All Questions ⁺⁰235615 Questions

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triangle inequality

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.)

tomtom Dec 10, 2023

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triangle inequality

Two of the sides of a 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.)

tomtom Dec 10, 2023

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22

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perimeter

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 ..

tomtom Dec 10, 2023

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perimeter

The perimeter of a triangle is an integer. If one side of the triangle is $1$, then what is the smallest possible value of the perimeter? (Assume that the triangle is non-degenerate.)

tomtom Dec 10, 2023

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triangle

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 $ABD$.

bader Dec 10, 2023

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help me

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.

bader Dec 10, 2023

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52

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help plz

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.

bader Dec 10, 2023

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44

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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.

bader Dec 10, 2023

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Geometry

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $20^\circ.$ Find the area of the rhombus.

bader Dec 10, 2023

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47

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Parallelogram

Find the area of parallelogram ABCD.

bader Dec 10, 2023

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35

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+1768

rectangle

The perimeter of a rectangle is $40,$ and the length of one of its diagonals is $10 \sqrt{2}.$ Find the area of the rectangle.

bader Dec 10, 2023

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44

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Square

An equilateral triangle is constructed on each side of a square with side length $2,$ as shown below. The four outer vertices are then joined to form a large square. Find the side length of the small square.

bader Dec 10, 2023

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help geometry

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

bader Dec 10, 2023

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52

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+1768

Geometry

Rectangle $ABCD$ contains a point $X$ such that $AX = 3$, $BX = 3$, and $CX = 3$. Find $DX$.

bader Dec 10, 2023

Dec 9, 2023

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Counting

In the array below, in how many different ways can we start with the letter A and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?
A
RRR
CCCCC read more ..

wiseowl Dec 9, 2023

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solve

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

wiseowl Dec 9, 2023

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quadratic

Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

wiseowl Dec 9, 2023

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Algebra

Expand (a + 2)(3a^2 - 2a - 12)(a^2 - 2a + 1).

wiseowl Dec 9, 2023

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Quadratic

Let a and b be the solutions to 5x^2 - 11x + 4 = 2x^2 - 7x + 9 + 7x^2 - 14x - 11. Find 1/a + 1/b.

wiseowl Dec 9, 2023

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Quadratic

Let $u$ and $v$ be the solutions to $3x^2 + 5x + 7 = x^2 - 6x + 8$ Find $1/u + 1/v$.

wiseowl Dec 9, 2023

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help algebra

Let a and b be the solutions to 7x^2 + x - 5 = 2x^2 - 3x + 1. Compute (a - 4) + (b - 4).

wiseowl Dec 9, 2023

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46

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quadratic

Let $a$ and $b$ be the roots of the quadratic $x^2 - 5x + 3 = 4x^2 - 8x + 23$ Find the quadratic whose roots are $a^2$ and $b^2.$

wiseowl Dec 9, 2023

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49

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System

For certain values of k and m, the system
3a + 2b = 5
6a - 4b = k - 7a + 8b
has infinitely many solutions (a,b). What are k and m? read more ..

wiseowl Dec 9, 2023

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38

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Problem on functions

(a) Let f : (-inf,0) U (0,inf) -> R be defined by f(x) = x + 1/x. Show that f has no inverse function.
(b) Let g : (0,inf) -> R be defined by g(x) = 1/x. Show that g has an inverse function.

tomtom Dec 9, 2023

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