🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{x+3}{x^2 - 5x + 6} + \frac{6}{x^2 - 7x + 12}$$. 2. **Factor the denominators:**

1. The problem asks us to find which number among 10, 60, 100, and 160 does NOT have the same prime factors as 40. 2. First, find the prime factors of 40.

1. **State the problem:** Evaluate the product of the fractions $\frac{37}{100}$ and $\frac{7}{10}$. 2. **Formula used:** To multiply two fractions, multiply the numerators togethe

1. **State the problem:** Simplify the expression $5 - 7 + 2(3 - 8)$. 2. **Apply the order of operations:** First, simplify inside the parentheses.

1. The problem is to calculate the division of two fractions: $\frac{3}{14} \div \frac{6}{7}$.\n\n2. The formula for dividing fractions is:\n$$\frac{a}{b} \div \frac{c}{d} = \frac{

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