🧮 algebra

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

1. **State the problem:** Find the vertex and intercepts of the quadratic function $y = x^2 - 8x + 7$. 2. **Formula and rules:** The vertex of a parabola $y = ax^2 + bx + c$ is at

1. Problem: Izračunaj rešitev enačbe ali izraza, ki ga želiš rešiti. 2. Ker ni podan noben izraz ali enačba, prosim, da natančno napišeš problem, ki ga želiš rešiti.

1. **State the problem:** Rewrite the quadratic expression $x^2 + 10x + 29$ in the form $(x + c)^2 + d$, where $c$ and $d$ are integers.

1. Problem: Določite koeficienta $a$ in $b$ v enačbi premice $y = ax + b$, ki je tangenta na graf funkcije $f(x) = x + 6 \sqrt[3]{x}$ v točki $\left(\frac{15}{11}, f\left(\frac{15}

1. The problem states: Given $a>b>c>1$ and $b^2=ac$, sort $A=\log_b c$, $B=\log_c a$, and $C=\log_a b$ in ascending order. 2. Recall the change of base formula for logarithms: $\lo

1. **Problem statement:** We have two perpendicular lines $l_1$ and $l_2$ intersecting at $(5,0)$. Line $l_2$ passes through $(0,7)$ and $(5,0)$, and line $l_1$ passes through $(0,

1. **State the problem:** Simplify the expression $$\frac{7c + \frac{y}{7c} - c - \frac{y}{c}}{x - c}$$. 2. **Rewrite the numerator:** Combine terms carefully: