🧮 algebra

1. We start with Bottle A containing 1.5 litres of water and Bottle B containing 100 millilitres of water. 2. Convert 1.5 litres to millilitres because we need to work in the same

1. **Stating the problem:** We want to calculate the product of the fraction $\frac{2}{7}$ multiplied by $-28$. 2. **Rewrite the expression:** The problem is

1. Énonçons le problème : développer et réduire l'expression $$ (5\sqrt{5} - 4)(5\sqrt{5} - (-4)) $$. 2. Simplifions l'expression dans la deuxième parenthèse : $$ 5\sqrt{5} - (-4)

1. We are asked to simplify the expression $$\frac{+36}{+6}$$. 2. Both numerator and denominator have a positive sign, which means the fraction is positive.

1. Le problème est de simplifier la racine carrée de la fraction $\frac{49}{49}$. 2. On utilise la propriété que $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ pour $a,b > 0$.

1. Énoncé du problème : Développer et réduire l'expression $$ (\sqrt{3} + 2)^2 $$. 2. Commencer par appliquer la formule de développement du carré d'une somme : $$ (a + b)^2 = a^2

1. Énoncé du problème : Calculer $\left(3\sqrt{11} + 3\right)\left(2\sqrt{11} + 2\right)$ et donner la réponse sous la forme $a + b\sqrt{c}$ où $a,b$ sont des nombres entiers ou fr

1. Stating the problem: Calculate the result of the division $+16 \div +8$. 2. Division of two positive numbers: When dividing two positive numbers, the result is also positive.

1. Énonçons le problème : Simplifier l'expression $$3\sqrt{5} \times (-4)\sqrt{8}$$ en une forme du type $$a\sqrt{b}$$ ou un entier/fraction si possible. 2. Réécrivons l'expression

1. Énonçons le problème : calculer $$2\sqrt{275} + 2\sqrt{44} + \sqrt{891}$$ et simplifier l'expression. 2. Factorisons les radicaux pour extraire les carrés parfaits.

1. **State the problem:** Solve the system of linear equations: $$2x + y - z + 3t = 5$$

1. The problem is to simplify the expression $(-15) \times \left(+ \frac{3}{5}\right)$.\n2. First, multiply the numbers ignoring the sign: $15 \times \frac{3}{5} = \frac{15 \times

1. We are asked to simplify and evaluate the expression $$4^{2020} + 2^{2017} - 15.$$\n\n2. Notice that $$4^{2020} = (2^2)^{2020} = 2^{4040}.$$\n\n3. So the expression becomes $$2^

Problem: Solve for $x$ given $x^{-1/3} = y$. 1. Observe the expression and rewrite the power in root form to understand it better.

1. We are asked to find the minimum integer value of the function $$y = 2^{3x+5} - 1$$. 2. The function is an exponential function with base 2, which is always positive.

1. We start by stating the problem: prove that for any real numbers $x$ and $y$, the inequality $$|x| + |y| < |x+y| + |x-y|$$ holds. 2. Recall the triangle inequality: for all real

1. State the problem: Solve the inequality $$2^{x-1} \geq 8$$. 2. Express 8 as a power of 2: Since $$8 = 2^3$$, rewrite the inequality as $$2^{x-1} \geq 2^3$$.

1. The problem asks us to find the sum of the roots of the quadratic equation $$3x^2 + 14x - 5 = 0$$. 2. Recall that for a quadratic equation $$ax^2 + bx + c = 0$$, the sum of the

1. The problem is to find the domain of the function $$y = \log_4 (1 - x)^7$$.\n\n2. Recall that the domain of a logarithmic function $$\log_a b$$ requires the argument $$b$$ to be

1. The problem asks us to find the amount in excess of 12000. 2. To solve this, subtract 12000 from the total amount given or found.

1. **State the problem:** Mr Simba's salary is 35000 per month and his wife's salary is 23000 per month. We want to find the total income tax they pay in one year given the tax rat