🧮 algebra

1. **State the problem:** Solve the system of linear equations: $$\frac{x}{6} - \frac{y}{2} = \frac{1}{6}$$

1. **State the problem:** We are given two ratios involving jellies, mints, and toffees: - Jellies to mints: $7n : 3$

1. **State the problem:** Solve the system of linear equations: $$-\frac{1}{4}x + 3y = 6$$

1. **State the problem:** Find the equation of the line in point-slope and slope-intercept form given points (-2, -5) and (5, 0). 2. **Find the slope $m$ using the formula:**

1. We are asked to solve an equation using substitution. 2. The substitution method involves replacing a complicated expression with a simpler variable to make the equation easier

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

1. **State the problem:** Simplify the expression $$\frac{x^2 + 13x + 12}{x + 1} \times \frac{5x + 10}{4x^2 - 16}$$. 2. **Factor all polynomials:**

1. **Fill in the blanks in the table:** Percent | Fraction | Decimal

1. **Problem statement:** A parking garage charges $5 for the first hour, $10 for up to two hours, and $12 for the entire day. Let $G$ be the dollar cost of parking for $t$ hours.

1. **Problem Statement:** Evaluate the piecewise function $$f(x) = \begin{cases} -2x + 3, & x < -1 \\ 2x^2, & x \geq -1 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{7^2 \times (-8)^{-5} \times 3^4}{7^5 \times 8^{-7} \times 3^3}$$. 2. **Recall the rules:**

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