🧮 algebra

1. **State the problem:** Miriam wants to tape a rectangle so that its area equals the area of a given right triangle. We need to find the perimeter of that rectangle.

1. The problem is to solve number 10, but since the exact problem statement is not provided, I will assume a common algebraic problem for demonstration: Solve for $x$ in the equati

1. **State the problem:** Solve the equation $$-2\sqrt{24x} + 13 = -11$$ for $x$. 2. **Isolate the square root term:** Subtract 13 from both sides:

1. **State the problem:** We have two rectangles H I J K and L M N O that are equivalent, meaning they have the same area. We need to find the length of side L M. 2. **Write down t

1. Stating the problem: Solve the equation $$3x - \sqrt{2} = \sqrt{6}$$ for $x$. 2. Isolate the term with $x$: Add $\sqrt{2}$ to both sides:

1. **Determine if the sequence is arithmetic or geometric, find the ratio (r) or difference (d), and give the next 3 terms.** **a.** 28, 18, 8, ...

1. The problem asks to find the value of the function $f(x) = \frac{2}{x^2}$ at $x = -5$. 2. The formula for $f(x)$ is given as:

1. **State the problem:** A customer receives 1 free ticket for every 7 tickets purchased. We want to find how many free tickets a customer receives for purchasing 63 tickets.

1. **State the problem:** Solve the equation $2z = -16$ using the multiplication property. 2. **Recall the multiplication property:** To isolate the variable, divide both sides of

1. **State the problem:** Factor the expression $$8s^2 + 4s$$. 2. **Identify the common factor:** Look for the greatest common factor (GCF) of the terms $$8s^2$$ and $$4s$$.

1. **State the problem:** Solve the system of linear equations:

1. **Problem:** Find the x- and y-intercepts of the linear equation $3x + 4y = 12$. 2. **Formula and rules:**

1. **Problem:** Simplify the algebraic expression $m + m + r + 7 - 3$. 2. **Formula and rules:** Combine like terms by adding or subtracting coefficients of the same variable and s

1. **State the problem:** Solve the equation for $y$ in the equation $$-3y + 8 = 83$$. 2. **Isolate the term with $y$:** Subtract 8 from both sides to get rid of the constant on th

1. **State the problem:** Solve for $m$ in the equation $$1 = 6\sqrt{-19} + 2m - 5$$. 2. **Rewrite the equation:** Add 5 to both sides to isolate terms with $m$:

1. **State the problem:** Solve for $b$ in the equation $$\sqrt{19b - 13} = \sqrt{19 + 11b}.$$\n\n2. **Formula and rules:** To solve equations involving square roots, we can square

1. **State the problem:** We are given points (1, 12), (3, 36), and (4, 48) and asked to write an equation of the form $y = kx$ that fits these points. 2. **Understand the form:**

1. The problem is to express a solution or set in interval notation. 2. Interval notation is a way to write subsets of the real number line using parentheses \( () \) for open inte

1. **Problem:** Simplify and factor the expression $4(7x + 6) - 3(6x - 7)$. Step 1: Distribute the constants:

1. **State the problem:** Given two functions $f(x) = \frac{3}{1 - 4x}$ and $g(x) = \frac{1}{x}$, find the compositions $(f \circ g)(x)$ and $(g \circ f)(x)$, and determine the dom

1. **State the problem:** Manny can put together 3 airplane models in 4.5 hours and 4 models in 6 hours. We need to find the time it takes to put together 1 model, write an equatio