🧮 algebra

1. The problem is to find the value of the distance given by the formula $$\text{distance} = \frac{1}{\sqrt{0.3}}$$. 2. First, calculate the square root of 0.3:

1. **State the problem:** Solve the equation $$4(11 - x) = 24$$ for $x$. 2. **Distribute the 4:** Multiply 4 by each term inside the parentheses:

1. State the problem: Solve the equation $$\frac{5 - x}{7} = 4$$ for $x$. 2. Multiply both sides of the equation by 7 to eliminate the denominator:

1. The problem is to evaluate the expression for distance given as $\frac{1}{\sqrt{0.1}}$ and verify the approximation. 2. Start by calculating the square root of 0.1:

1. Énoncé du problème : Étudier la nature de la suite $(u_n)$ définie par $u_0 \in \mathbb{R}$ avec $u_0 \geq 4$ et la relation de récurrence $u_{n+1} = 2u_n - 3$ pour tout $n \in

1. Let's analyze the expression $4x - 2x$. 2. Combine like terms: $4x - 2x = (4 - 2)x = 2x$.

1. **State the problem:** We need to find the solutions to the equation $$-\frac{1}{2}x^2 - x + 8 = x + 3$$ which means finding the values of $x$ where the quadratic function and t

1. **Simplify the expression** $4x^2 - 3x + 8 - 2x^2 + x - 2$ by combining like terms. Combine the $x^2$ terms: $4x^2 - 2x^2 = 2x^2$.

1. The problem is to solve the equation $3x - x = 2$ for $x$. 2. First, combine like terms on the left side: $3x - x = (3 - 1)x = 2x$.

1. **Simplify the first expression:** Given: $4x^2 - 3x + 8 - 2x^2 + x - 2$

1. The problem is to calculate $\left(-\frac{1}{2}\right)^7$. 2. When raising a fraction to a power, raise both numerator and denominator to that power: $$\left(-\frac{1}{2}\right)

1. **Stating the problem:** We want to understand what "standard form" means in algebra and see examples. 2. **Definition:** In algebra, the standard form of a linear equation is u

1. **State the problem:** Find and simplify the expression for $$f(g(h(x)))$$ given $$f(x) = x + 1$$, $$g(x) = x^2$$, and $$h(x) = \sqrt{x}$$. 2. **Evaluate the innermost function:

1. **Énoncé du problème** : On considère la suite $(u_n)_{n\in\mathbb{N}}$ définie par : $$u_0 = 3, \quad u_{n+1} = (a+1)(u_n + 2)$$

1. **State the problem:** We want to find the inequalities that define the region $R$ bounded by the lines $x=7$, $y=2$, and $y=x$. 2. **Analyze each boundary:**

1. The problem is to find the asymptotes of a function, but the specific function is not provided. 2. Asymptotes are lines that a graph approaches but never touches.

1. The problem is to express and understand the expression "2 times 3 to the power of x". 2. This expression can be written mathematically as $$2 \times 3^x$$.

1. The problem states that the diagonal line is given by the equation $y = x$. 2. The region described is the set of points where $y \geq x$, meaning all points on or above the lin

1. The problem is to find the inequalities that define the region $R$ bounded by the lines $x=6$, $y=x$, and $y=1$. 2. First, note the lines:

1. **State the problem:** Fully factorise the expression $$7x - 18x - 6 + 10x^2$$. 2. **Simplify the expression:** Combine like terms for the $x$ terms:

1. Solve $33x^2 - 16 \leq 0$: - Rewrite as $33x^2 \leq 16$.