Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
Find the values of $c$ and $d$ that satisfy the equation $7 \times 10^c + 7 \times 10^d = 70700$.
ExponentsEquationsSolving EquationsPowers of 10
2025/6/14
We are asked to find the domain of the function $f(x) = \sqrt{x^2 + x - 6}$.
DomainFunctionsQuadratic InequalitiesInequalitiesFactoring
2025/6/14
The problem asks us to identify which of the given functions is the same as the function $y = x$, wh...
FunctionsFunction EqualityReal NumbersAbsolute ValueSquare RootCube Root
2025/6/14
The problem asks us to find an expression for $y$ such that the given condition "jGty = x, where x i...
EquationsFunctionsReal NumbersCube RootAbsolute Value
2025/6/14
The problem is to find the solution set of the inequality $(6x + 1)(4x - 3) \le 0$.
InequalitiesQuadratic InequalitiesInterval NotationSolution Sets
2025/6/14
Let $A = (-2, +\infty)$ and $B = [5, +\infty)$. Find the complement of $B$ on $A$, which can be deno...
Set TheoryIntervalsSet OperationsComplement
2025/6/14
The problem asks to show that the sum of an arithmetic progression (AP) is given by the formula $S_n...
Arithmetic ProgressionSeriesSummation FormulaProof
2025/6/13
The problem states that $g = \sqrt{\frac{h-4}{5+h}}$. (a) We need to find the value of $g$ when $h=2...
EquationsVariable IsolationSquare RootsAlgebraic Manipulation
2025/6/13
We are given a quadratic function $f(x) = ax^2 + bx + c$, where $a, b, c$ are real numbers. The maxi...
Quadratic FunctionsOptimizationVertex of a ParabolaInequalities
2025/6/13
We are given the equation $\sqrt{ax+b} = d$ and asked to express $x$ in terms of $a$, $b$, and $d$.
Equation SolvingRadicalsLinear Equations
2025/6/13