🧮 algebra

1. **State the problem:** Calculate $$\frac{4.67 \times 10^{-5} \times 6.98 \times 10^{12}}{5.04 \times 10^{3}}$$ and express the answer in standard form to 3 significant figures.

1. **State the problem:** Simplify the expression $$\frac{2x + 4y}{9x - 18y} \times \frac{3x - 6y}{4x + 8y}$$. 2. **Identify common factors:**

1. The problem asks us to find the equation of a line parallel to the line $y = -\frac{1}{3}x + 1$ that passes through the point $(1, -2)$. 2. Recall that parallel lines have the s

1. The problem asks us to find the equation of a line parallel to the line given by $$y = -\frac{1}{3}x + 1$$ that passes through the point $(1, -2)$.\n\n2. Important rule: Paralle

1. **State the problem:** We have two sets defined by equations: Set A: $y=\frac{2x-1}{x}$

1. The problem asks to write the number 0.00654 in standard form. 2. Standard form (also called scientific notation) expresses a number as $a \times 10^n$ where $1 \leq a < 10$ and

1. The problem asks to write the number 0.00654 in standard form. 2. Standard form (also called scientific notation) expresses a number as $a \times 10^n$ where $1 \leq |a| < 10$ a

1. **State the problem:** Solve the equation $3(x-2)-(4x-5)=2$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $3(x-) - (4x - 5) = 2$. 2. **Clarify the expression:** The term $3(x-)$ seems incomplete or mistyped. Assuming it means $3(x - 1)$ for

1. The problem asks which real-world situation can be represented by the linear equation $$y=12x-4$$. 2. The general form of a linear equation is $$y=mx+b$$, where $$m$$ is the slo

1. The problem states that to join a dancing club, there is a $30 startup fee and a $4 monthly fee. 2. In word problems involving fees, the constant usually refers to the fixed amo

1. **State the problem:** We need to find an expression that represents the total cost to join an online learning community, which has a $20 startup fee and a $5 monthly fee. 2. **

1. **State the problem:** We need to find the positive number $a$ such that the area enclosed by the asymptotes of the graphs of the functions $$y=\frac{x}{x+a}$$ and $$y=\frac{ax+

1. **Énoncé du problème** : On considère la suite $(u_n)$ définie par : $$u_0 = \sqrt[3]{\frac{2}{7}}, \quad u_{n+1} = \sqrt[3]{\frac{(u_n)^3 + 1}{8}}$$

1. Állítsuk fel a feladatot: Oldjuk meg az egyenletet $$\frac{x^2 + 3x - 5}{x - 1} = 2$$. 2. Fontos szabály: Az egyenlet értelmezési tartománya kizárja azokat az $x$ értékeket, ame

1. **State the problem:** Find the equation of the trend line passing through the points $(-4, -36)$ and $(6, 54)$. The equation of a line is generally written as $y = mx + b$, whe

1. **State the problem:** Find the equation of the trend line in the form $y = mx + b$ that passes through the points $(-2, 1)$ and $(1, 7)$. 2. **Formula for slope:** The slope $m

1. **State the problem:** We are given the inequalities $0 < x < y^2 < x^2$ and $y > 1$. We need to sort the expressions $A = \log(y) y \sqrt{x}$, $B = \log(x) \frac{x^2}{y}$, $C =

1. **State the problem:** Find the equation of the line passing through the points $(1, 13)$ and $(3, 7)$. The equation is in the form $$y = mx + b$$ where $m$ is the slope and $b$

1. **Problemstellung:** Dennis wirft einen Basketball von Punkt A(0|2,75) ab, der durch B(2|4,85) fliegt und im Korb K(6|y_k) landet. Die Flugbahn ist eine Parabel mit Faktor $a =

1. The problem is to draw the graph of the inverse function of a given function. 2. The inverse function, denoted as $f^{-1}(x)$, reverses the roles of inputs and outputs of the or