🧮 algebra

1. **State the problem:** Mark and Tracy's combined ages total 44 years. We need to find Mark's current age given a complex age relationship. 2. **Define variables:** Let $M$ = Mar

1. **Problem Statement:** Factor the trinomial 4x^2 + 16x + 12. 2. **Formula and Rules:** To factor a trinomial of the form $ax^2 + bx + c$, find two numbers that multiply to $ac$

1. **Problem:** Find all possible values of $b$ for which $7x^2 + bx + 3$ is factorable into linear factors with integer coefficients and constants. 2. **Formula and rules:** For a

1. El problema consiste en analizar y resolver las expresiones dadas para $h$ en función de $SA$ y $s$. 2. Las fórmulas son:

1. The problem states that $y$ is inversely proportional to $x$. This means the relationship can be written as: $$y = \frac{k}{x}$$

1. **State the problem:** Solve the equation $5a + b = 16$ for one variable in terms of the other. 2. **Choose a variable to solve for:** Let's solve for $b$ in terms of $a$.

1. **State the problem:** Solve a system of linear equations using the elimination method. 2. **Explain the elimination method:** The elimination method involves adding or subtract

1. **State the problem:** Solve the equation $$\frac{2}{7} (z - 10) = -3$$ for $z$. 2. **Use the distributive property and isolate $z$:** Multiply both sides by 7 to eliminate the

1. **State the problem:** Simplify and solve the expression $$2(x^2 + x - 4)^2 - 4 + \frac{1}{16}$$. 2. **Rewrite the expression:**

1. **State the problem:** Expand the expression $ (x+3)^4 $ into a standard polynomial form. 2. **Formula used:** Use the Binomial Theorem which states:

1. **Problem statement:** We are given two functions $P(x)$ and $Q(x)$ with specified end behaviors: - $P(x) \to -\infty$ as $x \to +\infty$ and $P(x) \to +\infty$ as $x \to -\inft

1. **State the problem:** We have two functions $P(x)$ and $Q(x)$, both with degree 7, and their end behaviors are given: - $P(x) \to -\infty$ as $x \to +\infty$ and $P(x) \to +\in

1. **State the problem:** Solve the quadratic equation $$3x^2 = -8x - 2$$. 2. **Rewrite the equation in standard form:** Move all terms to one side:

1. **State the problem:** Gayle wants to buy a bicycle costing 119.90. She has saved 0.7 of the total cost. We need to find how much she has saved so far. 2. **Formula used:** To f

1. El problema es encontrar el vértice de la función cuadrática $$f(x) = x^2 - 2x + 3$$ y graficarla. 2. La fórmula para encontrar la coordenada $x$ del vértice de una parábola dad

1. **State the problem:** Solve the equation $$\frac{1}{6}(x + 6) = 11$$ for $x$. 2. **Use the distributive property:** Multiply both sides by 6 to eliminate the fraction.

1. **State the problem:** Solve the equation $$\frac{1}{6}(x + 6) = 11$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. Si

1. **Problem 1:** Find $x$ when $y = -x + 3$ and $y = 2$. 2. Since both expressions equal $y$, set them equal to each other:

1. The problem states that Angelia's savings account amount is given by the expression $$148.02(1.04)^{t-10}$$ where $t$ is the number of years since the account was opened. 2. We

1. **State the problem:** We want to find an equation that shows buying one item at regular price $x$ and a second identical item at 50% off is the same as buying both items for 25

1. The problem is to simplify the given expression or answer. 2. To simplify an expression, we combine like terms, factor where possible, and reduce fractions.