🧮 algebra

1. **State the problem:** Solve a quadratic equation using the square method (completing the square). 2. **General formula:** For a quadratic equation $ax^2 + bx + c = 0$, we can s

1. **State the problem:** Solve the quadratic equation $$m^2 + 24m + 63 = 0$$. 2. **Formula and rules:** We use the quadratic formula $$m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ whe

1. **State the problem:** Evaluate the expression $34 - 2 \times 8 + 12 + 4$. 2. **Recall the order of operations:** Multiplication comes before addition and subtraction.

1. **State the problem:** We are given a figure with points P, Q, and R, and values 12, 15, and y respectively, and we need to find the value of y. 2. **Analyze the problem:** The

1. **State the problem:** Evaluate the expression $$34 - 2 \cdot 8 + 12 \div 4$$ and find the prime factorization of 64. 2. **Evaluate the expression:**

1. The problem asks to write an equation in factored form for the 6th degree polynomial shown in the top-right graph. 2. From the description, the polynomial is degree 6 and has ze

1. **Stel het probleem vast:** We willen de afgeleide van de functie $f(x) = 7x^2$ bepalen. 2. **Formule en regels:** De afgeleide van een machtsfunctie $f(x) = ax^n$ is gegeven do

1. **State the problem:** Find the value of the expression $$4 \cdot 2^3 + 3(3 - 1)$$.

1. **State the problem:** Find the value of the expression $$5^2 - 3(2^2)$$. 2. **Recall the order of operations:** Calculate exponents first, then multiplication, and finally subt

1. Énoncé du problème : Identifier la fonction affine parmi les fonctions données et effectuer des calculs associés. 2. Les fonctions données sont :

1. **State the problem:** Solve the quadratic equation $$\frac{\sqrt{3}}{130}v^2 - \frac{4488 - 2176\sqrt{3}}{13}v + \frac{115600}{65} = 0$$ for $v$, giving all answers to three de

1. **State the problem:** Solve the equation $$\sqrt{3} \over 130 \cdot v^2 + \frac{4488 - 2176\sqrt{3}}{13} v + \frac{115600}{65} = 0$$ for $v$.

1. Il problema chiede di scomporre il denominatore della frazione $$\frac{4x^{2} - 4x + 1}{2ax + 2x - a - ?}$$, ma l'ultimo termine del denominatore non è chiaro. 2. Per procedere,

1. Probleem a: Los algebraïsch op: $$9^{3x-12} = 1^{x+10}$$ - We weten dat $$1^{x+10} = 1$$ voor alle $$x$$.

1. We are asked to find the grootste gemeenschappelijke deler (gcd) van 146 en 96. 2. De grootste gemeenschappelijke deler is het grootste getal dat beide getallen zonder rest deel

1. We start by stating the problem: Calculate $$\frac{(862 + 321) \times 66}{(368 + 810)} \bmod 5$$. 2. First, compute the sums inside the parentheses:

1. Enunciamo il problema: risolvere l'equazione $2x + 3 = 7$. 2. La formula base per risolvere equazioni lineari è isolare la variabile $x$.

1. **State the problem:** Solve the equation $$7x - 2 \times \{4 \times (2x - 7) - 5 \times [2 - 3 \times (x + 2) + 1]\} = 3 \times (5 - 13x)$$. 2. **Apply the distributive propert

1. **Problem:** Calculate the value of the expression $$5a + 3b - 4$$ for $$a = -3$$ and $$b = -2$$. 2. **Formula and rules:** To evaluate an algebraic expression, substitute the g

1. **Problema 1:** Calcolare il valore di $5a + 3b - 4$ per $a = -3$ e $b = -2$. 2. **Formula:** Sostituiamo i valori dati nell'espressione algebrica.

1. **State the problem:** We are given the function $f(x) = -2x^3$ and want to understand its behavior. 2. **Formula and rules:** The function is a cubic polynomial with a negative