🧮 algebra

1. **State the problem:** We need to find the product of the binomials $$(9x - 6)(9x + 6)$$. 2. **Recall the formula:** This is a difference of squares pattern, where $$(a - b)(a +

1. **State the problem:** Find the product of $2(x - 4)^2$. 2. **Recall the formula:** The expression involves squaring a binomial and then multiplying by 2.

1. **Problem 1: Find the actual length of the patio.** The scale is 1 centimeter = 0.5 meter.

1. **State the problem:** We want to maximize the function $f(x,y) = x^2 y$ subject to the constraint $x^2 + 5xy = 108$ with $x > 0$. 2. **Use the constraint to express $y$ in term

1. **State the problem:** We are given a table representing a linear function with points $(4,9)$, $(6,14)$, $(8,19)$, and $(10,24)$. We need to find which given relationship has t

1. The problem asks to describe the rate of change of the height of a tomato plant over time, given a linear graph. 2. The rate of change in a linear relationship is the slope of t

1. **State the problem:** A company makes first-aid kits with fabric and plastic bandages in a ratio of 3 to 9. A small kit has 16 fabric bandages. We need to find how many plastic

1. **State the problem:** We are given two functions $f(x) = \sin x$ and $g(x) = 3$, and we need to find the range of the combined function $$y = f(x) + g(x) = \sin x + 3.$$ 2. **R

1. **Problem Statement:** Given the functions $f(x) = \sqrt{x}$ and $g(x) = x^2$, we want to analyze the combined function $$y = f(x) - g(x) = \sqrt{x} - x^2$$ and determine which

1. **State the problem:** We are given two equations:

1. **State the problem:** Write the equation of the line in slope-intercept form $y=mx+b$ that passes through the points $(x_1,y_1)$ and $(2,7)$. 2. **Formula for slope:** The slop

1. The problem asks to write an equation for the given graphs. 2. The description of the graphs indicates they are exponential decay curves starting near $y=9$ when $x$ is close to

1. **State the problem:** Find the slope of the line passing through points $P(5, -5)$ and $Q(4, -5)$. 2. **Recall the slope formula:** The slope $m$ of a line through points $(x_1

1. The problem is to determine which ordered pairs satisfy the equation $$y = -\frac{3}{4}x - \frac{1}{2}$$. 2. To check if a point $ (x, y) $ is a solution, substitute $x$ and $y$

1. **State the problem:** We need to determine which ordered pairs satisfy the equation $$y = -\frac{2}{3}x + \frac{2}{3}$$. 2. **Recall the formula:** For each ordered pair $(x,y)

1. **State the problem:** We want to find an expression equivalent to $$5^8 \cdot 5^{-10}$$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same b

1. The problem is to understand the relationship between the variables A and b, both having the value 2. 2. We start by stating the given information: $A = 2$ and $b = 2$.

1. The problem is to find the solution to the equation or expression given by the user, but since no specific equation was provided, we will assume a general approach to solving an

1. **State the problem:** Simplify the expression $$\left(\frac{-9y}{x^3}\right)^2$$ without parentheses. 2. **Recall the power rule for quotients:** When raising a quotient to a p

1. **State the problem:** Solve the equation $$\frac{7}{5} - \frac{1}{3} v = -\frac{3}{4}$$ for $v$. 2. **Isolate the term with $v$:** Move $\frac{7}{5}$ to the right side by subtr

1. **State the problem:** There are 18 animals in total, some chickens and some cows. The total number of legs counted is 50. We need to find how many chickens and how many cows th