🧮 algebra

1. **State the problem:** Maggie has a 50 gift card and wants to buy games costing 1.99 each. She has a 5 off coupon for the entire purchase. We need to find an equation to represe

1. **State the problem:** We need to find an equation to represent the total area covered by employee offices and the break room. 2. **Identify given information:**

1. **State the problem:** Simplify the expression $$\frac{(xyz^2)^{-1}}{x^2y^{-1}z^3} \div \left(\frac{x^3y^2z^0}{x^4y^2z^{-3}}\right)^{-1} \times \frac{xy^2z^4}{x^{-3}y^2z^0}$$

1. **State the problem:** Simplify the expression $$\frac{8}{3v-6} + \frac{6v}{v+3}$$. 2. **Identify the denominators and factor if possible:**

1. **State the problem:** Simplify the expression $$\frac{x^a y^{2a}}{x^{2a-1}} \div \frac{(x^2 y)^a}{x^{3+a} y^{-1}}$$. 2. **Rewrite the division as multiplication by the reciproc

1. **State the problem:** Find the equation of the line passing through the points $(-4, 6)$ and $(-2, 0)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1, y_1)$

1. **State the problem:** We need to find the value of the composition \((f \circ g)(-2)\), which means \(f(g(-2))\). 2. **Identify given functions and values:**

1. **State the problem:** We need to order the numbers 20.85, -20.04, 20.75, and 20 from greatest to least. 2. **Recall the rule:** When ordering numbers from greatest to least, th

1. **State the problem:** Solve the inequality $$\left|\left(\frac{2}{5}\right)^x - \left(\frac{5}{2}\right)^{-2x}\right| < 2.$$\n\n2. **Rewrite the terms:** Note that $$\left(\fra

1. The problem is to find a formula that directly gives the answer to a given question without intermediate steps. 2. To provide a direct formula, you need to know the type of prob

1. **State the problem:** Solve the equation $$\frac{x - 2}{4} + \frac{x + 1}{2} = 1$$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to co

1. **State the problem:** We need to evaluate the expression $Y + \frac{x}{7} - 4$ given that $Y = -9$. 2. **Substitute the known value:** Replace $Y$ with $-9$ in the expression:

1. **State the problem:** Given the equation $y=\frac{x}{-3}-1$ and $x=27$, find the value of $y$. 2. **Formula used:** The equation is already given as $y=\frac{x}{-3}-1$.

1. **State the problem:** Subtract the fractions $\frac{9}{8} - \frac{3}{4}$. Make sure the answer is fully reduced. 2. **Formula and rules:** To subtract fractions, find a common

1. **State the problem:** We need to determine whether $\frac{4}{5}$ is less than, greater than, or equal to $\frac{8}{11}$. 2. **Recall the rule for comparing fractions:** To comp

1. **State the problem:** Simplify the expression $$(63x^2 + 9x) - (5x + 40)$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to the

1. **State the problem:** Solve the quadratic equation $x^2 - x - 2 = 0$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are given by

1. **Problem (b):** Calculate the time taken for a flight from Dublin to New York that covers 5112 km at an average speed of 818 km/h. 2. **Formula:** Time = Distance \div Speed

1. **State the problem:** Simplify the expression $ (9x)(7x+1) $. 2. **Use the distributive property:** Multiply each term inside the parentheses by $9x$. The distributive property

1. Stating the problem: Solve the inequality $$\frac{x^2 - 4}{x^{-x} - 2} > 0$$. 2. Analyze the numerator and denominator separately.

1. **Problem Statement:** (a) Find the height of a cuboid suitcase with length 40 cm, width 24 cm, and maximum volume 52800 cm³.