All Questions ⁺⁰237167 Questions

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+753

Algebra

The sum of the first three terms of a geometric sequence of integers is equal to seven times the first term, and the sum of the first four terms is $30$. What is the first term of the sequence?

crimefightingvigiI Mar 4, 2025

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1

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+753

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(2/x + x/2).
What is the domain of g?

crimefightingvigiI Mar 4, 2025

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+753

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f(x - 4x^2)
What is the domain of g?

crimefightingvigiI Mar 4, 2025

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+753

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = 5 - f(x) + f(5/x).
What is the domain of g?

crimefightingvigiI Mar 4, 2025

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+753

Algebra

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f((x + 1)(x - 2)).
What is the domain of g?

crimefightingvigiI Mar 4, 2025

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+21

Algebra

Let t be a root of f(x) = x^3 - x + 3. Evaluate t^6 - 4t^5 + 7t^4 - 3t^2 + 10t - 13.

co1inqiu Mar 4, 2025

+1

1

1

+21

Algebra

Let r, s, and t be solutions of the equation x^3 - 4x^2 - 7x + 12 = 0. Compute
\frac{rs}{t^2} + \frac{rt}{s^2} + \frac{st}{r^2}

co1inqiu Mar 4, 2025

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+21

Algebra

Let r, s, and t be solutions of the equation x^3 + 2x^2 - 5x + 15 = 0. Compute
\frac{1}{r - 2s - 2t} + \frac{1}{s - 2r - 2t} + \frac{1}{t - 2r - 2s}

co1inqiu Mar 4, 2025

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+21

Algebra

Suppose r and s are the values of x that satisfy the equation
x^2 - 2mx + (m^2 - 6m + 11) = 0
for some real number m. Find the minimum real value of (r - s)^2.

co1inqiu Mar 4, 2025

Mar 3, 2025

+1

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2

+11

Complex numbers... Help needed!

Let be a complex number so that
Find z, then calculate .

Mathematix1981 Mar 3, 2025

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+75

Algebra

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2mn - 18m + 7n - 3mn + 15m + 8n + ___

HumanBemg Mar 3, 2025

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+75

Algebra

Fill in the blanks, to complete the factorizaion:
(a^2 + b^2 - c^2)^2 - 4a^2 b^2 - 4a^2 c^2 + 4b^2 c^2 = (a + ___)(a + ___)(a + ___)(a + ___)

HumanBemg Mar 3, 2025

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+75

Algebra

Let r_1, r_2, r_3, r_4, and r_5 be the complex roots of x^5 - 4x^2 + 7x - 1 = 0. Compute
(r_1^2 + r_1^6 + 2)(r_2^2 + r_2^6 + 2)(r_3^2 + r_3^6 + 2)(r_4^2 + r_4^6 + 2)(r_5^2 + r_5^6 + 2)

HumanBemg Mar 3, 2025

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+75

Algebra

Factor 3xy - 4x^2 + 18y - 24x + 5x^2*y - 8y^3 + 20.

HumanBemg Mar 3, 2025

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+1734

Algebra

Let a_1, a_2, a_3, \dots, a_{10}, a_{11}, a_{12} be an arithmetic sequence. If $a_1 + a_3 + a_5 + a_7 + a_9 + a_{11} = 0$ and $a_2 + a_4 + a_6 + a_8 + a_{10} + a_{12} = 0$, then find $a_1$.

blackpanther Mar 3, 2025

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+1734

Algebra

The system of equations
\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 2
has exactly one solution. What is $z$ in this solution?

blackpanther Mar 3, 2025

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+1734

Algebra

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{3}.

blackpanther Mar 3, 2025

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+1734

Algebra

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator read more ..

blackpanther Mar 3, 2025

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+965

Algebra

Evaluate the infinite geometric series
0.4 + 0.036 + 0.0000324 + ...
Express your answer as a fraction with integer numerator and denominator.

magenta Mar 3, 2025

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+965

Algebra

The equation of the line below can be expressed in the form
\frac{x}{a} + \frac{y}{b} = 1.
Find a.
The lines passes through (5,8) and (-4,17).

magenta Mar 3, 2025

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+965

Algebra

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 20, Shirley runs screaming from the room. What number does Laverne say that sends read more ..

magenta Mar 3, 2025

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+188

New question :) someone help me please T_T

Triangle ABC is a 30-60-90 right triangle with right angle at C, angle ABC = 60 degrees, and hypotenuse of length 2. Let P be a point chosen at random inside ABC, and extend ray BP to hit side AC at D. What is the probability that BD < √2?
<read more ..

HumenBeing Mar 3, 2025

Mar 2, 2025

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+35

Question Askers

Guys, look at these guidelines: https://web2.0calc.com/questions/some-guidlines-for-question-askers
I think everyone on this site who asks a question should in fact show what they have tried. This is not a website to magically read more ..

Kromy Mar 2, 2025

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+753

Algebra

Evaluate
1 + \frac{i}{3} - \frac{1}{9} - \frac{i}{27} + \frac{1}{81},
where $i$ is the imaginary unit.

crimefightingvigiI Mar 2, 2025

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+753

Algebra

Evaluate
2 + \frac{6}{7} +\frac {18}{49} + \frac{54}{343} + 1 + \frac{2}{14} + \frac{3}{98}.

crimefightingvigiI Mar 2, 2025

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