🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{1 - \frac{4}{x+8}}{x + \frac{16}{x+8}}$$. 2. **Rewrite the expression:** To simplify, write the numerator and denominator

1. Problem: Solve the exponential equation $10^x = 100^{2x - 3}$ by finding a common base. 2. Recall that $100 = 10^2$, so rewrite the right side:

1. **State the problem:** We need to find the domain and range of the function $f$ based on the graph description. 2. **Recall definitions:**

1. **Problem:** Determine who has finished 4/5 of their project. 2. **Step 1: Calculate total fraction finished by each person by adding their parts.**

1. **State the problem:** Simplify the expression $$\frac{2 \cdot x \cdot x \cdot x - 8 \cdot x \cdot x \cdot x}{2 \cdot x}$$. 2. **Rewrite the expression:** The numerator is $$2x^

1. **State the problem:** We want to find the equation representing the combinations of 6-passenger cars ($x$) and 3-passenger cars ($y$) such that the total passengers per run is

1. The problem involves two inequalities: $$y \geq 3x + 1$$ and $$y \leq 3x - 3$$. 2. We want to find the solution set that satisfies both inequalities simultaneously.

1. The problem is to solve a grade 9 math question. Since no specific question was provided, let's consider a common algebra problem: Solve for $x$ in the equation $2x + 3 = 11$. 2

1. **Problem statement:** Two trains leave the station at 9 am. One blows its whistle every 12 minutes, the other every 9 minutes. After the initial whistle at 9 am, we want to fin

1. **State the problem:** Calculate the value of the expression $-2 - 4 - 4 \times 4 \times 7 \times -2$. 2. **Recall the order of operations:** Multiplication and division are per

1. **State the problem:** Simplify the expression $$(9 - 4) \times (-2) + (-6) \div 6 - (-9) \times 8$$. 2. **Apply order of operations (PEMDAS):**

1. **Énoncé du problème** : Déterminer le domaine et les zéros des fonctions

1. **State the problem:** Find the zeros of the function $$g(x) = \frac{x^2 - 16}{x - 4}$$ with domain $$\mathbb{R} \setminus \{4\}$$.

1. The problem is to convert temperatures from Celsius (°C) to Fahrenheit (°F) using the formula: $$\text{°F} = 32 + 1.8 \times \text{°C}$$

1. **State the problem:** Factor the quadratic expression $y = 8x^2 + 19x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that m

1. **Problem 1: Percentage increase in bid** The original bid is 42.99 and the new bid is 45.00. We want to find the percentage increase.

1. **State the problem:** We need to fill in the missing decimal and percentage values in the chart for the given fractions and decimals. 2. **Recall the formulas:**

1. **State the problem:** Calculate the total loss (in the red) for Premier Arts Company over four months: July, August, September (losses), and October (profit).

1. **State the problem:** Solve the system of equations: $$y^2 + xy = 5$$

1. The problem is to simplify the fraction $\frac{75}{120}$ to its simplest form. 2. To simplify a fraction, we divide both the numerator and denominator by their greatest common d

1. The problem is to simplify the fraction $$\frac{54}{63}$$. 2. To simplify a fraction, we divide the numerator and denominator by their greatest common divisor (GCD).