🧮 algebra

1. **Problem Statement:** Given the arithmetic sequence $-15, -7, 1, 9, \ldots$, write the recursive formula, explicit formula, and find the 52nd term using the explicit formula. 2

1. **Stating the problem:** We need to find the image (bayangan) of the line given by the equation $x + 2y - 1 = 0$ after a translation by the vector $T\left(-3, 2\right)$. 2. **Fo

1. **State the problem:** Simplify the fraction $\frac{14775000}{8650}$. 2. **Formula and rules:** To simplify a fraction, divide numerator and denominator by their greatest common

1. The problem is to simplify the fraction $\frac{6887500}{7250}$. 2. To simplify a fraction, we divide the numerator and denominator by their greatest common divisor (GCD).

1. Diketahui barisan aritmetika dengan suku ke-9 ($a_9$) = 11 dan suku ke-21 ($a_{21}$) = 35. 2. Rumus suku ke-n barisan aritmetika adalah $$a_n = a_1 + (n-1)d$$ dimana $a_1$ adala

1. **Stating the problem:** We want to find the value of $$\frac{8^{\frac{3}{5}} \times 94^{5}}{81^{\frac{1}{8}} \times 64^{\frac{1}{5}}}$$.

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: