🧮 algebra

1. **State the problem:** We are given the formula $$F = 1 - \left(\frac{M}{K}\right)^2$$ and need to transpose it to make $M$ the subject. 2. **Isolate the squared term:** Start b

1. **State the problem:** We are given the equation $$Z = \sqrt[3]{\frac{x^2}{w}}$$ and need to make $w$ the subject.

1. **State the problem:** Solve the equation $20 + x : (-3) = 18 \frac{1}{2}$ for $x$. 2. **Rewrite the equation:** The colon $:$ means division, so the equation is

1. **State the problem:** Solve the equation $$3x + \frac{2}{4} - x + \frac{1}{3} = 2x - \frac{2}{6} - 1 - \frac{x}{2}$$ for $x$. 2. **Simplify fractions:** Note that $\frac{2}{4}

1. Il problema chiede di risolvere la proporzione $\frac{x}{3,6} = \frac{0,4}{1,8}$. 2. La formula per risolvere una proporzione $\frac{a}{b} = \frac{c}{d}$ è $a \times d = b \time

1. Il problema chiede di risolvere la proporzione cerchiata in colonna: $$\frac{12}{9} = \frac{x}{15}$$. 2. La formula per risolvere una proporzione $$\frac{a}{b} = \frac{c}{d}$$ è

1. **State the problem:** Noel is a farm worker paid 00 per kaing basket of mangoes harvested. He works 20 days a month and saves 30% of his monthly income (since he spends 70%). W

1. The problem asks to find the value of 70%. 2. Percent means per hundred, so 70% means 70 out of 100.

1. نبدأ بكتابة المعادلة المعطاة: $$l^3 = x^2 - 3x$$ حيث نريد إيجاد قيم $x$ التي تحقق هذه المعادلة. 2. نفترض أن $l^3$ هو ثابت معين، لكن بما أن السؤال لا يحدد قيمة $l$، سنعتبر المعاد

1. **Problem Statement:** Find the value of $x$ that satisfies the equation $$8x^2 - 6x^3 = \frac{7}{3} - l$$ where $l$ is a constant.

1. نبدأ بكتابة المعادلة المعطاة: $$8 - 3x^{-2} = \frac{1}{7}$$ 2. الهدف هو إيجاد قيمة $x$ التي تحقق هذه المعادلة.

1. **Problem Statement:** Find the slope of the secant line to the curve $n(x) = 3x^2 - 2$ passing through the points $(1, n(1))$ and $(2, n(2))$. 2. **Formula:** The slope $m$ of

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle that to isolate $x$, we perform inverse operations to both sides of the equat

1. **State the problem:** We need to find and shade the region that satisfies the system of inequalities: $$y \geq x + 3$$

1. نبدأ بكتابة المعادلة المعطاة: $$8 = 3x - 6 - 3 = 1$$

1. **Problem:** Belege in dem Term a mit der Zahl -3 und b mit der Zahl \frac{1}{2} und berechne das Ergebnis für a) 2ab + a^2. 2. **Formel:** Setze die Werte in den Term ein: $$2a

1. **Show that the set of rational numbers $\mathbb{Q}$ is a Field.** A field is a set equipped with two operations (addition and multiplication) satisfying certain axioms: closure

1. **Stating the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} \sqrt[3]{x^2(x-1)} & x \geq 0 \\ \frac{x+3}{x^2 + 2x - 3} + 2 & x < 0 \\ a^2 x^2 - 10x -

1. The problem is to solve the equation $1h$ for $h$. 2. Since $1h$ means $1 \times h$, the equation simplifies to $h$.

1. **Problem statement:** Simplify the expression \((x^3+x^2y+xy^2+y^3)(x+y)-2x^3y-3x^2y^2-2xy^3\) and then calculate its value at \(x=-1\) and \(y=-1\).

1. Planteamos el problema 4: Dada la ecuación $$a^2 + 1 = 6x$$, debemos encontrar el valor de $$x^2 + \frac{1}{x^2}$$. 2. Observamos que la ecuación involucra $$a^2$$ y $$x$$, pero