🧮 algebra

1. **State the problem:** A doctor prescribes 550 mg of a drug, and after 4 hours, 330 mg remains. We need to find the decay factor. 2. **Formula used:** The amount of drug remaini

1. **State the problem:** Find the vertex of the parabola given by the function $$f(x) = -x^2 - 12x - 34$$. 2. **Recall the vertex formula:** For a quadratic function $$f(x) = ax^2

1. **State the problem:** Determine the domain and range of the parabola given by $$f(x) = 3x^2 - 24x + 47$$. 2. **Recall the domain of a quadratic function:** The domain of any qu

1. **State the problem:** Rewrite the linear equation $$20x + 13y = 13$$ in slope-intercept form, which is $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 2.

1. **State the problem:** Rewrite the equation $5x - 5y = -17$ in slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. **Start with the

1. **State the problem:** We know that 28,700 employees represent 19.3% of the total number of employees in the company. We need to find the total number of employees. 2. **Formula

1. **State the problem:** Solve the equation $x - 11 = \sqrt{41 - 4x}$ for $x$. 2. **Formula and rules:** To solve equations involving square roots, isolate the square root term an

1. **State the problem:** Solve the equation $$\sqrt{3n + 11} = \sqrt{n + 5}$$ and check for extraneous solutions. 2. **Formula and rules:** To solve equations involving square roo

1. El problema es simplificar la expresión $$\sqrt[3]{-54}$$. 2. Recordemos que la raíz cúbica de un número negativo es el negativo de la raíz cúbica del valor absoluto de ese núme

1. **State the problem:** Evaluate the expression $$10 \log\left(\frac{10^{78}}{10} + \frac{3 \times 10^{64}}{10} + \frac{6 \times 10^{54}}{10}\right)$$ to 2 significant figures. 2

1. **State the problem:** Simplify the expression $$7^1 y^3 y^3 y^3$$. 2. **Recall the rules:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^

1. **State the problem:** Simplify the expression $3b^3 \cdot 8b^5$. 2. **Recall the rules:** When multiplying terms with the same base, multiply the coefficients and add the expon

1. **Stel het probleem vast:** We moeten voor elke eerstegraadsfunctie (rechte lijn) een tekentabel opstellen. 2. **Belangrijke regels:**

1. We are asked to determine the value of $b$ in the linear function $f(x) = ax + b$ given the graph information. 2. The value of $b$ in the standard form of a linear equation $f(x

1. **State the problem:** Simplify the expression $$18 + 3(3x - 6)$$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses.

1. **State the problem:** Solve the equation $$-10p + 9p = 12$$ for the variable $p$. 2. **Combine like terms:** The terms $-10p$ and $9p$ are like terms because they both contain

1. **State the problem:** Mandy has a gift card worth 75 and each audiobook costs 3.75. We need to find the remaining balance after purchasing 7 audiobooks and after purchasing 15

1. **State the problem:** Simplify the expression $$\frac{6}{4 - \sqrt{5}}$$. 2. **Formula and rule:** To simplify a fraction with a radical in the denominator, multiply numerator

1. **State the problem:** A bank charges a monthly fee of 3.50 for a checking account with an initial balance of 32. We want to find how many months it takes for the balance to bec

1. **State the problem:** Solve the inequality $2x^2 - 5x - 3 < 0$. 2. **Formula and rules:** To solve a quadratic inequality, first find the roots of the quadratic equation $2x^2

1. Probleemstelling: Los die volgende algebraïese oefening op: maak die oefeninge klaar. 2. Omdat die gebruiker nie 'n spesifieke probleem gegee het nie, neem ons aan hulle vra vir