🧮 algebra

1. **State the problem:** We need to find the number of Lumberman units sold given the total company profit including warranty bonuses is 363570. 2. **Identify known values:**

1. The problem is to add the fractions $\frac{1}{3}$ and $\frac{1}{4}$.\n\n2. To add fractions, we need a common denominator. The denominators are 3 and 4. The least common denomin

1. Let's start by defining a rational number. A rational number is any number that can be expressed as the quotient or fraction $$\frac{p}{q}$$ where $$p$$ and $$q$$ are integers a

1. **Problème 1 : Vérifier si les vecteurs sont linéairement indépendants** On considère les vecteurs

1. The problem is to understand how to add expressions with the same base in algebra. 2. When you have terms with the same base raised to the same exponent, such as $a^n + a^n$, yo

1. The problem is to express the number 3 + 3 in exponent form. 2. First, simplify the expression: 3 + 3 = 6.

1. The problem is to simplify the expression $$z = (x - y)^2$$ where $$x = 14$$ and $$y = \frac{6}{5}$$. 2. Substitute the values into the expression:

1. **Problem statement:** Show that the nth term of the geometric sequence 4, 8, 16, 32, ... is given by the formula $a_{n-1} = 2^{n+1} - 4$. 2. **Identify the sequence:** The give

1. **State the problem:** Solve the quadratic equation $x^2 + 3x = 5$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem is to understand how to solve expressions involving exponents. 2. An exponent indicates how many times to multiply a base number by itself. For example, $a^n$ means

1. It seems like you meant to say "they are squared." This usually refers to squaring a number or an expression, which means multiplying it by itself. 2. For example, if you have a

1. **State the problem:** We have two functions defined for $x \geq 0$: $$f(x) = 232(0.4)^{x+2}$$

1. **State the problem:** Solve the equation $$18 = 3(2 + t)$$ for the variable $t$. 2. **Distribute the 3 on the right side:**

1. **State the problem:** Solve the equation $$2(x - 3) = 12$$ for $x$. 2. **Distribute the 2:** Multiply 2 by each term inside the parentheses:

1. **State the problem:** Solve the equation $$2(r - 1) = 8$$ for the variable $$r$$. 2. **Distribute the 2:** Multiply 2 by each term inside the parentheses:

1. **State the problem:** Solve the equation $2(x + 1) = 10$ for $x$. 2. **Distribute the 2:** Multiply 2 by each term inside the parentheses:

1. **State the problem:** Solve the equation $n - 13 = 16$ to find the value of $n$. 2. **Isolate the variable:** To solve for $n$, add 13 to both sides of the equation to cancel o

1. The problem is to solve the equation $x - 2 = 6$ for $x$. 2. To isolate $x$, add 2 to both sides of the equation:

1. The problem is to solve the equation $y + 14 = 19$ for $y$. 2. To isolate $y$, subtract 14 from both sides of the equation:

1. Let's start by understanding the problem: We want to find the Highest Common Factor (HCF) and Least Common Multiple (LCM) of given numbers. 2. Case 1: Find HCF and LCM of two nu

1. **State the problem:** Solve the equation $r + 2 = 7$ for $r$. 2. **Isolate the variable:** To find $r$, subtract 2 from both sides of the equation: