🧮 algebra

1. **State the problem:** Solve the equation $$\frac{x}{a} + \frac{x}{b} = 1$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to combine the fractions on the left sid

1. **State the problem:** We need to find the temperature at 11 pm given the temperature changes throughout the day starting from -7°C at midday. 2. **Understand the problem:**

1. **State the problem:** Simplify the expression $$\frac{15 e^{-2} f^{3}}{27 e^{-3} f^{-6}}$$. 2. **Recall the rules for exponents:**

1. The problem asks: What is the gradient?\n\n2. The gradient typically refers to the slope of a line or the vector of partial derivatives in multivariable calculus. For a line, th

1. **State the problem:** Solve the linear equation $(m+2)x + 5y = m$ for $y$ in terms of $x$ and $m$. 2. **Formula and rules:** To isolate $y$, we use the rule of transposition an

1. **State the problem:** Match each given equation with the corresponding colored graph based on the description and the shape of the graphs.

1. The problem is to match each given equation with its corresponding graph color based on the shape and direction of the curve. 2. The base function is $y=\sqrt{x}$, which is show

1. **State the problem:** Determine whether each given point lies on the specified line by substituting the point's coordinates into the line's equation and checking if the equatio

1. The problem is to understand and graph the function $y = |x - 2|$. 2. The absolute value function $|x - 2|$ represents the distance of $x$ from 2 on the number line.

1. **State the problem:** Solve the system of linear equations from set (4): $$\begin{cases} 4x + 3y = 17 \\ 7x + 4y = 26 \end{cases}$$

1. **State the problem:** Solve the one-step linear equation $$-2.9 = \frac{f}{4}$$ for the variable $f$. 2. **Formula and rule:** To isolate $f$, multiply both sides of the equati

1. **State the problem:** We have a cost function $$C(x) = 0.2x^2 - 10x + 200$$ where $x$ is the number of drinks sold. We want to find: (a) The number of drinks $x$ that minimizes

1. **State the problem:** We are given the system of equations: $$A + 4^2 + 10 = 30$$

1. **State the problem:** Solve the equation $A + 4^2 + 10 = 30$ for $A$. 2. **Recall the order of operations:** Calculate exponents before addition.

1. Let's solve a random algebra problem: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. The formula to isolate $x$ is to subtract 3 from both sides and then divide both sides by

1. **State the problem:** Simplify the expression $3x(x+4)(x-4)$. 2. **Recall the formula:** The expression involves a product of terms including a difference of squares: $(x+4)(x-

1. **State the problem:** Factor the quadratic expression $x^2 + 2x + 1$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, if it can be factored into $(x + m)(

1. **State the problem:** Solve the equation $2 - X = 10 + X$ for $X$. 2. **Write down the equation:**

1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$

1. **State the problem:** A coin collector has 42 coins in total, some are 10-value coins and the rest are 20-value coins. The total face value of all coins is 650. We need to find

1. **State the problem:** We need to find the dimensions (width and length) of a rectangular base where the length is 70 ft less than twice the width, and the perimeter is 790 ft.