🧮 algebra

1. **State the problem:** Tom cleans his room every $12$ days and Jerry every $16$ days. They start cleaning today (day $0$). We want to find the next day when both clean their roo

1. **State the problem:** Calculate the value of $$A=801324000(1+0.15)^{10}$$. 2. **Formula used:** This is a compound interest formula where $$A=P(1+r)^n$$, with $$P=801324000$$,

1. **State the problem:** Solve the equation $$\sqrt{x^2 - 4x + 13} + \sqrt{x^2 - 4x + 8} = 5$$ for $x$. 2. **Rewrite the expressions inside the square roots:**

1. **State the problem:** We need to find the equation of a parabola that passes through the points $(-4, 0)$, $(2, 6)$, and $(8, 0)$.

1. **Problem statement:** Compute the value of the expression $(-8)(-6)$. 2. **Formula and rules:** Multiplying two negative numbers results in a positive number.

1. **Understanding the problem:** Factoring means rewriting an expression as a product of simpler expressions called factors. 2. **Common factoring methods:**

1. **Problem:** Compute $(-4) + 2$. Formula: Addition of integers.

1. **State the problem:** Rationalize the denominator of the expression $$\frac{9}{4} \div (3\sqrt{5} + 6)$$. 2. **Rewrite the expression:** Division by a number is the same as mul

1. **State the problem:** Rationalize the denominator of the expression $$\frac{4}{3\sqrt{5} + 6} \cdot \frac{3\sqrt{5} - 6}{3\sqrt{5} - 6}$$. 2. **Formula and rules:** To rational

1. **Memahami masalah:** Seorang anak menabung dengan jumlah yang bertambah tetap setiap bulan, artinya tabungan tiap bulan membentuk barisan aritmetika.

1. **Nyatakan masalah:** Seorang anak menabung dengan jumlah uang yang bertambah tetap setiap bulan. Jumlah tabungan selama 12 bulan adalah 306000 dan selama 18 bulan adalah 513000

1. **State the problem:** Simplify the expression $$40-[3^2\times 3+2\times 2^3\times 2-(-10)\times 2]+90\div(-9)$$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exp

1. **State the problem:** Calculate $\text{sqr}((-5)^6)$, where $\text{sqr}$ means square root. 2. **Rewrite the expression:** We need to find $\sqrt{(-5)^6}$.

1. The problem is incomplete as the function or equation to graph is missing. 2. To graph a function, we need the explicit formula or equation.

1. The problem is to express the solution through equations. 2. To solve a problem using equations, first identify the variables and the relationships between them.

1. نبدأ بكتابة المعطيات: لدينا المعادلة $$ (2س - ص^2)(س^2 - ص^2) = 22 - 12 $$

1. **Problem 1:** Solve the inequality $$x^2 - 4x \leq 0$$ 2. **Step 1:** Factor the quadratic expression.

1. **State the problem:** Solve the inequality $$x^2 + x - 6 \geq 0$$. 2. **Factor the quadratic:**

1. **State the problems:** We need to solve the inequalities:

1. **State the problem:** Solve the inequality $$ (x+3)(x-2) \geq 0 $$ which is equivalent to $$ x^2 + x - 6 \geq 0 $$. 2. **Find the roots:** Set each factor equal to zero:

1. The problem asks to find the interval and test point for a given function or inequality. 2. Typically, to find intervals and test points, we first identify critical points where