🧮 algebra

1. Statement of the problem: Factor $x^2$. 2. Recognize that $x^2$ is a monomial and can be written as the product $x\cdot x$.

1. The problem is to solve the equation $$x^2 - 5x + 6 = 0$$. 2. Start by factoring the quadratic expression. We look for two numbers that multiply to 6 and add to -5. These number

1. The problem is to solve the quadratic equation $$3y^2 - 5y + 2 = 0$$. 2. Identify the coefficients: $$a = 3$$, $$b = -5$$, and $$c = 2$$.

1. **State the problem:** Solve the equation $$\frac{x}{3} \times y \times \frac{6}{2} = \frac{13}{6} \times 6$$ for the variables involved. 2. **Simplify both sides:**

1. The problem is to solve the equation $$\frac{x}{3} + \frac{6y}{x} = \frac{13}{6}$$ for one variable in terms of the other or to simplify it. 2. Start by eliminating the denomina

1. Problem statement: The formula is $v = J(l^2 - \frac{R h}{5})$. 2. Expand by distributing $J$ across the parentheses.

1. **State the problem:** Expand and simplify the expression $$(6n - 5)^2$$. 2. **Recall the formula:** The square of a binomial $$(a - b)^2$$ is given by $$a^2 - 2ab + b^2$$.

1. **State the problem:** Expand and simplify the expression $$(3c + 4)(2c + 5)$$. 2. **Apply the distributive property (FOIL method):** Multiply each term in the first parenthesis

1. The problem is to expand and simplify the expression $(x - 5)(3x + 7)$. 2. Use the distributive property (FOIL method) to multiply each term in the first parenthesis by each ter

1. The problem asks to write the number 4070 in standard form. 2. Standard form (also called scientific notation) expresses a number as a product of a number between 1 and 10 and a

1. The problem is to simplify the expression $\left(7^{\frac{1}{2}}\right)^4$. 2. Recall the power of a power rule: $\left(a^m\right)^n = a^{m \cdot n}$.

1. **State the problem:** Eva and Dexter share sweets in the ratio 1:2. Mo and Annie share the same total number of sweets as Eva and Dexter, but in the ratio 3:5. 2. **Part a:** I

1. The problem is to analyze the function $f(x) = |x + 2|$. 2. The absolute value function outputs the distance from zero, so $f(x)$ is always non-negative.

1. The problem is to evaluate the expression $16^{\frac{3}{2}}$. 2. Recall that an exponent of the form $a^{\frac{m}{n}}$ means the $n$th root of $a$ raised to the $m$th power: $$a

1. **Problem 25:** Given the linear equation $$n = 29.6 + 1.20t$$ where $$n$$ is the number of women (in millions) aged 35 to 44 in the labor force and $$t$$ is years since 1981. 2

1. **State the problem:** Solve the system of linear equations: $$4x + 20y = -4$$

1. **State the problem:** Solve the system of inequalities: $$9 - 3x < 3$$

1. **State the problem:** Solve the system of inequalities: $$-8 \leq 5x - 7$$

1. Stating the problem: Solve the inequality $$-5x - 8 \leq 7$$. 2. Add 8 to both sides to isolate the term with $$x$$:

1. The problem is to analyze the function $y = |x - 3| - 7$. 2. This is an absolute value function, which typically forms a V-shaped graph.

1. The problem is to analyze the function $$y = -|x| + \frac{1}{2}$$ and understand its shape and key features. 2. The function involves the absolute value of $x$, which normally c