🧮 algebra

1. **State the problem:** We need to find the rate of change of the amount Miguel earns with respect to the hours he works. This is the slope of the line passing through the points

1. The problem asks to find the slope of the line perpendicular to a given line and then write the equation of the perpendicular line using point-slope form. 2. The slope of the gi

1. **State the problem:** Find the equation of the line perpendicular to the line $4x - 3y = -8$ that passes through the point $(3, -2)$. 2. **Convert the given line to slope-inter

1. The problem asks for the slope of a line perpendicular to the line given by the equation $y = 8x + 5$. 2. Recall that the slope-intercept form of a line is $y = mx + b$, where $

1. **State the problem:** Find the slope of the line represented by the equation $f(t) = 2t - 6$. 2. **Recall the slope-intercept form:** The equation of a line in slope-intercept

1. **State the problem:** Find the equation of the line passing through points $(-6,7)$ and $(-3,6)$. 2. **Formula used:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$

1. The problem asks which value is an output of the function given the table of values for $x$ and $f(x)$. 2. Recall that the output of a function is the value of $f(x)$ correspond

1. **Identify which sequences are geometric and find the common ratio.** A geometric sequence has a constant ratio $r$ between consecutive terms: $$r = \frac{t_{n+1}}{t_n}$$

1. **Persamaan Kuadrat: Membedakan Persamaan Kuadrat dan Bukan Persamaan Kuadrat** Persamaan kuadrat adalah persamaan polinomial berderajat dua yang berbentuk umum:

1. **State the problem:** We need to find who makes the greatest profit percentage between the woman who buys and sells a car and her son who buys and sells a bicycle. 2. **Formula

1. **State the problem:** Amy wants to decide which type of bead to buy by comparing the unit cost of pink agate beads and pink silicone beads. 2. **Formula:** Unit cost is calcula

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

1. **State the problem:** Amy wants to decide which type of bead to buy by comparing the unit cost of pink agate beads and pink silicone beads. 2. **Formula:** Unit cost is calcula

1. **State the problem:** Simplify the expression $$\frac{3}{5} - \frac{5}{4} \left[ \frac{2}{3} - \frac{7}{5} \left(- \frac{2}{3} \right) \right]$$. 2. **Recall the order of opera

1. **State the problem:** Simplify the expression $$35 - 54 \left[ \frac{23}{1} - \frac{75}{1} \left(-\frac{23}{1}\right) \right]$$. 2. **Rewrite the expression clearly:**

1. **Problem a:** A $2500 Samsung 4K LED television is discounted by 30%. Determine the sale price. 2. **Formula:** Sale Price = Original Price - (Discount Rate \times Original Pri

1. The problem involves subtracting values from an expression involving $X_N$ and constants. 2. We start with the expression $180 - X - 130$.

1. Soal cerita SPLDV (Sistem Persamaan Linear Dua Variabel) menentukan yang kehilangan. 2. Misalkan kita punya dua variabel, misalnya $x$ dan $y$, yang mewakili dua hal yang ingin

1. The problem is to understand how to work with percents and proportional fractions. 2. Percent means "per hundred," so $x\%$ means $\frac{x}{100}$.

1. **Problem:** Determine the formula for the $n$-th term of the arithmetic sequence 3, 7, 11, 15, ... 2. **Formula:** The $n$-th term of an arithmetic sequence is given by:

1. **Problem 1: Write the equation of line (AB) given points A and B.** The formula for the slope $m$ of the line through points $A(x_1,y_1)$ and $B(x_2,y_2)$ is: