🧮 algebra

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + 2y + z = 0 \\ 2x + y + z = 1 \\ x + y + 2z = 1 \end{cases}$$

1. Let's clarify the problem: You are asking why an arbitrary value on the x-axis appears at a seemingly random point rather than a specific stated part. 2. In mathematics, the x-a

1. **State the problem:** Express the rational function $$\frac{2x^3 - 4}{(x+3)(x-1)}$$ in partial fractions. 2. **Understand the problem:** Partial fraction decomposition requires

1. The denominator of a fraction is the part below the fraction line. 2. A denominator cannot be zero because division by zero is undefined in mathematics.

1. The problem is to solve the inequality $\left| \frac{x-4}{3x+1} \right| \geq 0$. 2. Recall that the absolute value of any real number or expression is always greater than or equ

1. The problem is to solve the inequality $$\left|\frac{x+4}{3x+1}\right| \geq 0$$. 2. Recall that the absolute value of any real number or expression is always greater than or equ

1. **State the problem:** Simplify the expression $\frac{3}{2}x - x$. 2. **Recall the rule:** When subtracting like terms, subtract their coefficients and keep the variable the sam

1. The problem is to solve the inequality $|x^4 + 2x^2 + 1| < 0$. 2. Recall that the absolute value $|A|$ of any expression $A$ is always greater than or equal to zero, i.e., $|A|

1. Ange problemet. Problemet: Vilket av följande svarsalternativ är närmast värdet av $\sqrt{\frac{44\cdot 4100}{200}}$?

1. **State the problem:** Solve the inequality $|2x+1| \leq 0$. 2. **Recall the property of absolute value:** The absolute value $|A|$ is always greater than or equal to zero for a

1. **Problem statement:** Zeigen Sie, dass $$\sum_{i=1}^n (x_i - \mu)^2 = \left( \sum_{i=1}^n x_i^2 \right) - n\mu^2$$ wobei $$\mu = \frac{1}{n} \sum_{i=1}^n x_i$$ das arithmetisch

1. The problem is to solve the inequality $4|x-3| > 12$. 2. We start by isolating the absolute value expression. Divide both sides by 4:

1. **Problem:** Match the verbal expressions to their algebraic forms for items 1, 2, and 3. 2. **Step 1: Understand each verbal expression and translate it into algebraic form.**

1. **Problem statement:** Calculate $x^2$ for given values of $x$: 3, 2.4, -3, 5, and -10.5. 2. **Formula:** The square of a number $x$ is given by:

1. **State the problem:** We are given the equation $$6x^3 + 5x^2 - 4x + 22 = (A + B + C)x^3 + A(x - 1)^2 + B(x + 2) - C$$ and need to find the values of constants $A$, $B$, and $C

1. **Énoncé du problème :** On considère la suite $(u_n)$ définie par $u_0=1$ et la relation de récurrence $$u_{n+1} = 2 \times \frac{u_n + 1}{u_n + 2}$$ pour tout $n \in \mathbb{N

1. ปัญหาคือหาสมการวงกลมที่มีจุดศูนย์กลางอยู่ที่โฟกัสของพาราโบลา $y^2 - 2y - 8x - 7 = 0$ และมีไดเรกตริกซ์เป็นเส้นสัมผัสของวงกลมนั้น 2. เริ่มจากแปลงสมการพาราโบลาให้อยู่ในรูปมาตรฐานโด

1. ปัญหา: กำหนดให้พาราโบลา $P$ มีสมการ $$y^2 - 2y - 8x - 7 = 0$$ และมีไดเรกทริกซ์ $l$ ต้องการหาสมการวงกลมที่มีจุดศูนย์กลางอยู่ที่โฟกัสของ $P$ และมี $l$ เป็นเส้นสัมผัส 2. ขั้นแรก แป

1. **State the problem:** Find the perimeter of the trapezoid with sides labeled as $9x$, $5x + 1$, $8x - 2$, and $17x - 6$. 2. **Recall the formula for perimeter:** The perimeter

1. **State the problem:** We need to find the cost of each ride given the total cost and the number of times each ride was taken by Mike and Gavin.

1. The problem is to write the domain of the function shown on the graph as an inequality. 2. The graph shows a curve starting at an open circle at $x=2$, which means the function