🧮 algebra

1. **Problem 1: Find which rational function has a horizontal asymptote at $y = -2$.** 2. The horizontal asymptote of a rational function $h(x) = \frac{P(x)}{Q(x)}$ depends on the

1. **State the problem:** Simplify the expression $$\frac{4 - 3}{5x - 10} \times (x - 2)$$. 2. **Simplify the numerator:** Calculate $4 - 3$.

1. Masalah: Diberikan sistem persamaan linear dua variabel (SPLDV) berikut: $$3x - 4y = 10$$

1. **State the problem:** Solve the system of equations by substitution and clearing $x$: $$5x - 2y = -4$$

1. **State the problem:** We are given two equations: $$5x - 2y = -4$$

1. **State the problem:** A racer jogged $5 \frac{3}{5}$ kilometers in $\frac{7}{8}$ hours. We need to find his average speed in kilometers per hour.

1. **State the problem:** Solve the system of equations: $$3x - 4y = 10$$

1. **State the problem:** A rower travels upstream at 6 km/h and back downstream at 10 km/h. The total journey takes 48 minutes. We need to find the distance upstream. 2. **Define

1. **State the problem:** Find the equation of the line passing through the point $(-6, 3)$ and perpendicular to the line given by $6x - 5y = 5$. 2. **Rewrite the given line in slo

1. **State the problem:** Simplify the expression $$6 \cdot \left(\frac{1}{6} + \frac{3}{7}\right) + \frac{2}{7}$$. 2. **Use the distributive property:** Multiply 6 by each term in

1. **State the problem:** Determine if $x=43$ is a solution to the equation $$16 = x - 27$$ 2. **Write the equation and substitute the value:** Substitute $x=43$ into the equation:

1. Problem: Determine if $k=32$ is a solution to $k + 19 = 51$. 2. Substitute $k=32$ into the equation:

1. **State the problem:** Solve the linear equation $2x + 5 = 9$ for $x$. 2. **Write the formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtra

1. **State the problem:** We need to analyze the function $$y=\frac{(x+2)^3}{(x+1)^2}$$. 2. **Recall the formula and rules:** This is a rational function where the numerator is $(x

1. **State the problem:** We need to add the two fractions $$\frac{5}{n+5} + \frac{4n}{2n+6}$$.

1. **State the problem:** Simplify the expression $$6 - \frac{x + 5}{(7x - 5)(x + 4)}$$. 2. **Identify the formula and rules:** To simplify, we need to combine terms by finding a c

1. **State the problem:** Solve the expression $$\left(\frac{2}{7} + \frac{1}{3}\right) + \frac{2}{3}$$ using properties and mental math. 2. **Recall the formula and rules:** To ad

1. The problem is to make the letter in the brackets, which is $a$, the subject of the formula from the equation $k = 4a - b$. 2. Start with the original equation:

1. The problem is to express a function in the form $f(x)$. 2. A function $f(x)$ represents a rule that assigns each input $x$ to exactly one output.

1. **State the problem:** We need to find a polynomial function that matches the given graph with roots approximately at $x = -2$, $x = 0$, and $x = 4$. The graph passes through th

1. **State the problem:** Solve the inequality $ (x-2)^2 \leq 0 $. 2. **Recall the property of squares:** For any real number $a$, $a^2 \geq 0$ and $a^2 = 0$ if and only if $a=0$.