Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
We need to solve the equation $7(x+1) = 9 - (2x-1)$ for $x$.
Linear EquationsEquation SolvingVariable Isolation
2025/6/25
We are given the complex number $A = 1 + i + i^2 + \dots + i^{2009}$ and we are asked to determine i...
Complex NumbersGeometric SeriesComplex Number ArithmeticPowers of i
2025/6/25
We are given that $A = 1 + i + i^2 + ... + i^{2009}$. We are also given that $B = -\frac{1}{2} + i\...
Complex NumbersPowers of iSeries
2025/6/25
We are given $B = -\frac{1}{2} + i\frac{\sqrt{3}}{2}$ and $C = -\frac{1}{2} - i\frac{\sqrt{3}}{2}$. ...
Complex NumbersExponentsSimplification
2025/6/25
The problem states that $P = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$, $T = \begin{pmatrix} -3 \\ 1 \en...
VectorsMatrix OperationsVector Components
2025/6/24
We are given two matrices $P = \begin{pmatrix} 1 \\ 2 \end{pmatrix}$ and $T = \begin{pmatrix} -3 \\ ...
Matrix MultiplicationLinear TransformationsVectors
2025/6/24
The problem gives a function $f(x) = \cos^2 x + 2\sqrt{3} \cos x \sin x + 3\sin^2 x$. We need to: (9...
TrigonometryTrigonometric IdentitiesDouble Angle FormulasFinding Maximum and Minimum
2025/6/24
We are given two functions $f(x) = \frac{2x+7}{7}$ and $g(x) = \frac{3x-6}{6}$. We need to find $g(6...
FunctionsInverse FunctionsFunction Evaluation
2025/6/24
The problem asks to factor the quadratic expression $2x^2 - x - 15$.
Quadratic EquationsFactorizationAlgebraic Manipulation
2025/6/24
We are asked to evaluate $x^{\frac{1}{2}} = 4$. This means we need to find the value of $x$ that sat...
EquationsExponentsSquare RootsSolving Equations
2025/6/24