bIueb3rry

98 Questions
13 Answers

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Algebra

Find the foci of the ellipse shown below.
Enter your answer as a list of ordered pairs separated by commas.
Points on the ellipse are (-4,9), (-7,2), (-5,2), (-7, 1)

bIueb3rry 01.03.2025

0

4

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+414

Algebra

The real numbers x and y satisfy
x^2 + y^2 - 8x + 6y + 23 = 0.
Find the largest possible value of x + y.

bIueb3rry 01.03.2025

0

5

0

+414

Algebra

Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 2.

bIueb3rry 01.03.2025

0

5

0

+414

Algebra

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

bIueb3rry 01.03.2025

0

7

0

+414

Algebra

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

bIueb3rry 22.02.2025

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6

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+414

Algebra

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

bIueb3rry 22.02.2025

+1

2

1

+414

Algebra

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

bIueb3rry 22.02.2025

0

2

1

+414

Algebra

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

bIueb3rry 22.02.2025

0

5

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+414

Algebra

Let P(x) be a polynomial of the form
P(x) = 2x^3 + ax^2 - 23x + c,
such that 12 and 7 are roots of P(x). What is the third root?

For the polynomial in part (a), compute the ordered pair (a,c).

bIueb3rry 22.02.2025

0

5

0

+414

Algebra

Let P(x) be a polynomial of the form
P(x) = 2x^3 + ax^2 - 23x + c,
such that 3 and 1 are roots of P(x). What is the third root?
For the polynomial in part (a), compute the ordered pair (a,c).

bIueb3rry 22.02.2025

0

6

0

+414

Algebra

Let a and b be integer such that (2 + sqrt(5))(137) = a + b sqrt(5). Compute a^2 - 5b^2.

bIueb3rry 22.02.2025

0

3

1

+414

Algebra

Let (2 + \sqrt{5})(137) = a + b \sqrt{5}, where a and b are integers. Compute a^2 - 5b^2.

bIueb3rry 22.02.2025

0

4

1

+414

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).

bIueb3rry 21.02.2025

0

5

0

+414

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.

bIueb3rry 21.02.2025

0

7

0

+414

Algebra

Find a polynomial f(x) of degree 5 such that both of these properties hold:
* f(x) is divisible by x^3.
* f(x) is divisible by (x+1)^3.
Write your answer in expanded form. mehr ..

bIueb3rry 20.02.2025

0

6

0

+414

Algebra

Suppose the polynomial f(x) is of degree 3 and satisfies f(3) = 2, f(4) = -4, f(5) = 6, and f(8) = 8.
Determine the value of f(0).

bIueb3rry 20.02.2025

0

9

1

+414

Algebra

Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If $a_1 + a_3 = 5$ and $a_2 + a_4 = 6$, then find $a_1$.

bIueb3rry 26.01.2025

+1

13

0

+414

Algebra

When the same constant is added to the numbers $a,$ $b,$ and $c,$ a three-term geometric sequence arises. If $a = 60,$ $b = 100,$ and $c = 140,$ what is the common ratio of the resulting sequence?

bIueb3rry 26.01.2025