🧮 algebra

1. **State the problem:** We need to find the value of the blank rectangle in the equation $$\frac{2}{5} + \frac{2}{5} + \frac{2}{5} + \frac{2}{5} = \text{[blank rectangle]} \times

1. El problema nos presenta la ecuación $$\frac{7}{12} = [\quad] \times \frac{1}{12}$$ y nos pide completar el espacio en blanco. 2. Para resolver, recordemos que multiplicar por $

1. **State the problem:** Albert had 16.10 less than Peter. After Peter gave 2.50 to Albert, Peter had 4 times as much money as Albert. 2. **Define variables:** Let $P$ be the amou

1. **State the problem:** We need to find the square of the fraction $\frac{3}{2}$. 2. **Formula:** To square a fraction, square the numerator and the denominator separately:

1. Simplify each expression or ratio as given. **a)** Simplify $8 \times 8 \times 8 \times 8 \times 8 \times 8$.

1. **State the problem:** Solve the quadratic equation $-3x^2 + 2x + 1 = 0$. 2. **Formula used:** The quadratic formula is given by

1. Planteamos el problema: Resolver la expresión $$48 - \{6 + 3 \left[18 \div 3 - 2 + 4(5 - 2)(6 \div 3 - 1)\right]\} - 10$$. 2. Recordemos que debemos seguir el orden de operacion

1. **State the problem:** Solve the equation $$6x - 2x - 1 = 3x + 5$$ for $x$. 2. **Combine like terms on the left side:**

1. **State the problem:** Solve the linear equation $10x + 35 = 12x - 47$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation by

1. **State the problem:** Simplify the expression $$\frac{x^5 - 32}{x + 2}$$. 2. **Recall the formula:** This is a division of a polynomial by a binomial. Since the numerator is a

1. **State the problem:** Simplify the expression $3 - \left(16 \div (-2)\right) - \left(2 - 5.3\right) + (-2)^3 \div (-2)$. 2. **Recall order of operations:** Perform division and

1. **State the problem:** Simplify the expression $$\frac{(x+1)3}{x}$$. 2. **Rewrite the expression:** The numerator is the product of $(x+1)$ and $3$, so we have:

1. The problem asks to match each description (A, B, C, D) to the correct graph (1, 2, 3, or 4) based on the characteristics of the graphs and the descriptions. 2. Description A: "

1. **Problem statement:** Bella walked to the grocery store, and we want to find the total distance she traveled during her walk, not just the straight-line distance from home to t

1. **Stating the problem:** Simplify the expression $$4^3 \sqrt{3}$$. 2. **Recall the rules:**

1. The problem involves simplifying square roots and performing operations with them. 2. Recall the property of square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$ and t

1. **State the problem:** We need to analyze the function $$f(x) = \sin^3\left(\cos\sqrt{x^3 + 2x^2}\right)$$ and understand its behavior. 2. **Understand the function:** The funct

1. **State the problem:** We need to analyze and understand the function $$f(x) = \sin^3\left(\cos\sqrt{x^3 + 2x^2}\right)$$. 2. **Understand the function:** The function is a comp

1. **State the problem:** Find the quotient of $$\frac{7}{8} \div \frac{5}{4}$$ and simplify the answer completely. 2. **Recall the rule for dividing fractions:** To divide by a fr

1. **State the problem:** Find the quotient of $$\frac{1}{3} \div \frac{4}{9}$$ and simplify the answer completely. 2. **Recall the formula for dividing fractions:** To divide by a

1. **State the problem:** Peter needs to bake more than 336 loaves of bread for a festival. His bakery produces 28 loaves per hour. We want to find the inequality representing the