🧮 algebra

1. **State the problem:** We want to find how many copies can be made for 10 dollars if 30 copies cost 20 dollars. 2. **Identify the ratio:** The ratio of copies to dollars is give

1. **State the problem:** Solve the inequality $-2x \leq 14$ for $x$. 2. **Recall the rule for inequalities:** When dividing or multiplying both sides of an inequality by a negativ

1. **State the problem:** Solve the absolute value equation $$|2a + 7| = a - 4$$. 2. **Understand the absolute value definition:** For any expression $x$, $$|x| = \begin{cases} x &

1. **State the problem:** We are given the parabola equation $ (y + 1) = 8 (x - 3) $ and need to find its opening direction, vertex, focus, axis of symmetry, directrix, length of t

1. **Simplify each expression step-by-step:** **a)** $3(x - 2) + 6(5 - x)$

1. **State the problem:** We are given the parabola equation $ (y + 1) = 8(x - 3)^2 $ and need to find its opening direction, vertex, focus, axis of symmetry, directrix, length of

1. **Problem:** Transform the radical expression $$\sqrt[3]{9a^{6}b^{9}}$$ into rational exponents. 2. **Formula:** Recall that $$\sqrt[n]{x} = x^{\frac{1}{n}}$$. For variables wit

1. Énoncé du problème : Effectuer les opérations algébriques données en appliquant la distributivité et la simplification. 2. Rappel de la formule : Pour toute expression de la for

1. **Énoncé du problème :** Simplifier chaque expression algébrique donnée. 2. **Rappel de la règle distributive :** Pour toute expression de la forme $k(m + n)$, on distribue $k$

1. The problem asks to find 70% of 100. 2. To find a percentage of a number, use the formula: $$\text{Percentage of a number} = \frac{\text{percentage}}{100} \times \text{number}$$

1. Énoncé du problème : Effectuer les opérations algébriques données. 2. Rappel des règles importantes :

1. Stating the problems: f) Simplify $-45x \div 15$

1. **State the problem:** We need to solve the expression $-\frac{1}{4} - \frac{1}{7}$. 2. **Formula and rules:** When subtracting fractions, we find a common denominator and then

1. **State the problem:** We need to find four integers $a \leq b \leq c \leq d$ such that: - Their total sum is $a+b+c+d=44$.

1. **State the problem:** Solve the system of linear equations: $$6x + 2y = 19$$

1. **State the problem:** We are given two simultaneous equations:

1. **State the problem:** Multiply the fractions $\frac{5}{4}$ and $\frac{7}{10}$. 2. **Formula:** To multiply fractions, multiply the numerators together and the denominators toge

1. **State the problem:** We are given the quadratic function $$y = x^2 - 13x + 42$$ and need to analyze it, including finding its roots and graph features. 2. **Formula and rules:

1. **State the problem:** Find the factors of 81. 2. **Definition:** Factors of a number are integers that divide the number exactly without leaving a remainder.

1. **State the problem:** Solve for $g$ in the equation $$-3(g - 12.8) = -19.8$$. 2. **Use the distributive property:** Multiply $-3$ by each term inside the parentheses:

1. Solve the inequality $5 + 13 < 11$. Step 1: Combine like terms on the left side: $5 + 13 = 18$.