🧮 algebra

1. **State the problem:** Simplify the expression $(2x) x^2$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying terms with the same base, add the e

1. **State the problem:** Simplify the expression $n^2 \cdot n^3$ without using exponents. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same bas

1. Let's clarify the problem: we want to find the exact solution to an equation or expression that equals 2. 2. Typically, to solve for an exact solution, we use algebraic manipula

1. Let's clarify the context where we add 1 in math problems. 2. Often, adding 1 appears in formulas involving counting or sequences, such as when calculating the number of terms b

1. The problem is to find the coefficient of the term with degree 3 in a polynomial or expression. 2. The degree of a term is the sum of the exponents of the variables in that term

1. Énoncé du problème : On considère la fonction $$g(x) = 1 - 3(x - a)^2$$ définie sur l'intervalle $$I = [0, \infty)$$.

1. **Stating the problem:** We are given the linear equation $x + y = 8$ and asked to understand its graph and properties. 2. **Formula and rules:** This is a linear equation in tw

1. **State the problem:** Solve for $x$ in the equation $$\frac{x}{2} - \frac{3 - x}{4} = 0.$$\n\n2. **Formula and rules:** To solve equations with fractions, find a common denomin

1. The problem asks to find the monthly tax due on an income of P60,000. 2. To solve this, we need the tax rate or tax formula, which is not provided in the question. Assuming a ta

1. The problem is to find the value of $\ln(4)$, where $\ln$ denotes the natural logarithm, which is the logarithm to the base $e$ (Euler's number, approximately 2.71828). 2. The n

1. **State the problem:** Solve the exponential equation $$e^{2x} - 5e^{x} + 4 = 0$$ for $x$. 2. **Rewrite the equation:** Let $y = e^{x}$. Then $e^{2x} = (e^{x})^2 = y^2$. Substit

1. **State the problem:** Solve the exponential equation $$x^{2} 2^{x} - 2^{x} 13 = 0.$$\n\n2. **Rewrite the equation:** Factor out the common term $$2^{x}$$ to get:\n$$2^{x}(x^{2}

1. **Problem:** Match each function with its corresponding graph. 2. **Recall the properties of exponential functions:**

1. **Problem 1:** Solve the equation $$\frac{x+5}{3} + \frac{x-3}{2} = \frac{x+7}{3}$$ 2. **Problem 2:** Solve the equation $$\frac{3}{x-5} + \frac{4}{x+7} = \frac{5}{x-6}$$

1. **State the problem:** Simplify the expression $$\frac{1}{4} \times 21^2 \times \frac{12}{11}^2$$. 2. **Rewrite the expression:** The expression can be written as $$\frac{1}{4}

1. **Problem Statement:** We have two functions describing water flow in a tank over time $t$ from 0 to 7.

1. **Problem statement:** A person travels at 5 km/hr until the remaining distance equals the time traveled in hours. Then, they increase speed to 8 km/hr and complete the journey

1. **Problem Statement:** Determine if the function $f(x) = x^4 - x^2$ has a horizontal asymptote. 2. **Recall the definition:** A horizontal asymptote is a horizontal line $y = L$

1. **State the problem:** Express the rational function $$\frac{x^3 - 2x}{x^2 + 3x + 2}$$ as partial fractions. 2. **Factor the denominator:** The denominator is a quadratic polyno

1. **Stating the problem:** We are given multiple algebraic expressions and asked to analyze or simplify them. These include quadratic polynomials, rational expressions, and quarti

1. The problem asks to find 80 percent of 450,000. 2. To find a percentage of a number, use the formula: $$\text{Percentage value} = \frac{\text{percent}}{100} \times \text{total v