🧮 algebra

1. **State the problem:** We need to find the area of a rectangle where the length is 5 inches longer than the width, and the perimeter is 34 inches.

1. **State the problem:** Solve the equation $$\frac{7w}{w+2} - 8 = \frac{3w}{w+2}$$ for $w$. 2. **Identify the formula and rules:** This is a rational equation where terms have de

1. **State the problem:** Solve the equation $$2 + \frac{4}{y - 4} = \frac{6}{y - 4}$$ for $y$. 2. **Identify the domain:** The denominator $y - 4$ cannot be zero, so $y \neq 4$.

1. **State the problem:** Solve the linear equation $2x + 4y = 9$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by mo

1. **State the problem:** We are given two functions: $g(x) = x + 3$ and $h(x) = x^2$. We need to calculate: (i) $g(-5)$

1. **State the problem:** Find the slope of the line passing through the points $(-21, -41)$ and $(-22, -9)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)

1. **State the problem:** Find the slope of the line passing through the points $(29, 86)$ and $(99, 14)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ a

1. **State the problem:** You want to understand how to decide which number to divide both sides of an equation by when solving for a variable. 2. **General rule:** When you have a

1. **State the problem:** Simplify the expression $$\left(\frac{z^6}{4ab^{-2}}\right) \left(3a^2 b^5\right)^2$$. 2. **Recall the rules:**

1. **State the problem:** We want to find the percentage $x$ such that 15.5 is $x\%$ of 77.5. 2. **Formula used:** The general formula to find $x\%$ of a number is:

1. **State the problem:** Solve the equation $$\frac{2}{3} = \frac{3}{4} + \frac{2}{3}$$ for equality. 2. **Understand the problem:** We want to check if the left side equals the r

1. **State the problem:** Solve for $x$ in the equation $$\frac{2}{3} = \frac{x}{4}$$. 2. **Formula and rule:** To solve for $x$ in a proportion $\frac{a}{b} = \frac{c}{d}$, use cr

1. The problem is to solve a system of equations using the elimination method. 2. The elimination method involves adding or subtracting equations to eliminate one variable, making

1. **Problem statement:** There are two numbers. When the second number is subtracted from twice the first number, the result is 18. When 9 is added to the first number, the result

1. The problem is to multiply two numbers in scientific notation: $$(4.001 \times 10^{4}) \times (3.3 \times 10^{3})$$. 2. Recall the rule for multiplying numbers in scientific not

1. **State the problem:** Simplify the expression $$\frac{x^2 - 2cx + c^2}{x^2 - c^2}$$. 2. **Recognize the formulas:** The numerator is a perfect square trinomial and can be facto

1. Solve for $x$ in the equation $$\frac{-12\sigma^{12}}{x^{13}} + \frac{6\sigma^{6}}{x^{7}} = 0.$$ 2. Start by isolating terms: $$\frac{-12\sigma^{12}}{x^{13}} = -\frac{6\sigma^{6

1. **State the problem:** We need to complete the table of values for the functions $f(x) = 4^x - 3$ and $g(x) = 4x^2 + 2$ at $x = 1, 2, 3, 4$.

1. **State the problem:** Simplify the expression $$\frac{\sqrt{c+h}-\sqrt{c}}{h}$$ where $h \neq 0$. 2. **Recall the formula:** To simplify expressions involving differences of sq

1. The problem asks to classify a quadratic function as linear, nonlinear, or constant. 2. A quadratic function is generally of the form $$f(x) = ax^2 + bx + c$$ where $a \neq 0$.

1. **State the problem:** We analyze the graph of Michael Jordan's jump height $h$ as a function of time $t$. 2. **Identify the function type:** The graph is a parabola opening dow