🧮 algebra

1. **State the problem:** Simplify the expression $3[2k -(-2+k)]$. 2. **Recall the rule:** When you have a minus sign before parentheses, it changes the signs of the terms inside.

1. **State the problem:** We need to find the equation of the line in slope-intercept form $y=mx+b$ that represents the total number of appetizer recipes Zane knows ($y$) depending

1. **State the problem:** We need to find the equation of the line in slope-intercept form $y=mx+b$ that represents the relationship between hours spent writing ($x$) and total pag

1. **State the problem:** Tracy spent 10 dollars. She spent 38 dollars less than 3 times what Daniel spent. We want to find how much Daniel spent, represented by $x$. 2. **Write th

1. **State the problem:** Expand the expression $3[x + 2(x - 4)]$. 2. **Recall the distributive property:** $a(b + c) = ab + ac$. This means we multiply each term inside the bracke

1. **State the problem:** Expand and simplify the expression $$(3x + 2)(x - 4)$$. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **State the problem:** Solve the equation $$\frac{r + 5}{6} = \frac{r + 3}{4} + \frac{r - 1}{9}$$ for $r$. 2. **Identify the least common denominator (LCD):** The denominators a

1. **State the problem:** We are given two points on a line: $(-5,-4)$ and $(5,3)$. We need to find the equation of the line passing through these points and analyze its properties

1. **State the problem:** Find the equation of the line passing through the points (0, 2) and (2, 0). 2. **Formula used:** The slope-intercept form of a line is given by $$y = mx +

1. **State the problem:** Add the fractions $\frac{x+4}{x^2+2}$ and $\frac{x^2-2}{x-8}$ and simplify the result. 2. **Find the common denominator:** The denominators are $x^2+2$ an

1. The problem is to find the quotient rule for $6$ raised to the power of $4$. 2. The quotient rule in exponents states that for any nonzero base $a$ and integers $m$ and $n$,

1. The problem asks for the product rule applied to $6^4$. 2. The product rule in exponents states that when multiplying powers with the same base, you add the exponents: $$a^m \ti

1. **Problem Statement:** Investigate the function $f(x) = \sqrt{x}$ in the form $y = \sqrt{kx}$ and analyze the transformations for $y = \sqrt{x}$, $y = \sqrt{2x}$, $y = \sqrt{\fr

1. **State the problem:** We need to order the rational numbers 2.58, 2.62, \frac{5}{2}, and \frac{7}{3} from smallest to largest. 2. **Convert all numbers to decimals for easy com

1. **Stating the problem:** Graph the system of inequalities $$\begin{cases} y \geq x + 2 \\ y \leq x - 3 \end{cases}$$

1. **Stating the problem:** We need to compare the decimal number $0.398$ with the fraction $\frac{2}{5}$ and determine which of the statements is true: - $0.398 > \frac{2}{5}$

1. **State the problem:** We need to find the value of the sum $$\sum_{n=0}^{53} 40(1.03)^{n+1}$$ and round it to the nearest integer. 2. **Identify the type of series:** This is a

1. **Stating the problem:** We are given two rational numbers: 0.76 and \(\frac{3}{4}\). We need to determine which of the following statements is true: - 0.76 > \(\frac{3}{4}\)

1. **Stating the problem:** We are given two rational numbers: 0.650 and \( \frac{13}{20} \). We need to determine which of the following statements is true: 1. \(0.650 > \frac{13}

1. **State the problem:** Solve the equation $$\frac{r}{3} - \frac{r - 4}{3} = \frac{3}{2} - \frac{2r - 5}{6}$$ for $r$. 2. **Identify the common denominator:** The denominators ar

1. **Problem:** Write a system of inequalities for the graph showing two lines intersecting, shading on the top left side of the line with positive slope and the bottom right side