Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem consists of two questions. Question 1 asks to rewrite expressions with negative exponent...
ExponentsAlgebraic ExpressionsSimplification
2025/6/16
A group of farmers are plowing a field together. If we count both the cows and the farmers, there ar...
Systems of EquationsWord ProblemLinear Equations
2025/6/15
A rectangle has a width of 2 cm and a length of 9 cm. The width is increased by 1 cm and the length...
AreaRectangleLinear EquationsWord Problem
2025/6/15
The problem asks to evaluate two complex number related expressions: b) Evaluate $(1 - \sqrt{3}i)^8$...
Complex NumbersDe Moivre's TheoremRoots of Complex NumbersPolar Form of Complex Numbers
2025/6/15
We need to show that the dot product of a vector with itself is equal to the square of the magnitude...
VectorsDot ProductMagnitudeVector Spaces
2025/6/15
The problem describes a middle school where the total number of students last year was 440. This yea...
Systems of EquationsWord ProblemsPercentage Change
2025/6/15
We need to solve the following equation for $x$: $7.511 - [7.88 - (150.12 / x - 1.24)] / 0.48 = 1.01...
Equation SolvingLinear EquationsAlgebraic Manipulation
2025/6/15
We are given the equation $2.8x + 53 = 1000 - x = 3900$ and asked to solve for $x$. It seems like th...
Linear EquationsSolving EquationsAlgebraic Manipulation
2025/6/15
We need to solve the equation $9.501 - [(101.25 + x - 2.94) + 2.36] + 0.52 = 1.001$ for $x$.
Equation SolvingLinear EquationsOrder of Operations
2025/6/15
The problem asks us to verify the following trigonometric identity: $\frac{\cos x}{1 + \sin x} + \fr...
TrigonometryTrigonometric IdentitiesAlgebraic Manipulation
2025/6/15