🧮 algebra

1. **State the problem:** We are given the linear function $$W = 6F + 4000$$ where $W$ is the weight of the airplane and $F$ is the amount of fuel. 2. **Identify the domain:** The

1. **State the problem:** Solve the quadratic equation $$x^2 + (8.8 \times 10^{-6})x - (3.96 \times 10^{-7}) = 0.$$\n\n2. **Formula used:** The quadratic formula for an equation $$

1. **State the problem:** We have the linear function $$W = 6F + 4000$$ where $W$ is the weight of the airplane in pounds and $F$ is the amount of fuel in gallons. 2. **Identify do

1. **State the problem:** Solve the simultaneous equations: $$\sqrt{x} - \sqrt{y} = 1$$

1. **State the problem:** Simplify or analyze the quadratic expression $5x^2 + 6x - 8$. 2. **Recall the quadratic form:** A quadratic expression is generally written as $ax^2 + bx

1. Énoncé du problème : Déterminer l'équation de la droite sous la forme $y = mx + b$ à partir des graphiques donnés. 2. Rappel de la formule : L'équation d'une droite est $y = mx

1. **State the problem:** We have a large rectangle divided into six smaller rectangles arranged in two columns and three rows. The height is divided into three parts: $c^3$, $6c^2

1. Énoncé du problème : Déterminez l'équation de la droite passant par les points (0, 2) et (4, -2). 2. Formule utilisée : L'équation d'une droite en forme pente-interception est $

1. **Problem Statement:** Given two points (foci) of an ellipse, find the equation of the ellipse. 2. **Ellipse Definition:** An ellipse is the set of points where the sum of dista

1. The problem is to evaluate the function $f(x) = 2 - 3x$ at $x = \frac{1}{2}$. 2. The formula given is $f(x) = 2 - 3x$. To find $f\left(\frac{1}{2}\right)$, substitute $x$ with $

1. **Stating the problem:** We are given an ellipse defined by the equation $$\frac{x^2}{6} + \frac{y^2}{12} = 1$$ and two points \(P(2, 2)\) and \(Q\left(\sqrt{\frac{3}{2}}, 3\rig

1. **State the problem:** We have 125 ninth graders and 55 tenth graders on the honor roll last year.

1. **State the problem:** We know that 15 students represent 30% of the sixth-grade class. We need to find the total number of students in the class. 2. **Formula used:** To find t

1. **State the problem:** We have 150 ninth graders and 75 tenth graders on the honor roll last year. This year, ninth graders decreased by 8% and tenth graders decreased by 20%. W

1. **Problem statement:** A seamstress charges a bride 2180 including 23% VAT for a wedding dress. The materials were purchased including 23% VAT. The labour charge is twice the ma

1. **Problem:** Convert 65% to decimal and fraction. 2. **Formula:** Percent to decimal: divide by 100, so $65\% = \frac{65}{100} = 0.65$.

1. **State the problem:** Simplify the radical expression $$\sqrt{a^7}$$. 2. **Recall the rule:** The square root of a power can be rewritten using the property $$\sqrt{a^n} = a^{\

1. **State the problem:** Simplify the expression $$7q + 9r + \frac{3q + 10r}{5}$$. 2. **Understand the expression:** The expression consists of two parts: the sum of terms $7q + 9

1. **State the problem:** Simplify the radical expression $$\sqrt{a^7}$$. 2. **Recall the rule for radicals and exponents:** $$\sqrt{a^n} = a^{\frac{n}{2}}$$.

1. **Problemstellung:** Wir sollen den Ausdruck $$\frac{4(3v - 6w)}{4 \cdot 7} + \frac{7(9w - 7v)}{7 \cdot 4}$$ vereinfachen. 2. **Formel und Regeln:** Wenn zwei Brüche denselben N

1. **State the problem:** We need to sketch the function $$y = (x-1)(x^2 + x + 1)$$. 2. **Recall the formula and rules:** This is a product of a linear term and a quadratic term. T