🧮 algebra

1. The problem is to understand and analyze the given equations: $$y = 1.165 x \cdot 1.023^t$$

1. **State the problem:** Find the domain of the function $$f(x) = \sqrt{x^2 - 9}$$. 2. **Recall the domain rule for square roots:** The expression inside the square root must be g

1. **State the problem:** We are given that the speed $v$ of a vehicle is directly proportional to the power $p$ and the square of the radius $r$ of its wheels. Given $v=40$ m/s wh

1. The problem is to find the value of $|(2+2i)+/2|$. 2. First, clarify the expression. It seems to be $\left|\frac{2+2i}{2}\right|$, which means the magnitude of the complex numbe

1. **State the problem:** Find the domain of the function $$f(x) = \sqrt[3]{x+3}$$. 2. **Recall the domain rules for cube roots:** The cube root function $$\sqrt[3]{x}$$ is defined

1. **State the problem:** Given that $P$ varies directly as $Q$ and the cube of $R$, find the values of $x$ and $y$ from the table where $P=0.012$, $Q=0.5$, $R=0.2$ for the first s

1. **State the problem:** Solve the equation $$4x^2 + 12x + 9 = 0$$ graphically by drawing the graph of $$y = 4x^2 + 12x + 9$$ for $$-4 \leq x \leq 2$$.

1. **State the problem:** Find the value of $x$ such that $f(x) = \sqrt[3]{x - 2} = 0$. 2. **Recall the formula and rule:** The cube root function $\sqrt[3]{y}$ equals zero if and

1. El problema es graficar la función $$f(x) = \sqrt[3]{x} - 5$$ y marcar cinco puntos: uno donde $$\sqrt[3]{x} = 0$$ y dos puntos a la izquierda y dos a la derecha de ese punto. 2

1. **State the problem:** We are given two functions: (i) $y = e^{x+1} - 1$

1. **Énoncé du problème :** Pour un projet scolaire, Émile retourne des bouteilles consignées. Il reçoit 0,10 par bouteille. Il veut gagner 25. Combien de bouteilles doit-il retour

1. **State the problem:** Simplify or expand the expression $ (2x-1)^3 $. 2. **Formula used:** The cube of a binomial $(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$.

1. **State the problem:** Solve the equation $x + 0.5y = 6$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we need to move $x$ to the other side and then divide

1. **State the problem:** Solve the equation $$2|4 - x| + 3|4 - x| = 25$$ for the positive value of $x$. 2. **Combine like terms:** Since both terms involve $|4 - x|$, add the coef

1. **Énoncé du problème :** Émile reçoit 0,10 par bouteille retournée et veut gagner 25. Combien de bouteilles doit-il retourner ?

1. **State the problem:** We have a function $h(x) = a^x + b$ where $a$ and $b$ are positive constants. The graph passes through points $(0, 10)$ and $\left(-2, \frac{325}{36}\righ

1. **State the problem:** Solve the system of linear equations by graphing: $$2x + 5y = 1$$

1. The problem is to find the sum of the series $1 + 2 + 3 + 4 + 5 + \ldots + 1000$. 2. This is an arithmetic series where the first term $a_1 = 1$, the last term $a_n = 1000$, and

1. The problem asks: For which values of $n$ does the parabola $y = nx^2 + 4x - 2$ intersect the $x$-axis? 2. To find where the parabola intersects the $x$-axis, we set $y=0$ and s

1. Let's start by stating the problem: You want to know if there is an easy method to simplify algebraic expressions. 2. The general approach to simplification involves combining l

1. Muammo: $y = nx^2 + 4x - 2$ parabola $OX$ o'qiga qachon tutashadi? 2. Parabola $OX$ o'qiga tutashishi uchun $y=0$ bo'lganda ildizlar mavjud bo'lishi kerak.