All Questions ⁺⁰234661 Questions

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+1323

Pascal's Triangle

The entries in a certain row of Pascal's triangle are
\[1, n, \dots, n, 1.\]
The average of the entries in this row is 2. Find $n$.

blackpanther Feb 13, 2024

-1

24

0

+1323

Probability question

The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both contain read more ..

blackpanther Feb 13, 2024

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27

1

+1323

Geometric Probability

Triangle XYZ is equilateral, with O as its center. A point P is chosen at random. Find the probability that P is closer to point O than to any of the side lengths.

blackpanther Feb 13, 2024

Feb 12, 2024

0

22

1

+400

Symmetry

The graph of $y = ax^2 + bx + c$ has an axis of symmetry of $x = -1.$ If $a = 2,$ then find $b.$

omgitsrne Feb 12, 2024

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23

1

+400

Graph of Circle

Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80$.

omgitsrne Feb 12, 2024

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3

1

+400

Vertex

Find the vertex of the graph of the equation y = -2x^2 + 8x + 15 - 3x^2 + 7x - 25

omgitsrne Feb 12, 2024

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18

1

+400

Vertex of Parabola

Find the vertex of the graph of the equation $x - y^2 + 8y = 13 + 2y + y^2 - 7y - 14$.

omgitsrne Feb 12, 2024

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33

1

+400

Quadratic Roots

Let $a$ and $b$ be the roots of $x^2 + 7x - 4 = -x^2 + 9x + 6$. Find $(a + 3) + (b + 3).$

omgitsrne Feb 12, 2024

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18

1

+1341

Rate question

I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

kittykat Feb 12, 2024

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34

1

+1341

Ratios

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and read more ..

kittykat Feb 12, 2024

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13

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+1341

Rate question

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

kittykat Feb 12, 2024

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2

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+1475

Equation of line

A line passes through the points $P$ and $Q.$ If $P = (-8,2)$ and $Q = (4,-7),$ then write the equation of this line in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive.

parmen Feb 12, 2024

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3

1

+1475

System problem

The real numbers $a$ and $b$ satisfy $a - b = 1$ and $a^3 - b^3 = 1.$
(a) Find all possible values of $ab.$
(b) Find all possible values of $a + b.$
(c) Find all possible values of $a$ and $b.$

parmen Feb 12, 2024

0

3

1

+1475

Line

Express the equation of the line passing through points $(1,7)$ and $(2,-3)$ in the form $ax+by=c$, where $a$, $b$ and $c$ are integers, the greatest common divisor of $a$ and $b$ is $1,$ and $c<0$.

parmen Feb 12, 2024

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28

1

+1475

Minimum

Find the minimum value of the expression $x^2+y^2+2x-4y+8+10x-12y$ for real $x$ and $y$.

parmen Feb 12, 2024

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26

1

+0

help triangle

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

Vxrtate Feb 12, 2024

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28

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+0

Circumcircle

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

Vxrtate Feb 12, 2024

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