🧮 algebra

1. **State the problem:** Solve the equation $12 + b = 26$ for $b$. 2. **Formula and rules:** To isolate $b$, subtract 12 from both sides of the equation. This uses the subtraction

1. **State the problem:** Solve the inequality $$-1 \geq - \frac{12y}{5} - 17$$ for $y$. 2. **Isolate the term with $y$:** Add 17 to both sides to move constants to the left.

1. The problem is to find the function $F(x)$ of a straight line given points on the graph and the options for coefficients are limited to -5, -2, 2, or 5 for both slope and interc

1. **State the problem:** Simplify the expression $$\frac{4p^{-2} q^{4}}{8 p^{3} (q^{-2})^{3}}$$. 2. **Recall the exponent rules:**

1. **State the problem:** Simplify the expression $$\frac{a^3 \cdot a^{-5} \cdot b^{-2}}{(a \cdot a^{-4} \cdot b^2)^3}$$ so that all exponents are positive. 2. **Recall exponent ru

1. **Problem:** Find $g(-32)$ given options (A) 0, (B) 3, (C) 5, (D) 8. 2. Since the function $g$ is not explicitly given, we assume it is periodic or defined such that we can find

1. **Problem 1: Find $g(81)$ and $g(-32)$ for a periodic function $y = g(x)$ with period approximately 8.** 2. The function $g$ repeats every 8 units, so to find $g(81)$ and $g(-32

1. **Problem:** Wu saved 75 towards a new 250 mountain bike. What percent of the total cost of the bike has Wu saved? 2. **Formula:** To find the percentage saved, use the formula:

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} -6 & \text{for } x < 2 \\ x - 7 & \text{for } x > 5 \end{cases}$$

1. The problem asks to convert the mixed number $1 \frac{1}{2}$ into an improper fraction. 2. A mixed number consists of a whole number and a fraction. To convert it to an improper

1. **State the problem:** We are given two functions $f(x) = x^2 + 13x + 40$ and $g(x) = x + 8$. We need to find the sum $f(x) + g(x)$ and express it as a simplified polynomial. 2.

1. The problem asks to convert the mixed number $1 \frac{4}{5}$ into an improper fraction. 2. A mixed number consists of a whole number and a fraction. To convert it to an improper

1. The problem asks to convert the mixed number 3 1/4 into an improper fraction. 2. A mixed number consists of a whole number and a fraction. To convert it to an improper fraction,

1. The problem asks to convert the mixed number $2 \frac{1}{2}$ into an improper fraction. 2. A mixed number consists of a whole number and a fraction. To convert it to an improper

1. **State the problem:** Find the roots of the polynomial function $$f(x) = 4x^5 - 8x^4 - 5x^3 + 10x^2 + x - 2.$$\n\n2. **Recall the formula and rules:** To find roots, solve $$f(

1. **Problem Statement:** Verify that $(x+3)$ is a factor of $f(x) = 3x^3 + 2x^2 - 19x + 6$, find the remaining factors, write the complete factorization, and list all real zeros.

1. **State the problem:** Simplify the expression $10p - 4(8p - 2)$. 2. **Apply the distributive property:** Multiply $-4$ by each term inside the parentheses:

1. **State the problem:** Simplify the expression $6m - 2(-3m + 8)$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses:

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 8}{x^2 - 4x} \div \frac{x - 4}{x}$$. 2. **Rewrite division as multiplication by reciprocal:**

1. The problem is to find the result of dividing $\frac{5}{4}$ by $\frac{2}{3}$. Helena made a mistake in the first step. 2. Helena's mistake was that she flipped the wrong fractio

1. **State the problem:** Simplify the expression $$\frac{x+3}{x^2-9} - \frac{2}{x-3}$$. 2. **Recall the formula and rules:** The denominator $x^2-9$ is a difference of squares and