🧮 algebra

1. The problem is to expand and simplify the perfect square polynomial $ (c - 2)^2 $. 2. Recall the formula for the square of a binomial:

1. The problem asks to find the value of $x$ in the equation $$\frac{3x+1}{2} = 7.$$\n\n2. The formula used here is to solve linear equations by isolating the variable $x$.\n\n3. F

1. **State the problem:** Solve the equation $|x-1|=3$ for $x$. 2. **Recall the definition of absolute value:** For any real number $a$, $|a|=b$ means $a=b$ or $a=-b$ if $b\geq0$.

1. The problem asks to find the value of $x$ in the equation $$\frac{3x+2}{5} = 4.$$\n\n2. The formula used here is to solve for $x$ by isolating it on one side of the equation. We

1. **State the problem:** Solve the equation $$3x + 15 = 3(x + 6) - 3$$. 2. **Apply the distributive property:** Expand the right side:

1. The problem is to solve the equation $7 + x = \frac{1}{2}(4x - 2)$ and identify the step where a mistake occurs. 2. Start with the original equation:

1. **State the problem:** Expand the expression $u(u - 11)$. 2. **Recall the distributive property:** To expand, multiply $u$ by each term inside the parentheses:

1. **State the problem:** Expand the expression $x(x + 4)$. 2. **Recall the distributive property:** To expand, multiply $x$ by each term inside the parentheses:

1. **State the problem:** We need to find the variable $m$ from the equation $$\frac{k}{m} + \frac{x}{y} = p.$$\n\n2. **Isolate the term with $m$:** Subtract $\frac{x}{y}$ from bot

1. **State the problem:** Find the value of $x$ that satisfies the equation $$10 = 23^{x+1}$$. 2. **Rewrite the equation:** The equation is already in the form $$10 = 23^{x+1}$$.

1. The user asked to "make it simply," which suggests simplifying a mathematical expression or concept. 2. Since no specific expression or problem was provided, I will explain the

1. **State the problem:** We are given the function $f(x) = \frac{2x - 3}{-x + 3}$ and need to analyze its graph, including asymptotes and points. 2. **Identify vertical asymptote:

1. The problem asks to translate the statement "The quotient from dividing n by four is eight" into an equation. 2. The word "quotient" means the result of division.

1. **State the problem:** We have two zoo membership plans with costs depending on the number of family members $x$. Plan A costs $y = 20x + 15$ and Plan B costs $y = 15x + 30$. We

1. **State the problem:** We need to find and graph all vertical and horizontal asymptotes of the rational function $$f(x) = \frac{-7x + 1}{2x^2 - 6x - 8}$$. 2. **Find vertical asy

1. **State the problem:** Multiply the complex numbers $(5 - 4i)$ and $(6 - 3i)$ and write the answer in standard form $a + bi$. 2. **Recall the formula:** To multiply two complex

1. **State the problem:** Solve the system of equations using substitution: $$5x - 2y = -31$$

1. The problem asks to write the equation of $d(x)$ in terms of $p(x)$. 2. To express $d(x)$ in terms of $p(x)$, we need a relationship or formula connecting $d(x)$ and $p(x)$.

1. The problem is to simplify the expression: $$2 f (-5) - h (10) + 3 f (16)$$ given the functions values from the other expressions. 2. From the second expression: $$2 \times 2(3)

1. The problem asks for the estimated total sales from 1996 to 1998 based on the line graph. 2. From the graph description, the sales values are approximately:

1. The problem is to solve the system of equations: $$\begin{cases} x + 2y = 6 \\ x = -2 \end{cases}$$