🧮 algebra

1. We are asked to expand the binomial expression $(x + y)^4$. 2. The binomial theorem states:

1. The problem is to calculate the value of $5\sqrt{425}$, which means 5 times the square root of 425. 2. Recall the formula for multiplication with square roots: $a\sqrt{b} = \sqr

1. **State the problem:** Racer jogged $5 \frac{3}{5}$ kilometers in 7 hours. We need to find his average speed in kilometers per hour. 2. **Convert mixed number to improper fracti

1. The problem is to find the solution $(x,y)$ to the system of equations: $$y = 12x - 20$$

1. **State the problem:** We want to approximate $1.98^{10}$ using the first five terms of the binomial expansion of $(1+x)^n$ where $n=10$ and $x$ is chosen such that $1+x=1.98$.

1. **State the problem:** Simplify and solve the equation $\frac{k + k}{k} = 6$ for $k$. 2. **Use the formula and rules:** When adding like terms, $k + k = 2k$. Also, dividing a te

1. The problem is to solve the equation 11. 2. Since 11 is a constant and not an equation, it appears there might be a misunderstanding or missing information.

1. Let's clarify the problem: You are asking why we multiply at the beginning for the expression $(x-2)$. 2. Typically, when you see $(x-2)$ multiplied by something else, it is bec

1. **Problem 1: Find the slant asymptote of** $k(x) = \frac{3x^2 + 5x - 26}{x + 4}$. 2. To find the slant asymptote of a rational function where the degree of the numerator is exac

1. **State the problem:** A rower travels upstream at 6 km/h and returns downstream at 10 km/h. The total time for the round trip is 48 minutes. We need to find the distance travel

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: