🧮 algebra

1. **State the problem:** Simplify the complex fraction $$\frac{7 - 17i}{2 - 3i}$$ into the form $a + bi$ where $a$ and $b$ are real numbers. 2. **Formula and rule:** To simplify a

1. The problem asks to write ratios comparing cups of cereal to cups of pecans, identify the type of ratio, find the total snack mix amount, write ratios comparing each ingredient

1. The problem is to simplify the expression given by the user. 2. Since no specific expression was provided, simplification generally involves combining like terms, factoring, or

1. The problem involves writing and understanding ratios between quantities such as cups of cereal and cups of pecans, balloons blown up by Leo and Kathy, and tickets sold by class

1. **State the problem:** Solve the equation $$15 \cdot 8(3b + 1) = 4(7b + 3) - 9$$ for $b$. 2. **Rewrite the equation:** The problem is to find $b$ such that $$15 \times 8(3b + 1)

1. **State the problem:** Put the equation $3x - y = -6$ into slope-intercept form. 2. **Recall the slope-intercept form:** The slope-intercept form of a line is given by $$y = mx

1. **State the problem:** Put the equation $3x - 6y = -30$ into slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. **Isolate $y$:** S

1. **State the problem:** Put the equation $12y - 9x = -36$ into slope-intercept form $y = mx + b$. 2. **Recall the slope-intercept form:** The slope-intercept form of a line is $$

1. **State the problem:** Solve for $x$ in the equation $$-3(2x - 6) = -5 - (x - 8)$$. 2. **Apply the distributive property:** Multiply $-3$ by each term inside the parentheses on

1. **State the problem:** Solve for $x$ in the equation $$-4x + 2(x + 4) = -7x - (x + 1)$$. 2. **Apply the distributive property:** Expand the terms with parentheses.

1. **State the problem:** Solve for $x$ in the equation $$7x - 3(9x + 4) = 9(-x - 1) + x.$$\n\n2. **Apply the distributive property:** Multiply inside the parentheses:\n$$7x - 3 \t

1. **State the problem:** Solve for $x$ in the equation $$-x - (-7x - 4) = 8x + 6(-x + 5).$$ 2. **Apply the distributive property and remove parentheses:**

1. The problem involves understanding and comparing ratios in different forms: part-to-part, part-to-whole, and whole-to-part. 2. Ratios compare quantities and can be written as fr

1. The problem is to solve the equation or expression given by the user, but since no specific equation was provided, let's assume a simple example: solve $2x + 3 = 7$. 2. The form

1. **Simplify the expression:** $$3(2)^2 \div [2 \cdot (-2)] - 5$$ 2. **State the problem:** Simplify using order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Divi

1. **State the problem:** Simplify the expression $$\frac{x+8}{3x-1} + \frac{x+3}{x+1}$$. 2. **Find a common denominator:** The denominators are $3x-1$ and $x+1$. The common denomi

1. **Problem statement:** We are given the function $$f(x) = \frac{5x - 1}{x^2 - 3x + 2}$$ and need to analyze it. 2. **Step 1: Factor the denominator.** The denominator is a quadr

1. **State the problem:** Two birds, A and B, are flying at different heights and changing their altitudes at constant rates. We need to find their height equations, when they are

1. **State the problem:** Simplify the expression $$(-3v^3 u)^4$$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power:

1. **Stating the problem:** Simplify the expression $$\frac{x^2 - 5x + 6}{x^2 + x - 12} - 5$$. 2. **Factor the polynomials:**

1. **State the problem:** The PTA needs to raise 15000 from memberships. Each membership brings in 25. They already have 2500. We want to find how many memberships, $m$, are needed