🧮 algebra

1. The problem is to analyze the function $y=\sqrt{5-|x|}$.\n\n2. This function involves a square root and an absolute value. The domain is restricted by the square root, which req

1. **Problem statement:** A swimming club charges an annual fee and an hourly fee for pool time. Last year a member swam for 78 hours and paid 768, while another member swam for 10

1. **Problem:** Evaluate $\frac{6(w - 4)}{8}$ for $w = -4$. 2. **Formula:** Substitute $w$ into the expression and simplify.

1. **State the problem:** Solve the system of equations by elimination: $$8x - 8y = -16$$

1. **Stating the problem:** Solve the equation $$x^2 + \frac{1}{x^2} = \frac{17}{4}$$ for $x$. 2. **Use a substitution to simplify:** Let $$y = x + \frac{1}{x}$$. We know the ident

1. **Menyatakan masalah:** Diberikan fungsi kedalaman air kolam ikan berbentuk setengah lingkaran:

1. The problem asks to translate the phrase "Six fewer than a number" into a mathematical expression. 2. "A number" is usually represented by a variable, commonly $n$.

1. **Menyatakan masalah:** Diberikan fungsi harga tanah per meter persegi sebagai fungsi waktu setelah tahun 2025:

1. **Problem:** Emma is buying $7.50 worth of candy with a 30% discount. How much will she pay after the discount? 2. **Formula:** The price after discount is calculated by:

1. The problem is to find the coordinates of the vertex of a quadratic function whose graph is a parabola opening downwards with an approximate vertex at (3, 6). 2. The vertex form

1. **State the problem:** We are given three linear equations: $$y = 5x$$

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = \frac{x-1}{2}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, multiply both sides by the lea

1. The problem asks us to match each linear equation to the graph based on the points shown. 2. The equations are:

1. The problem is to calculate the slope of a line given two points or from a graph. 2. The formula for slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

1. **State the problem:** Solve the inequality $120 + 25x + 10x \geq 300$. 2. **Combine like terms:** $25x + 10x = 35x$, so the inequality becomes:

1. **State the problem:** Solve the system of equations by graphing: $$h = d^2 - 16d + 60$$

1. **Problem statement:** Given the function $f(x) = x^2 + 1$, find the values of $f(0)$, $f(5)$, $f(-5)$, $f(-x)$, $-f(x)$, $f(x+3)$, $f(4x)$, and $f(x+h)$. 2. **Formula:** The fu

1. **State the problem:** Solve the equation $9.4 + 64x^2 = 53$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** Solve the equation $$4x^2 + 7 = 71$$ for $$x$$. 2. **Isolate the term with $$x$$:** Subtract 7 from both sides:

1. Stating the problem: If 12% of a number is 48, find the number. 2. Formula used: Percentage problem formula is $$\frac{\text{percentage}}{100} \times \text{number} = \text{value

1. **State the problem:** Solve the inequality $x + 3y \ge 9$ for $y$ in terms of $x$. 2. **Isolate $y$:** To express $y$ in terms of $x$, subtract $x$ from both sides: