🧮 algebra

1. **State the problem:** Calculate the value of the expression $2^3 + 3 imes 2$. 2. **Recall the order of operations:** According to PEMDAS/BODMAS, exponents are evaluated first,

1. **Problem Statement:** Sketch the graph of the function $$f(x) = (x - 1)^2 (x + 1)^3$$. 2. **Identify the roots and their multiplicities:**

1. **Stating the problem:** Given the ratios $x : y = 0.5 : 1$ and $z : y = 0.6 : 1$, find the combined ratio $x : y : z$ and the ratio $x : z$. 2. **Understanding ratios:** Ratios

1. **Problem Statement:** We need to sketch the graphs of two functions:

1. Problem: Find the domain of the functions given. 2. For function a) $$f(x) = \frac{1 + 2x + x^3}{2x - 8x^3}$$

1. **State the problem:** We need to find the value of $$\sqrt{2.307197196 \times 10^{-28}}$$. 2. **Recall the property of square roots:** The square root of a product is the produ

1. Simplify by combining like terms: $a + 3b - 5 + 3a - 4$ Step 1: Group like terms: $(a + 3a) + 3b + (-5 - 4)$

1. Simplifying expressions Simplify algebraic expressions by combining like terms and using distributive property.

1. Énoncé du problème : Pour tout réel $a > 0$, justifier que $$a - \frac{1}{a} = \frac{(a - 1)(a + 1)}{a}$$ 2. Justification :

1. **State the problem:** We have a geometric progression (GP) where the third term is 6 less than the second term, and the second term is 9 less than the first term. We need to fi

1. The problem states that the ratio $r$ is given by $r = \frac{a_3}{a_2} = \frac{a_2}{a_1}$ and that $a_2^2 = a_1 a_3$. 2. This implies a geometric progression where the middle te

1. **Stating the problem:** We are given two equations involving sequences: $a_3 = 6 + a_2$ and $a_1 = a_2 - 9$. We want to find the values of $a_1$, $a_2$, and $a_3$ if possible.

1. **State the problem:** We have a geometric progression (GP) where the third term is 6 less than the second term, and the second term is 9 less than the first term. We need to fi

1. **State the problem:** We need to find which expressions have a sum equal to $\frac{7}{8}$.\n\n2. **Recall the rule for adding fractions:** When adding fractions with the same d

1. **Énoncé du problème :** Déterminer l'ensemble des réels $x$ pour lesquels chaque expression logarithmique a un sens, c'est-à-dire où l'argument du logarithme est strictement po

1. Problem: Identify which expressions have a sum of $\frac{7}{8}$.\n\n2. Calculate each sum:\n- $\frac{4}{8} + \frac{1}{8} + \frac{2}{8} = \frac{4+1+2}{8} = \frac{7}{8}$\n- $\frac

1. **State the problem:** Simplify the expression $\frac{25}{5} - \frac{3}{5}$.\n\n2. **Recall the rule for subtracting fractions:** When the denominators are the same, subtract th

1. The problem involves understanding and graphing inequalities on a number line. 2. The first inequality is $x \geq 8$, which means $x$ is any number greater than or equal to 8.

1. **State the problem:** Find the value of $\frac{4}{8} - \frac{3}{8}$. 2. **Formula used:** When subtracting fractions with the same denominator, subtract the numerators and keep

1. Let's clarify the problem and identify the equation or expression for which the value of $x$ was found incorrect. 2. Please provide the original equation or problem statement so

1. The problem states that $x$ is very small and cannot be 71. 2. This implies that any solution or expression involving $x$ must consider $x$ as a small value, typically close to