🧮 algebra

1. **State the problem:** Simplify the expression $\frac{5 \times 70 - 50}{10}$. 2. **Apply the order of operations:** First, multiply $5$ by $70$.

1. **State the problem:** Divide the polynomial $$2x^3 - 5x^2 + 3x + 7$$ by the binomial $$x - 2$$. 2. **Formula and method:** Use polynomial long division or synthetic division to

1. The problem is to write an equation. 2. An equation is a mathematical statement that asserts the equality of two expressions, typically written as $A = B$.

1. **State the problem:** We are given the rational function $$f(x) = \frac{x+3}{x^2 + 2x - 3}$$ and asked to analyze and graph it, including finding intercepts, domain, vertical a

1. **State the problem:** Write the equations of the vertical and horizontal lines passing through the point $(-1, -2)$. 2. **Recall the definitions:**

1. **State the problem:** Solve the equation $0.1^{2x-1} = 100$ for $x$. 2. **Recall the formula and rules:** We use the property of exponents and logarithms. Since $0.1 = 10^{-1}$

1. **State the problem:** Simplify the complex fraction $$\frac{\frac{x^2 - 1}{x^2 + x}}{\frac{x - 1}{x + 1}}$$ and find which expression it is equivalent to. 2. **Recall the rule

1. **State the problem:** Solve the equation $-4x^3 - 4x = 0$ for $x$. 2. **Factor the equation:** Factor out the common factor $-4x$:

1. The problem asks for the solution to a system of two linear equations based on their graph. 2. The solution to a system of linear equations is the point where the two lines inte

1. **State the problem:** We need to determine which of the given equations does NOT have $\frac{3}{2}$ as a solution. 2. **Recall the method:** To check if $x=\frac{3}{2}$ is a so

1. **State the problem:** Solve the equation $$\frac{5y}{4} - \frac{y}{2} = -\frac{3}{4}$$ for $y$. 2. **Identify the formula and rules:** To solve for $y$, combine like terms and

1. **Problem Statement:** Given the graph of a parabola opening upwards with vertex at (6,0), x-intercepts near 1 and 10, and y-axis and x-axis labeled as described, find: (a) doma

1. **Problem statement:** Find the x-intercept of a line, state the condition for its existence, explain it geometrically, find the gradient by rearranging to gradient-intercept fo

1. **Problem statement:** We are given two lines on a coordinate plane and need to find their point of intersection, which is the solution to the system of linear equations represe

1. **Stating the problem:** Vi ska identifiera vilket ekvationssystem som kan lösas med den givna bilden som visar två linjer. 2. **Analysera linjerna:** Den röda linjen ser ut att

1. **State the problem:** Solve the equation $$45 = 3x + \sqrt{x - 5}$$ for $x$. 2. **Isolate the square root term:**

1. Planteamos el problema: Resolver la ecuación $$45 = 3x + \sqrt{x} - 5$$ para encontrar el valor de $x$. 2. Primero, sumamos 5 a ambos lados para aislar términos con $x$:

1. **State the problem:** Rewrite the expression $$8^{0.5} \cdot 2^{\frac{3}{5}}$$ as a single power of 2. 2. **Recall the formula and rules:**

1. **State the problem:** We need to simplify the expression $$\frac{3 \sqrt{3}}{5 \sqrt{75}}$$. 2. **Recall the rules:** Simplify square roots and fractions by factoring and cance

1. **State the problem:** We are given the function $$y = \frac{ax + b}{cx + d}$$ where $$a, b, c, d$$ are constants and $$c \neq 0$$.

1. **State the problem:** Sue wants to make 60 gingerbread men. The recipe quantities given are for 20 gingerbread men. We need to find how much of each ingredient is required for