🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{x^4}{9y^3} \times \frac{25y^8}{4x^2} \times x^3 y^3 \times \frac{x^4 y^7}{27}$$. 2. **Write the expression clearly:**

1. **State the problem:** Given the table with values of $d$ and $m$, find the formula for $m$ in terms of $d$. 2. **Analyze the data:** The table is:

1. The problem is to express a given number or expression as a fraction. 2. To write a number as a fraction, identify the numerator (top number) and denominator (bottom number).

1. The problem appears to involve simplifying or understanding the expression $\sqrt[\binom{x_i x_i \sin x \sin x \cos x \pi \tan x}{ }]{}$, which is not a standard mathematical ex

1. **Problem 1: Which store sells batteries at a better unit rate?** We are given:

1. The problem states that a cleaning spray contains $\frac{1}{2}$ cup of vinegar for every 4 teaspoons of lemon oil. We want to find how many cups of vinegar are needed for 2 teas

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