🧮 algebra

1. **State the problem:** Solve the logarithmic equation $$\log_2(5 + 2x) - \log_2(4 - x) = 3$$. 2. **Recall the logarithm property:** The difference of logarithms with the same ba

1. The problem asks to find $D(15)$, which means we need to find the distance Lamar can drive when there are 15 liters of gas in the tank. 2. From the graph description, the functi

1. **State the problem:** We are given a linear function $R(x)$ representing the cost in dollars to rent a room for $x$ hours. We need to find $R(4)$ and interpret its meaning. 2.

1. مسئله: تعیین دامنه توابع داده شده. 2. تابع a: $3x^2 + 4x - 3$

1. **State the problem:** Solve for $c$ in the equation $$\frac{\sqrt{3}}{2} = \frac{34 \frac{1}{2}}{c}.$$ 2. **Convert the mixed number to an improper fraction:**

1. The problem is to understand where the factor $\frac{1}{2}$ comes from in a given formula or context. 2. Often, the factor $\frac{1}{2}$ appears in formulas involving areas of t

1. **Problem statement:** Two hoses together fill a pool in 2 hours. Hose A alone fills the pool in 3 hours. We need to find how long hose B alone takes to fill the pool. 2. **Form

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + 6y = -9 \\ -x + 3y = 9 \end{cases}$$

1. **State the problem:** Solve the quadratic equation $y = 2x^2 + 7x - 15$ for $x$ when $y=0$. 2. **Formula used:** To find the roots of a quadratic equation $ax^2 + bx + c = 0$,

1. **Problem 2a:** Express $2x^2 - 8x + 5$ in the form $a(x + b)^2 + c$, where $a$, $b$, and $c$ are integers. 2. The formula to complete the square for a quadratic $ax^2 + bx + c$

1. **State the problem:** We need to determine which expressions equal 80 when $w=4$. 2. **Evaluate each expression:**

1. The problem states that the total cost $y$ including the protection plan is given by the equation $$y = 1.2x$$ where $x$ is the cost of the computer alone. 2. Nathan pays a tota

1. **Solve the system:** $$\begin{cases} 10x - y = 9 \\ -10x + y = -9 \end{cases}$$

1. **State the problem:** Solve the equation $5(u + 4) - 7u = 26$ for $u$. 2. **Apply the distributive property:** Multiply 5 by each term inside the parentheses.

1. **State the problem:** Solve the equation $$4(x - 2) + 2x = -32$$ for $x$. 2. **Apply the distributive property:** Multiply 4 by each term inside the parentheses.

1. The problem is to identify the property used in the equation $A + (-A) = 0$. 2. This equation shows that when you add a number and its additive inverse (the negative of the numb

1. **State the problem:** Solve the system of equations by elimination: $$-v + w = 7$$

1. The problem asks for the focus of the previous problem, which typically involves a conic section such as a parabola. 2. The focus of a parabola given by the equation $y = ax^2 +

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations.

1. The problem is to solve the equation given by the user. However, no specific equation was provided, so I will demonstrate solving a simple algebraic equation as an example: $2x

1. **State the problem:** Convert the quadratic equation $y = x^2 + 10x + 22$ into vertex form. 2. **Recall the vertex form:** The vertex form of a quadratic is $$y = a(x-h)^2 + k$