🧮 algebra

1. Problem: Simplify and analyze the function $f(x) = 6x^3 - 9x + 4$. Step 1: Identify the terms and powers of $x$.

1. **State the problem:** Simplify the expression $2a + 3a$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable part the same.

1. We are asked to evaluate the function $f(x) = \frac{x + 1}{2x^2 - x - 3}$ at $x = -1$. 2. The formula for the function is given as:

1. The problem is to solve the equation: $x = 2$. 2. Since the equation is already solved for $x$, the solution is simply $x = 2$.

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations. Important rules:

1. **State the problem:** Solve the system of linear equations using the elimination method: $$\begin{cases} x + y + z = 3 \\ 13x + 2z = 2 \\ -x - 5z = -5 \end{cases}$$

1. **State the problem:** Solve a system of linear equations using the elimination method. 2. **Explain the elimination method:** The elimination method involves adding or subtract

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + y + z = 3 \\ 13x + 2z = 2 \\ -x - 5z = -5 \end{cases}$$

1. **Problem statement:** We have hot chocolate amounts measured hourly from 9am to 5pm: 300, 100, 300, 500, 300, 100, 300, 500, 300 mL. We want to find the amplitude, equation of

1. **Problem:** Find the critical points and analyze the function $f(x) = \frac{x^3}{9} - 3x$. 2. **Formula and rules:** To find critical points, we use the derivative $f'(x)$ and

1. The problem is to rationalize the denominator of the fraction $$\frac{7}{4 + \sqrt{7}}$$. 2. To rationalize the denominator, we multiply numerator and denominator by the conjuga

1. The problem asks to write the expression $$\sqrt[3]{x^5} + \sqrt[4]{y^2}$$ in terms of rational exponents. 2. Recall the rule for converting radicals to rational exponents: $$\s

1. **State the problem:** Rationalize the denominator and simplify the expression $$\sqrt{\frac{5}{x^3}}$$. 2. **Rewrite the expression:** We can write the square root of a fractio

1. **State the problem:** Rationalize the denominator of the expression $$\frac{\sqrt{10}}{3\sqrt{2}}$$. 2. **Recall the rule:** To rationalize a denominator containing a square ro

1. **Problem:** Solve the system using substitution for part (a): $$\ell_1: y = 3x - 4$$

1. Masalah: Hitung nilai dari $16^{\frac{1}{2}} + 27^{\frac{2}{3}} - 125^{\frac{1}{3}}$. 2. Rumus dan aturan penting:

1. The problem is to find the value of $p$ in a given question. 2. Since the specific question details are not provided, I will explain the general approach to find $p$ in algebrai

1. The problem states that the width of the shaded regions is $x-8$. 2. To understand this, we need to know what $x$ represents and how the width is calculated.

1. **State the problem:** We need to find the product of $4X^2$ and $3X^2$. 2. **Formula used:** When multiplying terms with the same base, multiply the coefficients and add the ex

1. **State the problem:** Simplify the expression $-10X + (-4X)$. 2. **Recall the rule:** When adding terms with the same variable, add their coefficients.

1. **State the problem:** We need to simplify the expression by adding the terms involving $x^2$, specifically $8x^2 + (-5x^2)$. 2. **Recall the rule for adding like terms:** When