All Questions ⁺⁰236027 Questions

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+551

Algebra

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

Pythagorearn Oct 19, 2024

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5

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+551

Algebra

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

Pythagorearn Oct 19, 2024

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5

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+1455

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?

kittykat Oct 19, 2024

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3

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+1455

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 ..

kittykat Oct 19, 2024

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+1455

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?

kittykat Oct 19, 2024

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7

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+1455

Algebra

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.

kittykat Oct 19, 2024

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+1839

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.

ABJeIIy Oct 19, 2024

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5

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+1839

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.

ABJeIIy Oct 19, 2024

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5

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+1839

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.

ABJeIIy Oct 19, 2024

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3

1

+1839

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.

ABJeIIy Oct 19, 2024

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6

1

+54

Balls and Boxes

In how many ways can 4 balls be placed in 4 boxes if 3 balls are indistinguishably white, 1 ball is black, and the boxes are indistinguishable?

RedDragon1 Oct 19, 2024

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7

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+976

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

Hi6942O Oct 19, 2024

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6

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+976

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 $DE$?

Hi6942O Oct 19, 2024

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8

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+976

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 $BD$?

Hi6942O Oct 19, 2024

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5

1

+54

C&P

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling?

RedDragon1 Oct 19, 2024

Oct 18, 2024

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+310

Geometry

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

MEMEG0D Oct 18, 2024

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4

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+310

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?

MEMEG0D Oct 18, 2024

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5

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+310

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 $AB$.

MEMEG0D Oct 18, 2024

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3

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+310

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 $WXYZ$?

MEMEG0D Oct 18, 2024

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+606

Number Theory

Starting at the same time, Bill rings a bell every $36$ seconds, and Wendy blows a whistle every $90$ seconds, and Sam blows a horn every $385$ seconds. How many minutes will it be before both Bill and Wendy and Sam simultaneously make a sound?

cooIcooIcooI17 Oct 18, 2024

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+606

Number Theory

As shown in class, the Euclidean algorithm can be used to find solutions to equations of the form
ax + by = c.
Use the Euclidean algorithm to find integers $x$ and $y$ such that $6x + 3y = 1,$ with the smallest possible positive read more ..

cooIcooIcooI17 Oct 18, 2024

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5

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+606

Number Theory

You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $52$ pieces of candy per scoop to the vat, and another machine that can remove exactly $39$ pieces of candy with a different scoop from read more ..

cooIcooIcooI17 Oct 18, 2024

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