🧮 algebra

1. The problem asks for the first five terms of an arithmetic sequence where the first term $a_1 = 2$ and the common difference $d = 7$. 2. The formula for the $n$-th term of an ar

1. **State the problem:** We need to find the area of a square rug where each side measures $8x + 1$ feet. 2. **Formula for the area of a square:** The area $A$ of a square with si

1. **State the problem:** Simplify the expression $$\frac{14a^{16}b^{13}}{-7a^{10}b^{11}}$$. 2. **Formula and rules:** When dividing powers with the same base, subtract the exponen

1. **State the problem:** We need to find the exponents in the expression \((x^{a} + 2)(x^{b} + 8) = x^{8} + 10x^{4} + 16\) such that the equation is true. 2. **Recall the formula:

1. **State the problem:** We need to find the area of the shaded region, which is the area of the large square minus the area of the smaller square hole inside it. 2. **Write the f

1. **State the problem:** Find the product of $[(x - 7) + y][(x - 7) - y]$. 2. **Recall the formula:** This is a product of conjugates, which follows the difference of squares form

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)