All Questions ⁺⁰232867 Questions

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+48

Geometry

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

jumbcan Jun 24, 2024

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+48

Geometry

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

jumbcan Jun 24, 2024

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+48

Geometry

In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?

jumbcan Jun 24, 2024

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+48

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

jumbcan Jun 24, 2024

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+48

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

jumbcan Jun 24, 2024

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+48

Geometry

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

jumbcan Jun 24, 2024

Jun 23, 2024

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+14

help me :(

If and , then what is the value of

NotThatSmart ●●●

onyulee Jun 23, 2024

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+32

Geometry

Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length read more ..

jumbean Jun 23, 2024

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+486

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.

Rangcr897 Jun 23, 2024

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+486

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.

NotThatSmart ●

Rangcr897 Jun 23, 2024

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+283

Sam writes down positive integers, without squares and cubes. Its starts as , what is the 1000th term, or number

Sam writes down positive integers, without squares and cubes. Its starts as , what is the 1000th term, or number

Lilliam0216 Jun 23, 2024

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+283

Sam wants to color the three sides of an equilateral triangle. He has five different colors to choose from. In how many different ways can S

Sam wants to color the three sides of an equilateral triangle. He has five different colors to choose from. In how many different ways can Sam color the sides of the triangle? (Two colorings are considered the same if one coloring can be rotated and/or read more ..

Lilliam0216 Jun 23, 2024

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+26

Number Theory: HELP!!

If a, b, and c are positive integers less than 13 such that:
2ab + bc + ca ≡ 0 (mod 13)
ab + 2bc + ca ≡ 3abc (mod 13)
ab + bc + 2ca ≡ 8abc (mod 13) read more ..

colinqiu Jun 23, 2024

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+486

Geometry

Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.

Rangcr897 Jun 23, 2024

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4

+486

Geometry

Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length AB. read more ..

NotThatSmart ●●●●

Rangcr897 Jun 23, 2024

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+1237

Number Theory

Let $m$ be a positive integer such that $m$ has exactly $12$ positive divisors. How many distinct prime factors does $m$ have?

ABJeIIy Jun 23, 2024

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6

+486

Geometry

A circle is inscribed in a quarter-circle, as shown below. If the radius of the quarter-circle is $4,$ then find the radius of the circle.

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Rangcr897 Jun 23, 2024

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+1790

Polynomials

Let b be a constant. What is the smallest possible degree of the polynomial f(x) + b \cdot g(x), where f(x) = 2x^5 - 6x^4 - 4x^3 + 12x^2 + 7x - 5 and g(x) = x^6 - 17x^5 + 2x^4 + 6x^3 + 11x^2 - 8x + 1.

LiIIiam0216 Jun 23, 2024

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+83

What does the blue check mark mean next to title?

Im fairly new to this website and dunno a lot of the things. please help me :)

shmewy Jun 23, 2024

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+1790

Algebra

Let f be a cubic polynomial such that f(0) = 5, f(2) = 8, f(3)=13, and f(7) = -5. What is the sum of the coefficients of f?

LiIIiam0216 Jun 23, 2024

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+1790

Algebra

Determine all of the following for f(x) \cdot g(x), where f(x) = -7x^4-3x^2 + 2 and g(x) = 2x^8 - 3x^7 + 5x^6 + 3x^5 - 11x^4 + 3x^3 - 18x^2 + 17x - 5.
Leading term:
Leading coefficient:
Degree: read more ..

LiIIiam0216 Jun 23, 2024

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+1790

Algebra

There exists a polynomial f(x) and a constant k such that
(x^2 - 2x - 5) f(x) = x^4 - 2x^3 + kx^2
What is k?

LiIIiam0216 Jun 23, 2024

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+1790

Algebra

What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 4x^2 + 8x + 7)?

LiIIiam0216 Jun 23, 2024

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+1790

Algebra

What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x + 7x + 1)?

LiIIiam0216 Jun 23, 2024

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+283

Triangle

Sam wants to color the three sides of an equilateral triangle. He has five different colors to choose from. In how many different ways can Sam color the sides of the triangle? (Two colorings are considered the same if one coloring can be rotated and/or read more ..

Lilliam0216 Jun 23, 2024

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