🧮 algebra

1. **State the problem:** Calculate the product of the three fractions $$\frac{4}{21} \times \frac{7}{6} \times \frac{9}{11}$$. 2. **Formula and rules:** When multiplying fractions

1. **State the problem:** Calculate the product of the fractions $\frac{9}{10} \times \frac{2}{7} \times \frac{5}{6}$.\n\n2. **Formula and rules:** To multiply fractions, multiply

1. Masalah: Cari range dari fungsi $h(x) = 2x$ dengan domain $\{1, 2, 3, 4\}$.\n\n2. Formula: Range adalah himpunan nilai output fungsi ketika domain tertentu diberikan.\n\n3. Lang

1. **State the problem:** Factor the expression $$-2x(16x^2 - 40x - 25)$$ using the MT (Middle Term) Test Method. 2. **Recall the MT Test Method:** This method is used to factor qu

1. **Problem:** Solve for $p$ in the equation $5p^{-3} = 8 \times 5^{-2}$. 2. **Formula and rules:** Recall that $a^{-n} = \frac{1}{a^n}$ and properties of exponents allow us to ma

1. **State the problem:** Given the equation $5p^{-3} = 8 \times 5^{-2}$, find the value of $p$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$-3 \cdot (-2x^2 + 3x - 1) + 2 \cdot (4x^2 - 5x + 3) - \frac{5}{8} \cdot (-3x^2 - 2x + 7)$$. 2. **Recall the distributive propert

1. The problem involves understanding the data represented by a line graph with a peak at 86 and then a steep decline. 2. The vertical axis shows values up to 86, which likely repr

1. **State the problem:** Simplify the expression $2x \times 2x^2$. 2. **Recall the multiplication rule for exponents:** When multiplying terms with the same base, add the exponent

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** We are given input-output pairs: inputs $5,6,7,8$ and outputs $11,14,17,20$. We want to find the expression (function) that relates the input $x$ to the o

1. The problem is to solve the compound inequality $-2x > -5 > -15$. 2. Compound inequalities can be split into two separate inequalities: $-2x > -5$ and $-5 > -15$.

1. **Problem:** Find an equation whose roots are $a^3\beta$ and $\alpha\beta^3$, where $a$ and $\beta$ are roots of $2x^2 - 4x + 1 = 0$. 2. **Step 1: Identify sum and product of ro

1. **State the problem:** Simplify the expression $$(5x-3)(x+1) - 6x + 10x^2 + (3-5x)^2$$. 2. **Recall formulas and rules:**

1. **State the problem:** Simplify the expression $$(5x-3)(x+1)-6x+10x^2+(3-5x)^2$$. 2. **Recall formulas and rules:**

1. **Problem statement:** We need to find how many students are selected in total for the competition if 20% of the boys and 25% of the girls from all classes are selected. 2. **St

1. مسئله را بیان می‌کنیم: مجموع دو عدد برابر با $\frac{45}{12}$ است و یکی از اعداد $\frac{11}{3}$ واحد بزرگتر از دیگری است. باید عدد بزرگتر را پیدا کنیم. 2. فرض کنیم عدد کوچکتر $x$

1. **State the problem:** Solve the equation $6 + 2x = x - 6$ for $x$. 2. **Write down the equation:**

1. Let's start by understanding the problem: you want a detailed explanation of equations, why we use them, and the reasoning behind each step. 2. Equations are mathematical statem

1. **Problem statement:** Simplify the expression $\frac{3}{2} + \frac{5}{2} \div \frac{5}{4}$. 2. **Recall the division of fractions rule:** Dividing by a fraction is the same as

1. **State the problem:** Solve the equation $3y + 15 = 5y + 1$ for $y$. 2. **Write down the equation:**