🧮 algebra

1. **State the problem:** Solve the equation $$\frac{3}{2p} - \frac{1}{2} = \frac{\frac{1}{3}}{\frac{1}{4}p + 1}$$. 2. **Rewrite the equation for clarity:** The right side is a com

1. **State the problem:** Solve the equation $$\frac{3}{2}p - \frac{1}{2} = \frac{1}{3} \div \frac{1}{4}p + 1$$ for $p$. 2. **Simplify the right side:** Recall that dividing by a f

1. Masalah yang diberikan adalah menyelesaikan pertidaksamaan nilai mutlak $$|x - 2| < 3$$ dan menggambarkan hasilnya pada garis bilangan. 2. Ingat bahwa pertidaksamaan nilai mutla

1. The axis of symmetry is a line that divides a figure or graph into two mirror-image halves. 2. For a quadratic function in the form $y = ax^2 + bx + c$, the axis of symmetry is

1. Problem: Determine $f(-x)$ and $-f(-x)$ for each function and use these to decide if the function is even, odd, or neither. 2. Recall definitions:

1. The problem is to understand the rules for graphing a quadratic equation. 2. A quadratic equation is generally written as $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are consta

1. The problem is to factor the expression $x^2$. 2. Notice that $x^2$ is a perfect square, which means it can be written as the product of $x$ and $x$.

1. The problem is to solve a quadratic equation, which is generally written as $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are constants and $a \neq 0$. 2. The easiest and most u

1. The problem is to solve a quadratic equation of the form $ax^2 + bx + c = 0$ where $a \neq 0$. 2. The quadratic formula to find the roots is given by:

1. The problem is to analyze the function $F(x) = -2$. 2. This is a constant function, meaning for every value of $x$, $F(x)$ is always $-2$.

1. **State the problem:** Factor the quadratic expression $x^2 - 4$. 2. **Recognize the form:** The expression is a difference of squares since $x^2$ is a perfect square and $4$ is

1. The problem is to factor the quadratic expression $x^2 - 4$. 2. Recognize that this is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b)(a + b)$$.

1. The problem is to find the next number in the sequence: 13, 17, 71, 71, 17, 21, 25, ? 2. Let's analyze the sequence step-by-step:

1. The problem is to find the next number in the sequence: 31, 17, 48, 65, 113, 178, 291, ? 2. First, calculate the differences between consecutive terms:

1. The problem is to find the next number in the sequence: 6, 8, 12, 18, 26, 28, 32, ? 2. First, calculate the differences between consecutive terms:

1. The problem is to find the next number in the sequence: 11, 8, 8, 15, 15, 12, 12, ? 2. Observe the pattern by grouping the numbers in pairs: (11, 8), (8, 15), (15, 12), (12, ?).

1. **Problem statement:** Let $R$ be an integral domain with positive characteristic and suppose the group of units $R^\times$ is finite. Given $a,b \in R^\times$ with $a+b \neq 0$

1. The problem is to factor the expression $x^3$. 2. Recognize that $x^3$ is a perfect cube, which can be written as $x \cdot x \cdot x$.

1. Énoncé du problème : On cherche à formuler une équation de la droite qui relie le temps de vol $t$ à l'altitude $a$ de l'avion Strato 2Ca, connaissant deux points : $(a_1, t_1)

1. The problem is to factor the expression $x^3$. 2. Recognize that $x^3$ is a perfect cube, which can be written as $x \cdot x \cdot x$.

1. The problem is to factor the quadratic expression $x^2 - 4$. 2. Recognize that this is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b)(a + b)$$.