🧮 algebra

1. The problem involves comparing fractions: $\frac{1}{2}$ and $\frac{1}{4}$.\n\n2. To compare fractions, we can find a common denominator or convert them to decimals. The denomina

1. **State the problem:** Solve for all values of $x$ such that the equation holds true. 2. **General approach:** Since no specific equation is given, the general method to solve f

1. **State the problem:** Solve the quadratic equation $$-x^2 + 7x - 18 = 0$$. 2. **Identify coefficients:** Here, $$a = -1$$, $$b = 7$$, and $$c = -18$$.

1. **State the problem:** We are given a storefront window with an area of 154 square feet and a height of 7 feet. We need to find the perimeter of the window. 2. **Recall the form

1. Planteamos el problema: Simplificar la expresión $$\frac{x^{2} - 1}{x^{3} + 8} \cdot \frac{x^{9} - x^{8} - 6x^{7}}{x^{5} + x^{4}} \div \frac{x^{3} - 4x^{2} + x + 6}{x^{6} - 16}$

1. **Stating the problem:** Simplify the expression $$\sqrt{\frac{45}{11x}}$$ and related radical expressions given. 2. **Recall the rule:** The square root of a fraction is the fr

1. **Problema:** Construir a matriz quadrada $A$ de ordem 3, definida por $$a_{ij} = \begin{cases} 2^{i+j}, & \text{se } i < j \\ i^2 - j + 1, & \text{se } i \ge j \end{cases}$$

1. **State the problem:** We need to estimate the solutions to the equation $$10x - 5x^2 - 1 = 1.2$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to

1. **State the problem:** Solve for $a$ in the equation $$a^3 + a^2 = 36.$$\n\n2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$a^3 + a^2 - 36

1. Il problema riguarda il dominio della funzione $f(x) = -x^2$. 2. Il dominio di una funzione è l'insieme di tutti i valori di $x$ per cui la funzione è definita.

1. **State the problem:** We need to evaluate the expression $$\frac{3 \times 5}{6 - 4 + 3}$$. 2. **Recall the order of operations:** Multiplication and division are performed befo

1. **State the problem:** We need to find the value of $p$ such that the expressions $2(p + 5)$ and $3(2p - 1)$ are equal. 2. **Write the equation:**

1. Planteamos el problema: Simplificar y encontrar el valor de $x$ en cada proporción dada. 2. Recordemos que para resolver proporciones de la forma $$\frac{a}{b} = \frac{c}{d}$$ p

1. **Problem Statement:** Find the following for matrices

1. The problem asks for the equation of the image of the line $y = \frac{1}{2}x + 3$ after reflection over the mirror line $y = 0$. 2. Reflection over the line $y=0$ (the x-axis) c

1. **State the problem:** Find the value of $p$ such that the expressions $2(p + 5)$ and $3(2p - 1)$ are equal. 2. **Write the equation:**

1. **State the problem:** We are given a table showing the labour hours, wood blocks, and paint tins required to manufacture toy buses and trains, along with their costs. We need t

1. **Problem:** Office Products has a box of 250 binder clips on sale for 9.99. The list price is 10.99. If you buy 4 boxes, find (a) sale price, (b) amount you save, and (c) total

1. **State the problem:** We are given a rectangle where the length $l$ is 4 units greater than the width $w$, so $l = w + 4$. The perimeter $P$ of the rectangle is given by the fo

1. **State the problem:** We are given the perimeter formula for a rectangle: $$P = 2(x + y)$$ where $x$ and $y$ are the lengths of the sides. 2. **Formula and explanation:** The p

1. **State the problem:** Solve the equation $1.2 \times 46 = 72 \times 48$ for verification or simplification. 2. **Calculate each side:**