🧮 algebra

1. The problem is to simplify or understand the expression $x^3 - x^2 + x_1$. 2. Note that $x_1$ typically denotes a variable or a subscripted variable, different from $x$. If $x_1

1. The problem is to find a quadratic function $y = ax^2 + bx + c$ given the y-intercept and roots. 2. The y-intercept is the point where $x=0$, so $y=c$. Given the y-intercept $(0

1. The problem asks to find the function $j(x)$ given points $(-1,-1)$ and $(4,y)$ where $y$ is unknown. 2. We need to determine the function type or rule for $j(x)$ using the give

1. **State the problem:** Solve the equation $2x + 3 = 9$ for $x$. 2. **Isolate the variable term:** Subtract 3 from both sides to get rid of the constant on the left.

1. The problem is to evaluate the expression $0.1/14 \times 10^{-3}$.\n\n2. First, rewrite the expression clearly: $$\frac{0.1}{14} \times 10^{-3}$$\n\n3. Calculate $\frac{0.1}{14}

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 3x + 2y + z = 8 \\ 2x + y + 2z = 9 \\ 2x + 2y + 3z = 13 \end{cases}$$

1. **State the problem:** Simplify the expression $$\sqrt{\frac{5x^2}{6}} + 1 \sqrt{\frac{36}{6x}}$$. 2. **Simplify each square root separately:**

1. **State the problem:** Simplify the expression $$\frac{2yx + 4y}{x + 1} \times \left(- \frac{x}{y} + \frac{xy^{-1}}{x + 2}\right)$$. 2. **Simplify the first fraction:** Factor o

1. The problem asks to evaluate $24^0$. 2. According to the exponent rules, any non-zero number raised to the power of zero equals 1.

1. The problem asks us to find the value of $x$ in the equation $$5^{28} \div 5^{7} \times 5^{2} = 5^{x}.$$\n\n2. Recall the laws of exponents: when dividing powers with the same b

1. The problem is to simplify the expression $x + \frac{1}{x}$. 2. Since $x$ and $\frac{1}{x}$ are unlike terms (one is $x$ and the other is its reciprocal), they cannot be combine

1. The problem is to simplify or analyze the expression $x + \frac{1}{x}$. 2. This expression is a sum of a variable $x$ and its reciprocal $\frac{1}{x}$.

1. The problem asks us to find the value of $c$ in the equation $$3^{15} \div 3 = 3^c.$$\n\n2. Recall the property of exponents: when dividing powers with the same base, subtract t

1. **State the problem:** Simplify the expression $$\frac{7d^3 f h^2}{21 d^5 h}$$. 2. **Simplify the coefficients:** $$\frac{7}{21} = \frac{1}{3}$$.

1. **Énoncé du problème :** Étudier la fonction $f(x) = x^2 - 4x + 3$ définie sur $\mathbb{R}$.

1. **State the problem:** Calculate the value of the expression $\frac{40000}{100} \times 12 \times \frac{12}{10}$.\n\n2. **Simplify step-by-step:**\n- First, simplify $\frac{40000

1. **Étudier les variations des fonctions f et g** - Pour $f(x) = x^2 - 2x$ :

1. The problem asks to calculate the value of $[V1 + V4] - [V2 - V3]$ based on the directed graph. 2. From the graph, the known edge weights are:

1. Evaluate the expression $$\frac{11}{22}x^{-22} + \frac{11}{33}x^{-33} + \frac{11}{22}x^{-44}$$ for given options. Step 1: Simplify each term.

1. **State the problem:** Simplify the expression $1\pi \sqrt{\pi^2} (2-1)(2+1)$. 2. **Simplify inside the square root:** $\sqrt{\pi^2} = \pi$ because the square root of a square i

1. **State the problem:** Simplify the expression $\frac{1}{\pi} \cdot \frac{\sqrt{\pi}}{(2-1)(2+1)}$. 2. **Simplify the denominator:** Calculate $(2-1)(2+1) = 1 \times 3 = 3$.