🧮 algebra

1. **State the problem:** We need to find the combined budget for Sales, Engineering, and Media departments given the total annual budget is 100000000. 2. **Identify the percentage

1. The problem is to simplify the expressions: 200 - 2a^2 and 3a^5 - 4a^3. 2. For each expression, we look for common factors to factor out.

1. **State the problem:** Simplify the expression $$\frac{-3x^4 - 3x^3 - 9x^2}{3x^2}$$. 2. **Formula and rules:** When simplifying a fraction with polynomials, divide each term in

1. The problem asks for the equation of the trend line passing through two points on a scatter plot. 2. The two yellow points given are approximately $(0,8)$ and $(9,4)$.

1. **State the problem:** Simplify the expression $$\frac{-3x^4 - 3x^3 - 9x^2}{3x^2}$$. 2. **Formula and rules:** When dividing polynomials, divide each term in the numerator by th

1. **State the problem:** Anwar built a square deck with an area of 256 square feet. He wants to build a railing on three sides of the deck. We need to find the total length of the

1. **State the problem:** Paul and Kate bought a total of 6 CDs, paying 78 in total. Each CD Paul bought costs 12, and each CD Kate bought costs 15. We need to find how many CDs Ka

1. **State the problem:** Write the quadratic function $$f(x) = 4 - 9x - 3x^2$$ in vertex form $$f(x) = a(x - h)^2 + k$$ and identify the vertex. 2. **Rewrite the function in stand

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