🧮 algebra

1. **State the problem:** Solve the inequality $$89 - f \geq 86$$ for the variable $f$. 2. **Isolate the variable:** To solve for $f$, we want to get $f$ alone on one side of the i

1. **State the problem:** Solve the inequality $$-2 \leq -78 - p$$ for $$p$$. 2. **Isolate the variable:** To solve for $$p$$, we want to get $$p$$ alone on one side of the inequal

1. Planteamos el problema: resolver y graficar las funciones dadas, e indicar dominio y rango. 2. Para funciones lineales como a) y b), la fórmula general es $y = mx + b$, donde $m

1. **State the problem:** Calculate Social Security (SS) tax, Medicare tax, and total deductions for given gross pay values using the tax rates. 2. **Formulas and tax rates:**

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. **State the problem:** Simplify the expression $$9 - 45 \cdot \frac{7}{5} - \left[12 + 7 - 21 \cdot \frac{9}{3}\right]$$. 2. **Recall order of operations:** Perform multiplicati

1. **State the problem:** Factorize the quadratic expression $x^2 + 3x + 2$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that mult

1. **State the problem:** Solve the quadratic equation $x^2 - 4 = 0$. 2. **Formula and rules:** This is a difference of squares equation, which can be factored using the identity $

1. The problem asks about the roots of a quadratic equation. 2. A quadratic equation is generally written as $ax^2 + bx + c = 0$ where $a \neq 0$.

1. **State the problem:** Find the axis of symmetry for the quadratic function $$y = x^2 - 11x + 24$$. 2. **Formula used:** The axis of symmetry for a quadratic function in the for

1. The problem asks for the name of the point where a parabola changes direction. 2. In algebra and calculus, this point is known as the vertex of the parabola.

1. The problem is to understand how to solve equations simply and systematically. 2. The general formula or approach to solve an equation is to isolate the variable on one side.

1. **State the problem:** Find the point where the quadratic function $y = x^2 + 2x + 1$ touches the x-axis. 2. **Recall the formula:** The quadratic touches the x-axis where $y=0$

1. **State the problem:** We are given the function $$f(x) = \frac{6x+5}{2-\sqrt{14+5x}}$$ and we want to understand its behavior and domain. 2. **Identify the domain restrictions:

1. **State the problem:** Find the minimum value of the quadratic function $$y = x^2 + 6x + 10$$. 2. **Recall the formula:** A quadratic function $$y = ax^2 + bx + c$$ has its vert

1. **State the problem:** We are given the function $$f(x) = \frac{6x+5}{2-\sqrt{14+5x}}$$ and we want to analyze or simplify it. 2. **Identify the domain:** The expression under t

1. State the problem: Solve $a^3+a^2=36$ for $a$. 2. Set up the equation in standard form: $$a^3+a^2-36=0$$

1. **State the problem:** Determine if the situation is exponential growth or decay and write the equation modeling the population of the school after $x$ years. 2. **Identify grow

1. **State the problem:** Simplify the expression: $$4 - \{6 + [-5 + (12 - 8)]\} - 5 + \{4 + [3 - (4 - 8) + (-5 - 10)]\} - [(8 + 3) - (5 - 1)] + [8 - 3) - (5 + 1)] + \{9 - [2 - (1

1. **State the problem:** Find the prime factorization of 630. 2. **Recall the formula and rules:** Prime factorization means expressing a number as a product of prime numbers.

1. **State the problem:** We are given a recursive arithmetic sequence defined by $a_n = a_{n-1} + 7$ with the first term $a_1 = -5$. We need to find the values of $a_4$ and also a