All Questions ⁺⁰234503 Questions

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+1752

help with 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 ..

bader Jan 21, 2024

0

5

0

+1752

Circle

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

bader Jan 21, 2024

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31

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+1752

bisectors

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

bader Jan 21, 2024

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28

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+1752

Triangles

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

bader Jan 21, 2024

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24

0

+1752

Bisectors

In the diagram, $\overline{CX}$ bisects $\angle ACB$. Find the ratio of the area of triangle $BCX$ to the area of triangle $ACX$. Express your answer as a common fraction. read more ..

bader Jan 21, 2024

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38

0

+1752

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.</ read more ..

bader Jan 21, 2024

-1

35

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+1877

Probability

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 ..

tomtom Jan 21, 2024

-1

22

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+1877

Geometric probability

Let PQR be an equilateral triangle, centered at O. A point X is chosen at random inside the triangle. Find the probability that X is closer to O than to any of the sides. (In other words, find the probability that XO is read more ..

tomtom Jan 21, 2024

-1

27

0

+1877

Expected value

The grid below is made up of line segments, like the line segment in red. There are a number of paths that go from A to B in the grid, where every step goes to the right or up. If we choose a line segment at random, then what is the expected number read more ..

tomtom Jan 21, 2024

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19

1

+1348

help domain

Find the smallest real number $x$ in the domain of the function $$f(x) = \sqrt{(x-3)^2-(x+3)^2}.$$

sandwich Jan 21, 2024

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6

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+1348

Domain question

Find the number of real numbers that are not in the domain of the function $$f(x) = \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3}.$$

sandwich Jan 21, 2024

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27

1

+1348

Domain

Find the sum of all real numbers $x$ that are not in the domain of the function $$f(x) = \frac{1}{x^2+7} + \frac{1}{x^3 - x^4} + \frac{1}{x^2 - 3x + 2}.$$

sandwich Jan 21, 2024

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22

0

+1348

help algebra

If $f(x)$ is a function whose domain is $[-8,8]$, and $g(x)=f\left((x^2 - 2)/(x + 1)\right)$, then the domain of $g(x)$ is an interval of what width?

sandwich Jan 21, 2024

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18

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+1348

Function

Let
$$f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.$$
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?

sandwich Jan 21, 2024

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23

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+1348

Domain

The function $f(x)$ is defined only on domain $[-1,2]$, and is defined on this domain by the formula
$$f(x) = 2x^2-8x+1.$$
What is the range of $f(x)$? Express your answer as an interval or as a union of intervals.

sandwich Jan 21, 2024

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28

1

+39

please help :( (btw due tomorrow)

The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is . If the polygon has 9 sides, then find the smallest angle, in degrees.

rerebas Jan 21, 2024

Jan 20, 2024

0

9

1

+550

Coordinates

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 20.
The line is y = -4.

booboo44 Jan 20, 2024

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25

0

+550

Algebra

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

booboo44 Jan 20, 2024

0

38

0

+550

Lines

The line $y = mx$ bisects the angle between the two lines shown below. Find $m$.
The two lines are y = x and y = 2x.

booboo44 Jan 20, 2024

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24

1

+1348

Domain

Find the smallest integer value of $c$ such that the function $f(x)=\frac{2x^2+x+5}{x^2+4x+c+12x+x^2}$ has a domain of all real numbers.

sandwich Jan 20, 2024

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16

1

+1348

Domain

Find the domain of the function $$f(x) = \frac{1}{x+8} + \frac{1}{\sqrt{x - 8}} + \frac{1}{\sqrt{8 - x}}.$$ Express your answer as a union of intervals.

sandwich Jan 20, 2024

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