

worpsterler Oct 27, 2024

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2

+5

geometry about polyhedron - help!

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is 3, then find the volume of the resulting polyhe read more ..

userlikesmath Oct 27, 2024

+1

17

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+921

Algebra

Select all the points that satisfy y < 2x - 3.
0 1 2 3 4 5 6 7 8 9
4 -5 3 8 1 0 -2 -7 -5 3 -4 -8 -9 -12 11 10 1 4 5 6 8 3
5 7 -4 5 4 0 1 2 -8 -9 -2 2 3 -4 8 7 -1 5 -4 -2 3 -4 -5 read more ..

gnistory Oct 27, 2024

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21

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+921

Algebra

Jeri finds a pile of money with at least 200. If she puts $50$ of the pile in her left pocket, gives away $\frac{1}{8}$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $200$ read more ..

gnistory Oct 27, 2024

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26

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+921

Algebra

Write the equation for the perpendicular bisector of the line segment connecting the points (-3,8) and (-5,8) in the form y = mx + b.
Note: The perpendicular bisector of the line segment $\overline{AB}$ is the line that passes read more ..

gnistory Oct 27, 2024

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16

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+921

Algebra

Fill in the blanks with integers, and select the correct operator (+or-), to give an equation whose graph is the line that passes through the point (-7,2) and is parallel to the graph of 2x+3y=-5.

gnistory Oct 27, 2024

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20

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+921

Algebra

The line below has a slope of $\frac{2}{5}.$ Find the $x$-intercept.
The line passes through (0,0).

gnistory Oct 27, 2024

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14

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+921

Algebra

Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

gnistory Oct 27, 2024

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15

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+921

Algebra

If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?

gnistory Oct 27, 2024

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14

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+921

Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$

gnistory Oct 27, 2024

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19

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+27

question plz help

Compute the length of the segment tangent from the origin to the circle that passes through the points (3, 4), (6, 8) and (5, 13).

Halplz Oct 27, 2024

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15

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+1855

Geometry

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The line is x = 4, and the equation of the circle is x^2 + y^2 = 25.

ABJeIIy Oct 27, 2024

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13

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+1855

Geometry

Let $k$ be a positive real number. The line $x + y = 3 + k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.

ABJeIIy Oct 27, 2024

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20

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+1855

Geometry

Two circles intersect at two points, $P$ and $Q$. The equations of the two circles are $x^2 + (y - 1)^2 = 1$ and $(x - 1)^2 + y^2 = 1$. Find the length PQ.

ABJeIIy Oct 27, 2024

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15

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+4

Probability

an integer between 500 and 999, inclusive, is chosen at random. what is the probability that it is an even integer whose digits are all different?

nekokashi Oct 27, 2024

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13

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+1208

Geometry

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

AnswerscorrectIy Oct 27, 2024

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16

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+1208

Geometry

In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.

AnswerscorrectIy Oct 27, 2024

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