All Questions ⁺⁰237779 Questions

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18

1

+381

Algebra

Parts (a)-(c) refer to the graph of
-4x^2 + y^2 - 2y = -3y^2 + 8x + 9y + 15
which is a hyperbola.
Find the center of the hyperbola.

cwimie Feb 22, 2025

0

23

0

+381

Algebra

Find the vertices of the hyperbola from part (a).
-4x^2 + y^2 - 2y = -3y^2 + 8x + 9y + 15

cwimie Feb 22, 2025

0

23

0

+381

Algebra

Find the asymptote of the hyperbola from part (a) with positive slope.
Enter your answer as an equation of the form $y = mx + b$.
-4x^2 + y^2 - 2y = -3y^2 + 8x + 9y + 15

cwimie Feb 22, 2025

0

24

0

+381

Algebra

Find the constant k so that the equation
4x^2 + 9y^2 - 8x + 54y + k = 2x^2 + 5y^2 - 12x + 34y
represents an ellipse which has an area of 6 \pi.

cwimie Feb 22, 2025

0

17

0

+1524

Algebra

An ellipse and a hyperbola have the same foci, $A$ and $B$, and intersect at four points. The ellipse has major axis $24,$ and minor axis $13.$ The distance between the vertices of the hyperbola is $5$. Let $P$ be one of the points of intersection read more ..

learnmgcat Feb 22, 2025

0

2

16

0

+1524

Algebra

Find the quotient and remainder when p(x) is divided by q(x), where p(x) = x^2 + 2 and q(x) = x^4 + 11x^2 - 7x + 10.

learnmgcat Feb 22, 2025

0

20

0

+1524

Algebra

Find the quotient and remainder when p(x) is divided by q(x), where p(x) = 9x^4 + x^3 - 12x + 21 and q(x) = x.

learnmgcat Feb 22, 2025

0

1

7

1

+1524

Algebra

Find the quotient and remainder when p(x) is divided by q(x)$, where p(x) = x^4 - x^2 + 3x - 7 and q(x) = x^2 + 2x - 5.

learnmgcat Feb 22, 2025

0

25

0

+56

Algebra

Find an ordered pair of constants (a,b) such that the polynomial f(x)=x^3+ax^2+(b+2)x+1 is divisible by x^2-3.
Enter your answer as an ordered pair in the format $(a,b)$, where $a$ and $b$ are replaced by appropriate numbers. read more ..

NotThatSmartTwo Feb 22, 2025

0

23

0

+56

Algebra

Given that x = 2 is a root of p(x) = x^4 - 3x^3 + 11x^2 - 25x + k for some constant k, find all the roots of p(x) (real and nonreal).
Enter your answer as a list of numbers separated by commas.

NotThatSmartTwo Feb 22, 2025

0

20

0

+56

Algebra

The polynomial
g(x) = x^3 - x^2 - (m^2 + m + 18) x + 2m^2 - 14m - 6
is divisible by x - 5 and all of its zeroes are integers. Find all possible values of m.

NotThatSmartTwo Feb 22, 2025

0

19

0

+56

Algebra

Let f(x) be a polynomial such that f(0) = 4, f(1) = 8, and f(2) = -6. Find the remainder when f(x) is divided by x.

NotThatSmartTwo Feb 22, 2025

0

22

0

+864

Algebra

Let f(x) = x^{10}+5x^9-8x^8+4x^7-x^6-33x^5+4x^4-22x^3+8x^2-3x-5.
Without using long division (which would be horribly nasty!), find the remainder when f(x) is divided by x^2 - 4.

RedDragonl Feb 22, 2025

0

20

0

+864

Algebra

Suppose P(x) is a polynomial of smallest possible degree such that:
* P(x) has rational coefficients.
* P(-2) = P(\sqrt{5}) = P(\sqrt{7}) = P(\sqrt{17}) = 0.
* P(-1) = 13.
Determine the value of P(0).

RedDragonl Feb 22, 2025

0

17

0

+864

Algebra

Find a monic quartic polynomial f(x) with rational coefficients whose roots include x = 1 + \sqrt{5} - 7 + \sqrt{3}. Give your answer in expanded form.

RedDragonl Feb 22, 2025

0

23

0

+864

Algebra

There are integers b, c for which both roots of the polynomial x^2 - x - 3 are also roots of the polynomial x^3 - bx^2 - c. Determine the ordered pair (b,c).

RedDragonl Feb 22, 2025

0

21

0

+417

Algebra

Solve the system of equations
x + y + 2z = 1
-2x - 4y + 2z = 7
10x - 17x + 13z = 8 read more ..

nathanl6656 Feb 22, 2025

0

1

20

0

+417

Algebra

Solve the system of equations
5x + 3z = 1
-x + y - z = 0
2x - 3y + 7z = -4

nathanl6656 Feb 22, 2025

0

1

12

0

+417

Algebra

Given that
5a - 7b + 3c = 19
4a + 2b - 8c = 4
7a + 5b + 3c = -11 read more ..

nathanl6656 Feb 22, 2025

0

3

12

0

+417

Algebra

Find all values of z such that z^4 - 4z^2 + 3 = 5z^2 + 11z^3 - 40.

nathanl6656 Feb 22, 2025

0

29

0

+519

Algebra

Find all values of x satisfying
sqrt(4x - 3) + 40/sqrt(4x - 3) = 12x + 14.

bIueb3rry Feb 22, 2025

0

22

0

+519

Algebra

What is the domain of the function f(x) = sqrt(6x - 3 + x^2)?

bIueb3rry Feb 22, 2025

+1

8

1

+519

Algebra

What is the domain of the function f(x) = sqrt(5 - 8x + x^2)?

bIueb3rry Feb 22, 2025

0

14

1

+519

Algebra

What is the range of the function f(x) = sqrt(5 - 8x + x^2)?

bIueb3rry Feb 22, 2025

0

10

1

+1271

Algebra

What is the domain of the function g(x) = (6x + 7)(2x - 3)?

Akhain1 Feb 22, 2025

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