🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{x^2 - 4x + 3}{x^2 - 9}$$. 2. **Recall the formulas and rules:**

1. **Problem:** Simplify the expression $$\frac{16m^2}{24m^7}$$. 2. **Formula and rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m

1. **State the problem:** Simplify the expression $$\frac{y^2 - 36}{5y^2 - 26y - 24}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor both numerato

1. **State the problem:** We need to find which of the given numbers has the greatest value among $4.\overline{2}$, $\sqrt{24}$, $\pi + 1$, and $\frac{9}{2}$.\n\n2. **Convert each

1. The problem asks to identify which of the given inequalities involving square roots is incorrect. 2. Recall that the square root function gives the positive number whose square

1. **State the problem:** Find the product and simplify the expression $$(9m^4)(-8m^3)$$. 2. **Recall the multiplication rules:** When multiplying coefficients (numbers), multiply

1. **State the problem:** Simplify the expression $$3(4u^2 - 1)$$. 2. **Formula and rules:** Use the distributive property, which states that $$a(b + c) = ab + ac$$. Here, multiply

1. **State the problem:** Solve the quadratic equation $x^2 + 6x = 25$. 2. **Complete the square:** To solve by completing the square, add the square of half the coefficient of $x$

1. **State the problem:** Solve the quadratic equation $$x^2 - 10x = -9$$ by completing the square. 2. **Formula and rule:** To complete the square for an equation of the form $$x^

1. **State the problem:** Simplify the expression $$\sqrt{\sqrt{\left(\frac{m^{3}}{m^{-11}}\right)^{4}}}$$. 2. **Use exponent rules:** Recall that $$\frac{a^{x}}{a^{y}} = a^{x-y}$$

1. **State the problem:** Simplify the expression $$\left\{\left[\left(\frac{1}{4}\right)^3 \cdot \left(\frac{2}{3}\right)^3\right]^{-1} \cdot \left(\frac{1}{6}\right)^4\right\}^{-

1. **State the problem:** Simplify each algebraic expression by combining like terms. 2. **Recall the rule:** Like terms have the same variable raised to the same power. Combine th

1. **State the problem:** Factor completely the polynomial $$25x^2 - 9$$. 2. **Formula and rules:** Recognize this as a difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$.

1. **State the problem:** We are given two polynomials:

1. **Problem statement:** A sports car worth 20000 decreases in value by 15% each year. 2. **Modeling the depreciation:** The value after $t$ years is given by the formula for expo

1. **State the problem:** We need to identify the exponential function from the given options based on the graph. 2. **Recall the general form of an exponential function:**

1. **State the problem:** We are given two points on the graph of an exponential function: (1, 24) and (2, 144). We need to find the function of the form $$f(x) = a b^x$$ where $a$

1. **Stating the problem:** Isabelle needs to complete 20 more practice hours. She drives 4 hours a week for 3 weeks. We want to find expressions that represent the change in her r

1. **Stating the problem:** Isabelle needs to complete 20 more practice hours. She drives 4 hours each week for 3 weeks. We want to find expressions that represent the change in he

1. The problem is to determine if a given relation is a function. 2. A function is a relation where each input (x-value) corresponds to exactly one output (y-value).

1. **State the problem:** Solve the linear equation for $y$ and understand its graph. 2. **Given equation:**