🧮 algebra

1. **State the problem:** Juan's bill was 27 and he left a 20% tip. We need to find the amount of the tip. 2. **Formula:** Tip amount = (Percentage tip) \times (Bill amount)

1. **Problem:** Solve the equation $5 \cdot (x + 1) = 10 - 3 \cdot x$ for $x$. 2. **Formula and rules:** Use the distributive property $a(b+c) = ab + ac$ to expand expressions.

1. The problem asks if the ratios $\frac{11}{14}$ and $\frac{6}{7}$ form a proportion. 2. Two ratios form a proportion if they are equal, i.e., if

1. **State the problem:** Solve the equation $8 \div 2(4 - x) = 1$ for $x$. 2. **Recall the order of operations:** Division and multiplication have the same precedence and are eval

1. **State the problem:** Calculate the expression while keeping fractions in their fractional form. 2. **Formula and rules:** When performing arithmetic with fractions, use the fo

1. **State the problem:** Simplify the expression $$-3\begin{pmatrix}0 & 6 \\ -5 & 3\end{pmatrix} + \begin{pmatrix}-9 & 8 \\ 5 & 1\end{pmatrix} - 2\begin{pmatrix}4 & 6 \\ -4 & -7\e

1. **Problem Statement:** Find the LCM (Least Common Multiple) and HCF (Highest Common Factor) of the algebraic expressions given in part (a): $45xy$ and $135x^2y$. 2. **Formulas a

1. Το πρόβλημα ζητά να εξηγήσουμε τη συνάρτηση $f(x) = 1 - 1$ και τη συνάρτηση γινόμενο. 2. Αρχικά, εξετάζουμε τη συνάρτηση $f(x) = 1 - 1$.

1. Vamos fatorar a expressão 4.11: $$4x^2 + 4xy + y^2$$ 2. Observe que essa expressão é um trinômio quadrado perfeito, pois pode ser escrita como o quadrado de um binômio.

1. The problem is to resolve the expression or equation labeled as 4.11. Since the user did not provide the explicit expression, I will assume it is a typical algebraic problem inv

1. **State the problem:** We need to analyze and understand the function $$y = -6 |x - 5|$$ and describe its graph. 2. **Recall the formula and properties:** The absolute value fun

1. Vamos resolver a fatoração da expressão do exercício 4.10: $$ (2x + 1)^2 + 4(2x + 1) $$ 2. Primeiro, observe que a expressão tem um termo comum: $$ (2x + 1) $$.

1. **State the problem:** Simplify the expression $$\frac{4p^3 - p^2 + 2p}{3p - 1}$$ using synthetic division and write the result in standard form. 2. **Rewrite divisor:** The div

1. **State the problem:** Solve each equation for the variable and then arrange the solutions in numerical order from least to greatest. 2. **Equation 1:** $-5n - 8(1 + 7n) = -8$

1. **State the problem:** Solve the inequality $$5x - 3 \leq 3x + 11$$ and represent the solution on a number line and as a solution set. 2. **Write the inequality:** $$5x - 3 \leq

1. **State the problem:** We need to find the value of $y$ when $$-5 = \frac{y - 7}{9}.$$\n\n2. **Use the formula and rules:** To solve for $y$, multiply both sides of the equation

1. **State the problem:** Solve the equation $$(x-1)^2 + 2(x-1) + x^2 = 0$$ for $x$. 2. **Expand and simplify:**

1. **State the problem:** Solve the equation $$\sqrt{112} + y\sqrt{28} = 5\sqrt{7}$$ for $y$. 2. **Simplify the square roots:**

1. **State the problem:** Khloe wants to make 4 servings of a recipe that calls for 2 3/4 cups of beans for 12 servings. We need to find how many cups of beans she needs for 4 serv

1. **State the problem:** Grayson wants to make 5 servings of trail mix. The original recipe makes 15 servings and calls for 5 2/3 cups of almonds. We need to find how many cups of

1. The problem is to solve for $u$ in the equation $V = u$. 2. Since the equation is already isolated for $u$, the solution is straightforward.