Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem asks to evaluate the expression $\log_8 256 + \log_8 4 - \log_8 7 + \log_8 224$ using th...
LogarithmsLogarithmic PropertiesExponent Rules
2025/4/23
We are given that $84\%$ of $N$ is equal to $105\%$ of $(N-120)$. We need to find what percentage of...
PercentageEquation SolvingLinear EquationsWord Problem
2025/4/23
Simplify the expression $\sqrt[3]{192x^3y^5z^{10}}$.
SimplificationRadicalsExponentsAlgebraic Expressions
2025/4/23
The problem asks us to simplify the expression $\frac{1}{(x+1)(x+2)} - \frac{5}{(x+2)(x-3)}$.
Fractional ExpressionsSimplificationAlgebraic ManipulationRational Expressions
2025/4/23
We are given a system of two equations: $\frac{1}{2}y - \frac{1}{2}x = 1$ $x^2 + y^2 = 20$ We need t...
Systems of EquationsQuadratic EquationsSubstitutionSolution Verification
2025/4/23
The problem has two parts. Part 1: Given that $x+3 \ge 7$, show that $x \ge 4$. Part 2: Given that $...
InequalitiesAlgebraic Manipulation
2025/4/23
The problem requires us to analyze the exponential function $f(x) = 3 \cdot 2^x$ and potentially gra...
Exponential FunctionsGraphingFunction Analysis
2025/4/23
The problem presents a sequence of numbers: $-6, -7.2, -8.64, -10.368, ...$ and asks us to identify ...
Sequences and SeriesGeometric SequenceCommon Ratio
2025/4/23
The problem consists of two inequalities. First, given $x+3 \ge 7$, prove that $x \ge 4$. Second, gi...
InequalitiesAlgebraic Manipulation
2025/4/23
We are asked to write the equation of the line in slope-intercept form ($y=mx+b$) for the given prob...
Linear EquationsSlope-Intercept FormWord ProblemsGraphing
2025/4/23