🧮 algebra

1. **State the problem:** We have a function defined as $f(x) = 6x - 5$ where $x \in \mathbb{R}$. We need to find the values of $x$ for which $f(x) = x^2$. 2. **Set up the equation

1. **State the problem:** We need to solve each integer addition problem using integer addition rules. 2. **Rules for integer addition:**

1. Let's solve the quadratic equation $x^2 - 6x - 10 = 0$ step by step. 2. The formula to solve any quadratic equation $ax^2 + bx + c = 0$ is the quadratic formula:

1. **State the problem:** Solve the quadratic equation $$x^2 - 6x - 10 = 0$$ for $x$ and give each answer correct to 2 decimal places. 2. **Recall the quadratic formula:** For any

1. **State the problem:** We are given that a 25 cent return deposit represents 6.25% of the total cost of a 2 litre soft drink. We need to find the total cost of the soft drink. 2

1. **State the problem:** We need to solve the system of inequalities graphically: $$y \geq \frac{1}{3}x + 4$$

1. **Problem 4a:** What percent of 200 is 11? The formula for percentage is:

1. **State the problem:** Solve the linear equation $-5x + 4 = -4x + 9$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Find the domain and range of the function $$y = (x + 3)^2 - 5$$. 2. **Recall the formula and properties:** This is a quadratic function in vertex form $$y

1. **State the problem:** Simplify the expression $$\left(\frac{x^{-2}}{x y^{2}}\right)^3$$. 2. **Recall the rules:**

1. **State the problem:** We need to find the interval over which the function $m$ is negative. 2. **Analyze the function:** The function $m$ is a decreasing straight line that cro

1. **State the problem:** Simplify the expression \( \frac{x^2 + 4x - 32}{2x^2 + 9x - 5} \cdot \frac{3x^2 - 75}{3x^2 - 11x - 4} \div \frac{6x^2 - 18x - 60}{x^3 - 4x} \). 2. **Recal

1. The problem asks how the point $(0,3)$ looks on a graph that also has a feature where the function does not exist (DNE) at the top of the graph. 2. Plotting the point $(0,3)$ me

1. The problem is to solve the phrase "Solve in order," which typically means to solve a given expression or equation step-by-step in the correct sequence. 2. Since no specific exp

1. The problem asks: What is the slope? 2. The slope of a line is a measure of its steepness and is calculated as the ratio of the vertical change to the horizontal change between

1. The problem involves understanding and adding two fractions represented by alien icons. 2. The formula for adding fractions is $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$

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

1. **State the problem:** We are given a graph representing the relationship between the number of books read ($x$) and the number of points earned ($y$). We need to determine whic

1. **State the problem:** We are given two square models: the first is divided into three horizontal parts with the top part white and two orange bands below; the second is divided

1. **State the problem:** Tristan took his computer to a repair store. The technician worked for 4.75 hours and charged $50 for parts. The total bill was $643.75. We need to find t

1. **State the problem:** Convert the polar equation $$r = 4\sin(2\theta)$$ to rectangular coordinates. 2. **Recall the formulas:**