🧮 algebra

1. **Problem statement:** The number of cases of a disease increases by the same factor each year. Given the initial number of cases and the number of cases at the end of several y

1. **State the problem:** We have a sugar concentration in blood that decreases by the same factor every hour. Given the concentrations at times 0, 1, 2, and 3 hours, we want to fi

1. **State the problem:** We need to find a polynomial function $m(x)$ of degree 4 with zeros at $0$, $5$, and $3 - 2i$. 2. **Recall the important rule:** For polynomials with real

1. **State the problem:** We need to find all values of $x$ such that $k(x) = 3x^2 - 19x - 14 > 0$. 2. **Recall the formula and rules:** For a quadratic function $ax^2 + bx + c$, t

1. The problem is to explain the number 20 with fewer steps. 2. We can express 20 as a product of its prime factors: $$20 = 2 \times 10$$.

1. Let's solve a simple linear equation as an example: $2x + 4 = 12$. 2. The goal is to isolate $x$ on one side of the equation.

1. Let's understand the problem: Connor works 35 hours a week and gets paid 18.25 for each hour he works normally. 2. If he works extra hours (called overtime), he gets paid more f

1. **Problem statement:** Zahid is paid a set wage of 774.72 for a 36-hour week, plus time-and-a-half for overtime. He worked 43 hours in one week. Find Zahid's earnings that week.

1. **Problem statement:** Determine if the points are collinear by checking if the gradients (slopes) between pairs of points are equal. 2. **Formula for gradient:** The gradient $

1. **Problem statement:** Calculate the wage for a mechanic who works a 12-hour day with a normal pay rate of 42.50 per hour. 2. **Rules:**

1. **State the problem:** Solve the equation $x^2 - y^2 = z^2$ for one of the variables or analyze its structure. 2. **Recognize the formula:** The equation resembles a difference

1. **State the problem:** Simplify the expression $$(-5x^5 y^3)^3$$. 2. **Recall the power of a power rule:** When raising a power to another power, multiply the exponents: $$\left

1. **State the problem:** Simplify the expression $$(-6x^5 y^5)^4$$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power:

1. Das Problem ist, dass du eine Erklärung auf Deutsch möchtest. 2. Da keine spezifische Frage gestellt wurde, erkläre ich, wie man eine einfache lineare Gleichung löst.

1. **State the problem:** We are given two functions: $$f(x) = \frac{x - 3}{x - 1}$$

1. The problem asks for the vertex of the quadratic function $f(x) = x^2 + 4x + 6$. 2. The vertex of a parabola given by $f(x) = ax^2 + bx + c$ can be found using the formula for t

1. **State the problem:** We need to analyze the function $f(x) = -(x + 1)^2 + 2$ and identify its graph, vertex, and axis of symmetry. 2. **Recall the vertex form of a quadratic f

1. **State the problem:** Solve the system of linear equations: $$6x + 2y = 6$$

1. **State the problem:** Solve the system of equations: $$y = \frac{1}{2}x + 5$$

1. **Stating the problem:** We are given a table showing the relationship between grams and packages. The grams values are 52.8 and 132, and the packages values are 1, 4, and 6. We

1. **State the problem:** Solve the system of equations by graphing: $$y = \frac{3}{2}x + 1$$