🧮 algebra

1. **Stating the problem:** We are given several fractions and mixed numbers representing lengths and heights, and a relation $m \frac{6}{8} = \frac{5}{2}$. We want to understand h

1. The problem is to add the fractions $\frac{6}{11}$ and $\frac{3}{5}$.\n\n2. To add fractions, we need a common denominator. The denominators here are 11 and 5.\n\n3. The least c

1. **Énoncé du problème :** Nous avons une fonction $g$ définie par le tableau :

1. **State the problem:** Simplify the expression $$(6x-3)(2x-1)$$. 2. **Formula used:** To simplify the product of two binomials, use the distributive property (also known as FOIL

1. **Problem 1: Simplify** $$(6x - 3)(2x - 1)$$ 2. Use the distributive property (FOIL method) to multiply each term:

1. **State the problem:** Simplify the expression $$4(2x+5)-3(x-2)$$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **Stating the problem:** Simplify and understand the expression $y = x^2 (x-3)^2$. 2. **Formula and rules:** The expression involves powers and multiplication. Recall that $(a b

1. Find the components of the vector between two points by subtracting the coordinates of the initial point from the terminal point. 2. For 2D vectors, the component form is $\vec{

1. Énonçons le problème : Trouver les solutions de l'équation $$(j + z)^6 + (j^2 - z^2)^3 + (j - z)^6 = 0.$$ 2. Observons que l'équation est une somme de puissances de termes en $j

1. The problem is to convert 0.02 per cent into a decimal or fraction. 2. Recall that "per cent" means "per hundred," so 0.02 per cent is $0.02$ out of 100.

1. The problem is to understand the number 0.02 and express it in different forms. 2. We can write 0.02 as a fraction by recognizing it has two decimal places, so it is \frac{2}{10

1. **State the problem:** Simplify the expression $$\frac{3x + 3}{x^2 + 3x + 2} - \frac{2}{x + 1}$$. 2. **Factor the denominator:** The quadratic in the denominator can be factored

1. **State the problem:** Determine if the quadratic equation $x^2 - 5x + 6 = 0$ has distinct real roots. 2. **Recall the formula:** For a quadratic equation $ax^2 + bx + c = 0$, t

1. **State the problem:** Simplify and solve the expression $$\frac{(3x^2 + 3) \cdot 2}{x + 1} = (2x^2 + 3x + 2)(x + 1)$$. 2. **Rewrite the problem clearly:**

1. **Problem:** Add the fractions $\frac{1}{6} + \frac{5}{9}$. 2. **Formula:** To add fractions, find a common denominator, then add the numerators:

1. The problem is to solve the equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic formula or factorization to solve quadratic equations. The quadratic formula is $$x = \frac{-b \

1. **Problem 6:** Solve the system $$\begin{cases} x^2 - y^2 = 11 \\ x + 2y = 4 \end{cases}$$

1. **Stating the problem:** We need to find the values of $x$ and $y$. However, the problem does not provide any equations or relationships involving $x$ and $y$. 2. **Formula and

1. Solve the system \(\{x^2 - y^2 = 11, x + 2y = 4\}\). - From the linear equation, express \(x = 4 - 2y\).

1. **State the problem:** Solve the expression $$v = 1 + x - \frac{4\sqrt{x}}{x}$$ properly. 2. **Recall important rules:**

1. The problem is to solve the equation $\log_{10}(0.5) = -0.003t$ for $t$. 2. Recall that $\log_{10}(x)$ is the logarithm base 10 of $x$, and it gives the power to which 10 must b