🧮 algebra

1. The problem is to solve the equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic formula or factorization to solve quadratic equations. The quadratic formula is $$x = \frac{-b \

1. The problem asks to express $-8$ raised to the power of 4 in repeated multiplication form without evaluating it. 2. The general rule for powers is: $a^n = a \times a \times \cdo

1. **Problem Statement:** Find the domain and range of the function $f$. Since the function $f$ is not explicitly given, let's consider a general approach to find domain and range.

1. Evaluate each expression step-by-step. ### a) $7^2 + (-2)^3 \div (-2)^2$

1. **State the problem:** Calculate the value of the expression $2e^0 (1-0)$. 2. **Recall the formula and rules:**

1. The problem is to understand why the multiplication $2 \times 1 \times 1 = 2$.\n\n2. The formula used here is the multiplication of numbers, which means combining quantities. Th

1. **State the problem:** We need to find the expression for $f_1(x) - g_1(x)$ given $f_1(x) = 4 + 0.50x$ and $g_1(x) = 3 + 0.45x$. 2. **Write the subtraction:**

1. **State the problem:** A factory produces 1200 cars per week, and 2% of these cars are painted blue. We need to find how many blue cars are produced each week. 2. **Formula used

1. **State the problem:** Calculate $\frac{3}{4}$ of 16. 2. **Formula used:** To find a fraction of a number, multiply the fraction by the number.

1. **State the problem:** Mason asked 175 people if they can speak more than one language. 36% said they can. We need to find how many people that is. 2. **Formula used:** To find

1. **State the problem:** Evaluate the function $f(x) = 300 + 0.68(600 - 600)$.\n\n2. **Understand the expression:** The function involves a constant term 300 and a product of 0.68

1. **Problem 1:** Insert two rational numbers between (i) $\frac{2}{7}$ and $\frac{3}{4}$, (ii) $\frac{5}{6}$ and $\frac{3}{8}$. **Step 1:** Understand that rational numbers betwee

1. Let's state the problem: We want to understand why $$|x| + |y|$$ squared is different from $$|x + y|$$ squared. 2. The expressions are:

1. **State the problem:** Simplify and analyze the expression $$\sqrt{\frac{X+3}{2}} - X$$. 2. **Recall the formula and rules:** The square root function $$\sqrt{y}$$ is defined fo

1. **State the problem:** Solve the equation $$\sqrt{\frac{X+3}{2}} - 2 = 0$$ for $X$. 2. **Isolate the square root:** Add 2 to both sides to get $$\sqrt{\frac{X+3}{2}} = 2$$.

1. **State the problem:** Solve the equation $5x + \frac{6}{3} + \frac{3}{2} + x = 2x$ for $x$. 2. **Simplify the fractions:**

1. **State the problem:** Solve the equation $5x + \frac{3}{6} + \frac{3}{2} + x = 2x$ for $x$. 2. **Combine like terms and simplify fractions:**

1. **State the problem:** Simplify the expression $4.57x + 3.655x + 1.911x$. 2. **Formula and rule:** When adding terms with the same variable, add their coefficients.

1. **State the problem:** Simplify the expression $4.57x + 3.655x + 1.911x$. 2. **Formula used:** When adding like terms, add their coefficients and keep the variable the same: $$a

1. **State the problem:** Simplify the expression $4.57x + 3.655x + 1.911x$. 2. **Formula and rules:** When adding terms with the same variable, add their coefficients.

1. **State the problem:** Simplify the expression $4.57x + 3.655x + 1.911x$. 2. **Formula and rules:** When adding terms with the same variable, add their coefficients.