All Questions ⁺⁰234908 Questions

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+120

Algebra

Find the largest value of x for which
x^2 + y^2 = 4x + 5y
has a solution, if x and y are real.

jaekg Oct 3, 2024

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1

+20

Quick geometry question

In quadrilateral , sides and are extended past and , respectively, to meet at point . If , , , and , then what is ?

imsmarter1234 Oct 3, 2024

Oct 2, 2024

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2

+386

Algebra

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

cooIcooIcooI17 Oct 2, 2024

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5

+386

Algebra

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

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cooIcooIcooI17 Oct 2, 2024

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+386

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?

cooIcooIcooI17 Oct 2, 2024

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+386

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 ..

cooIcooIcooI17 Oct 2, 2024

+1

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0

+78

Number theory

Determine the tens digit of 7^1993

nerdboy Oct 2, 2024

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+563

Counting

Let n be a positive integer, and let S = {1, 2, 3, ..., n}. Three subsets A, B, C of S are chosen at random.
(a) Find the probability that A contains all elements 1, 2, 3, ..., n.
(b) Find the probability that B contains read more ..

gnistory Oct 2, 2024

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+598

Geometry

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 13$, $SU = 14$, $TU = 4$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

booboo44 Oct 2, 2024

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0

+598

Geometry

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 20^\circ$, then what is $\angle ABH$ in degrees?

booboo44 Oct 2, 2024

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+598

Geometry

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 62^\circ$ and $\angle STU = 29^\circ$, read more ..

booboo44 Oct 2, 2024

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1

+598

Geometry

In trapezoid ABCD, \overline{AB} \parallel \overline{CD}. Find the area of the trapezoid.

booboo44 Oct 2, 2024

+1

1

1

+78

Number Theory

The product of all the prime numbers between 1 and 100 is equal to P. What is the remainder when P is divided by 16?

nerdboy Oct 2, 2024

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1

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+864

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?

Hi6942O Oct 2, 2024

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1

0

+864

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.

Hi6942O Oct 2, 2024

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+1352

Geometry

Altitudes $\overline{AP}$ and $\overline{BQ}$ of an acute triangle $\triangle ABC$ intersect at point $H$. What is the area of triangle $ABC$?

blackpanther Oct 2, 2024

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+65

Solving Linear Inequalities

Solve the following inequality for x.
x-9≤2(9-x)

Alyssiaca Oct 2, 2024

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+563

Algebra

Find the largest integer k such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.

gnistory Oct 2, 2024

Oct 1, 2024

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1

0

+892

Algebra

Suppose $a(x) = 2x + 5 - 3x^2 + x^3$ and $b(x) = 4 - x^2 + 4x^4$. Find $(a\circ b)(3) - (b\circ a)(3).$

Rangcr897 Oct 1, 2024

+1

1

3

+78

number theory

What is the smallest positive multiple of 450 whose digits are all zeroes and ones?

nerdboy Oct 1, 2024

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1

1

+78

easy algebra

if x^4 is greater than 10000 but less than 20000, what is the sum of all possible integer values of x?

nerdboy Oct 1, 2024

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1

+78

number theory

What is equivalent to the digit n (0-9) if 12n5n is divisible by 12?

nerdboy Oct 1, 2024

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1

+892

Algebra

Let x \mathbin{\spadesuit} y = \frac{x^2}{y} for all x and y such that y\neq 0. Find all values of $a$ such that $a \mathbin{\spadesuit} (a + 1) = 9$. Write your answer as a list separated by commas.

Rangcr897 Oct 1, 2024

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1

1

+78

Geometry

What is the value of the perimeter of the smallest right triangle that has sidelengths equal to or greater than 1?

nerdboy Oct 1, 2024

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1

0

+78

Coversin

What is the value of covers(100°)?

nerdboy Oct 1, 2024

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