🧮 algebra

1. The problem is to analyze the quadratic expression $x^2 - 12x + 35$. 2. First, we can factor the quadratic to find its roots. We look for two numbers that multiply to $35$ and a

1. **State the problem:** Simplify the expression $5 - 3(g - 2)$. 2. **Distribute the $-3$ across the parentheses:**

1. **State the problem:** Factor the quadratic expression $x^2 + 15x + 54$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b=15$, and $c=5

1. The problem is to multiply $2.7 \times 10^{-4}$ by $6.3 \times 10^{6}$. 2. Multiply the decimal parts: $2.7 \times 6.3 = 17.01$.

1. The problem is to evaluate the expression $\frac{36}{2} + 2 \times 2$. 2. According to the order of operations (PEMDAS/BODMAS), we first perform division and multiplication from

1. The problem asks if the equation $6(5-2)=18$ is true. 2. First, simplify inside the parentheses: $5-2=3$.

1. The problem is to factor the expression $m^2 - 36n^2$. 2. Recognize that this is a difference of squares, which has the general form $a^2 - b^2 = (a - b)(a + b)$.

1. The problem asks to sketch a graph with the following characteristics: - Domain: $[-2, 3]$

1. Solve the equation $3x - 8 = \frac{3x}{2} + 10$. Step 1: Multiply both sides by 2 to clear the fraction:

1. **State the problem:** Leo is building a rectangular garden bed. Each side requires $2 \frac{3}{4}$ meters of wood per layer, and he plans $1 \frac{2}{3}$ layers in height. Each

1. The problem is to analyze the expression $3x^2 + 6$. 2. This is a quadratic expression where the coefficient of $x^2$ is 3 and the constant term is 6.

1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{-64a^6} \cdot \sqrt{64a^6}}{-4a^3 - 2a^3}$$. 2. **Simplify the numerator:**

1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{-64a^6} \cdot \sqrt{64a^6}}{-4a^3 - 2a^3}$$. 2. **Simplify the numerator:**

1. The problem is to solve the equation $$2x + 3 = 7$$ for $x$. 2. Start by isolating the variable term $2x$ on one side. Subtract 3 from both sides:

1. Stating the problem: Simplify the expression $$\frac{\sqrt{\left(-13 p^{2} q\right)^{2}+\left(-12^{2} p^{4} q^{2}\right)}}{-5 p^{2} q}$$. 2. Simplify inside the square root:

1. The problem is to solve the equation 12. 2. Since 12 is a constant and not an equation, there is no variable to solve for.

1. The problem asks to describe the graph of the equation $y = 88$. 2. This is a horizontal line because the value of $y$ is constant and does not depend on $x$.

1. **Problem statement:** Simplify the expression $$2x^4 (x - 16)(x + 2)$$. 2. **Step 1: Expand the binomials**

1. Solve the system of linear equations: $$7x + \frac{5y}{8} = 26$$

1. **State the problem:** We want to find how many counters (dots) are in the 10th term of the given pattern. 2. **Analyze the pattern:**

1. The problem states that Rob thinks of a number with one decimal place that rounds to 6 when rounded to the nearest whole number. 2. To round to 6, the number must be at least 5.