🧮 algebra

1. **Problem:** Factor the trinomial $n^2 - 8n + 15$ completely. 2. **Formula and rules:** For a quadratic trinomial $ax^2 + bx + c$ where $a=1$, factorization looks for two number

1. Problem 40 is not provided, so we will solve problem 44: Solve the inequality $$8 - 10 > -3$$. 2. Write the inequality: $$8 - 10 > -3$$.

1. **State the problem:** Solve the equation $2x + 5 = 17$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inverse operat

1. **State the problem:** Simplify the expression $x + 4 \cdot x - 2$. 2. **Recall the order of operations:** Multiplication comes before addition and subtraction.

1. The problem is to simplify the expression or concept as requested. 2. Simplifying means making the expression easier to understand or work with, often by combining like terms or

1. The problem is to find the domain of the function $f(x) = \sqrt{8 - x}$.\n\n2. The domain of a square root function requires the expression inside the root to be non-negative be

1. **State the problem:** Ethan wants to bake cupcakes. Each batch requires $1 \frac{2}{3}$ cups of sugar. He has 15 cups but must save $\frac{2}{3}$ cup for his wife. How many bat

1. The problem is to solve the equation 17. Since 17 is a constant and not an equation, it seems you might want to solve for a variable or clarify the problem. 2. If you meant to s

1. **Define the variable:** Let $x$ be the cost of each song in dollars. 2. **Write an equation:** Georgina started with $50 and spent money on 18 songs, each costing $x$. She has

1. Planteamos el problema: Encontrar los valores de $a$ y $b$ para que la función $$f(x) = \frac{ax^2 + bx + 5}{2x - 7}$$ tenga como asíntota oblicua la recta $$y = 2x - 3$$. 2. Re

1. The problem is to find the next term in the sequence: 29, 17, 5, ... 2. Observe the pattern by finding the difference between consecutive terms:

1. **Problem Statement:** Solve the equation $2x + 3 = 11$ for $x$. 2. **Formula and Rules:** To solve a linear equation, isolate the variable $x$ by performing inverse operations.

1. The problem is to solve the equation or system given (though not explicitly stated, we assume a typical algebraic problem). 2. Since no specific equation is provided, let's cons

1. **Problem statement:** In a class, there are 3 more girls than boys. Let $x$ represent the number of boys in the class.

1. The problem asks to find the 60th term of the arithmetic sequence 4, -1, -6, ... 2. An arithmetic sequence has a constant difference between consecutive terms. The formula for t

1. **State the problem:** Solve the equation $-6x + 1 = 13$ for $x$. 2. **Use the formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Remember, add

1. The problem asks to find the common ratio of the geometric sequence 8, -40, 200, ... 2. Recall that in a geometric sequence, the common ratio $r$ is found by dividing any term b

1. Planteamos el problema: calcular el valor de $b$ para que $$\lim_{x \to \infty} \sqrt{x^2 + bx + 2 - (x + 1)} = 3$$

1. **State the problem:** Find the equation of the perpendicular bisector of the segment with endpoints A(-2, -2) and B(-10, 4). 2. **Find the midpoint of segment AB:**

1. **State the problem:** Evaluate the expression $-4^2 + (-10) \times 2 \div (-2)$. 2. **Recall order of operations:** We follow PEMDAS (Parentheses, Exponents, Multiplication and

1. **State the problem:** Simplify the expression $$(-7 + (-3)^2) \div 1 - 4$$ using the order of operations. 2. **Recall the order of operations:** Parentheses, Exponents, Multipl