All Questions ⁺⁰234659 Questions

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Counting

For nonnnegative integers a and b, where a >= 2 and b >= 2, simplify
binom{a + b}{2} + binom{2a + b}{2} + binom{a + 2b}{2} - binom{a - b}{2}

gnistory Aug 13, 2024

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+1055

Geometry

Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.

learnmgcat Aug 13, 2024

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+296

Geometry

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

Stanry Aug 13, 2024

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4

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+296

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

Stanry Aug 13, 2024

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+1

Issues with Complex Equations on Web2.0calc

Hi everyone,

I’ve been using Web2.0calc for some time now, and it’s been great for basic calculations. However, I’ve encountered issues when working with more complex equations involving multiple variables and functions. Sometimes, the read more ..

SameulChukwezi Aug 13, 2024

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+467

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.

ChiIIBill Aug 13, 2024

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+467

help algebra

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

ChiIIBill Aug 13, 2024

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+38

I also need some help with this one-

Consider the complex numbers and in the complex plane below:
[asy]
size(250);
import TrigMacros;
real big = 5;<#> for (int i = 1; i < big+1; ++i)<#> {<#> draw(Circle((0,0),i), lightblue + linewidth(0.4));<#> read more ..

JRFPLSHelp Aug 13, 2024

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+820

Geometry

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

Hi6942O Aug 13, 2024

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+820

Geometry

In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

Hi6942O Aug 13, 2024

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+38

I need help on this problem-

Consider the complex numbers v, w and z in the complex plane below:
[asy]
size(250);
import TrigMacros;
real big = 4;
for (int i = 1; i < big+1; ++i)<#> {<#> draw(Circle((0,0),i), lightblue + linewidth(0.4));<#> read more ..

JRFPLSHelp Aug 13, 2024

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+6

How many possible distinct arrangements are there of the letters in the word Mississippi?

Read the title to see the problem

SnappyRiffs Aug 13, 2024

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+484

Geometry

Triangle ABC is rotated completely around side BC, sweeping out a solid in space. Find the volume of the solid.
AB = 5, AC = 5, CB = 5

gnistory Aug 13, 2024

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+484

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.

gnistory Aug 13, 2024

Aug 12, 2024

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+1341

Geometry

A quadrilateral has angles of $q$, $4q + 17^\circ $, $8q + 21^\circ$, and $15q + 148^\circ $. Find the largest angle of the quadrilateral, in degrees.

kittykat Aug 12, 2024

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+1341

Geometry

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

kittykat Aug 12, 2024

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+556

Geometry

All the sides of a triangle are integers. If the perimeter of the triangle is $3,$ 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 ..

booboo44 Aug 12, 2024

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+556

Geometry

Triangle $ABC$ has altitudes $\overline{AD},$ $\overline{BE},$ and $\overline{CF}.$ If $AD = 12,$ $BE = 20,$ and $CF$ is a positive integer, then find the largest possible value of $CF.$

booboo44 Aug 12, 2024

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+32

geometry

There are four cities: Capital City, Little Village, Mytown, and Yourtown. The distance from Capital City to Little Village is 5 miles. The distance from Capital City to Mytown is 21 miles. The distance from Mytown to Yourtown is 43 miles. The distance read more ..

surfz Aug 12, 2024

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+32

geometry!

Two of the sides of an acute triangle are shown. The length of the third side is also a positive integer. How many different possible values are there for the third side length? (Assume that the triangle is non-degenerate.)
(Two read more ..

surfz Aug 12, 2024

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+1323

Algebra

Solve the inequality (x - 2)(x + 6) \le (x - 2)(x + 5). Write your answer in interval notation.

blackpanther Aug 12, 2024

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+1323

Algebra

Solve the inequality x(x + 6) > 16 - x + 14 + x^2. Write your answer in interval notation.

blackpanther Aug 12, 2024

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