All Questions ⁺⁰236088 Questions

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Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$

AnswerscorrectIy Dec 2, 2024

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+895

Algebra

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

AnswerscorrectIy Dec 2, 2024

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+895

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

AnswerscorrectIy Dec 2, 2024

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+895

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 3 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 30 miles per hour, the trip takes 3 hours and 45 read more ..

AnswerscorrectIy Dec 2, 2024

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+58

Some help with a geometry question (High school math)

I'm trying to practice for math challengers in February next year by looking at some of the previous iteration's answers, and I'm kind of stuck on this question.
A 6cm diameter, 5 cm tall cylinder is partially filled with water. read more ..

choutowne Dec 2, 2024

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+407

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.

MeIdHunter Dec 2, 2024

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+407

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $4,$ and the area of triangle $PSR$ is $8.$ Find the area of trapezoid read more ..

MeIdHunter Dec 2, 2024

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+445

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

crimefightingvigiI Dec 2, 2024

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+445

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $100$ square foot wall in $10$ minutes, then how long would it take the $15$ members to paint a $100$ square foot wall, in minutes?

crimefightingvigiI Dec 2, 2024

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+445

Algebra

Seven years ago, Grogg's dad was $9$ times as old as Grogg. Four years ago, Grogg's dad was $6$ times as old as Grogg. How old is Grogg's dad currently?

crimefightingvigiI Dec 2, 2024

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+445

Algebra

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/9 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

crimefightingvigiI Dec 2, 2024

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+281

Algebra

The solutions to
2x^2 - 10x + 13 = -6x^2 - 18x - 15
are a+bi and a-bi, where a and b are positive. What is a\cdot b?

jaekg Dec 2, 2024

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+10

Examine the Inequality (x-9)2+7>0

Alice examined the inequality (x-9)2+7>0 and announced, without solving algebraically or graphing, that the solution to the inequality is all real numbers.
What did Alice see by inspection that told her the solution was all real read more ..

ariellacabrera Dec 2, 2024

Dec 1, 2024

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+281

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 ..

jaekg Dec 1, 2024

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+281

Algebra

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

jaekg Dec 1, 2024

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+10

AP Satistics

Sometimes machines used to fill soda cans can overfill or underfill. For one such machine, the distribution of the amount of soda filled into 12-ounce cans is approximately normal with a mean of 12.05 ounces and a standard deviation of 0.02 ounces. Let S= the read more ..

ariellacabrera Dec 1, 2024

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+1520

Algebra

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

blackpanther Dec 1, 2024

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+1520

Algebra

Find the largest integer k such that the equation 5x^2 - kx + 8 - 2x^2 + 25 =0 has no real solutions

blackpanther Dec 1, 2024

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+1520

Algebra

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2.

blackpanther Dec 1, 2024

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