🧮 algebra

1. **State the problem:** Graph the function $$y = |\log_2(3 - \frac{1}{2}x)| + 5$$ and show each transformation step by step. 2. **Recall the base function:** The base function is

1. **State the problem:** Identify which ratios are equivalent to the ratio $2:20$. 2. **Recall the rule for equivalent ratios:** Two ratios $a:b$ and $c:d$ are equivalent if and o

1. The problem asks us to identify which ratios are equivalent to $5:9$. 2. Two ratios $a:b$ and $c:d$ are equivalent if the cross products are equal, i.e., $a \times d = b \times

1. The problem asks to identify which ratios are equivalent to $5:3$. 2. Two ratios $a:b$ and $c:d$ are equivalent if their cross products are equal, i.e., $a \times d = b \times c

1. **State the problem:** We are given two functions $f(c) = 3c - 8$ and $g(c) = \sqrt{14 - c}$. We need to evaluate the composition $(f \circ g)(-11)$, which means $f(g(-11))$. 2.

1. **State the problem:** We need to find an expression equivalent to $0.5(-14a - 22)$ and write it in the form $[\ ]a - [\ ? ]$. 2. **Use the distributive property:** Multiply $0.

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 $$\begin{cases} y \geq x + 2 \\ y \leq x - 3 \end{cases}$$