Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are given that $\sin \alpha - \cos \alpha = \frac{7}{13}$. We need to find the value of $A$, wher...

TrigonometryAlgebraic ManipulationTrigonometric IdentitiesAbsolute ValueSolving Equations
2025/6/15

Krystyna has some raisins. She gave one fourth of her raisins to Irena. She then eats 6 raisins, aft...

Word ProblemLinear EquationsProblem Solving
2025/6/14

Given that the graph of the function is symmetric with respect to the origin, and $f(2) = 1$, find t...

FunctionsOdd FunctionsSymmetry
2025/6/14

The problem asks to find the value of $a_4$ in a geometric sequence $\{a_n\}$, given that $a_1 = 2$ ...

Sequences and SeriesGeometric SequenceFinding a term
2025/6/14

We are asked to find the inverse function of $y = \sqrt{x-2} + 1$ for $x \ge 2$.

Inverse FunctionsFunctionsSquare RootsDomain and Range
2025/6/14

The problem asks to find the graph of the function $f(x) = 0.5^x$. This is an exponential function o...

Exponential FunctionsGraphingFunction AnalysisExponents
2025/6/14

The problem asks us to find the geometric mean (or the equal ratio middle term) of $\sqrt{2}$ and $\...

Geometric MeanSequences and SeriesRadicals
2025/6/14

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