🧮 algebra

1. The question asks why we choose $x$ instead of $y$ or $z$ for step 5. 2. In algebra or problem-solving, the choice of variable often depends on clarity, simplicity, or the probl

1. **State the problem:** We have pennies (1 cent), nickels (5 cents), and dimes (10 cents). There are 13 coins total, worth 83 cents. We want to find how many of each coin there a

1. **Planteamiento del problema:** Tenemos la función $f(x) = x^2 + 4x$ definida en el intervalo $[0,3]$ y queremos analizarla. 2. **Fórmula y reglas importantes:** La función es u

1. **State the problem:** Simplify the expression $$\frac{x+1}{x-4} - \frac{x+4}{5x-20}$$. 2. **Identify the denominators:** The denominators are $x-4$ and $5x-20$.

1. **Problem statement:** We are asked to calculate the differences and sums of integers using the subtraction rules given: subtracting a number is the same as adding its opposite.

1. The problem asks us to determine which ordered pair satisfies the inequality $$6x - 2y > 12$$. 2. To check if an ordered pair \((x, y)\) is a solution, substitute the values of

1. The problem involves understanding and placing inequalities on a number line. 2. Inequalities describe ranges of values for $x$ such as $x < 2$, $0 < x$, or $x \geq 1$.

1. El problema consisteix a trobar l'àrea de la regió sombrejada que és la diferència entre l'àrea del rectangle exterior i l'àrea del rectangle interior. 2. Les dimensions del rec

1. The question asks where the value 0.07 comes from in part b. 2. Typically, 0.07 represents a decimal form of a percentage, often 7%.

1. The problem asks to solve the quadratic equation graphically for the first equation: $x^2 - 3x - 3 = 0$. 2. The general form of a quadratic equation is $ax^2 + bx + c = 0$.

1. **State the problem:** Find the inverse function of \( f(x) = \frac{7x - 4}{2} \). 2. **Recall the formula and rule:** To find the inverse function \( f^{-1}(x) \), we swap \( x

1. The problem asks to find the value of $y$, but no equation or context is provided. 2. To solve for $y$, we need an equation or expression involving $y$.

1. **State the problem:** Find the inverse function of $f(x) = x^3 - 12$. 2. **Recall the definition of inverse function:** The inverse function $f^{-1}(x)$ satisfies $f(f^{-1}(x))

1. **State the problem:** Simplify the expression $\left(\frac{4^2}{2^2} + 3^2\right) \div 13 + \left(5^2 - 2^4 - 5\right)^2 - 3^2$. 2. **Calculate powers:**

1. The problem asks to find two points, but it is unclear which points or what context is given. 2. To find points, we usually need an equation, a graph, or specific conditions.

1. **State the problem:** We want to find the function $C(n)$ that models the total cost to a customer who attends $n$ workout sessions at a gym.

1. **State the problem:** Simplify the expression $3 \times 2^3 + 3^2 \times (3 \times 5 - 2^3) - 3^2 \times 7 - 2^1 \times 5$. 2. **Recall exponent rules:**

1. **State the problem:** Solve for $w$ in the equation $$\frac{5w}{4} = -25$$. 2. **Formula and rule:** To solve for $w$, use the multiplicative property of equality which states

1. **State the problem:** Solve for $w$ in the equation $$12 = - \frac{3}{5} w$$. 2. **Formula and rules:** To isolate $w$, we need to divide both sides of the equation by the coef

1. **Stating the problem:** We need to evaluate the expression $$\frac{1}{5} \times \frac{5}{6}$$ based on the shaded portions of the circles. 2. **Understanding the expression:**

1. **State the problem:** Solve the linear equation $7 + 3x = 9x + 1$ for $x$. 2. **Write down the equation:**