🧮 algebra

1. **State the problem:** Solve the linear equation $2y + 2x = -10$ for $y$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by performing algeb

1. **State the problem:** We need to solve the system of equations by graphing: $$y = -\frac{6}{5}x$$

1. **State the problem:** We are given the linear equation $$Y = 52.50 - 0.85X$$ and asked to find the value of $X$ when $Y=6$ and when $Y=4$. 2. **Formula and approach:** To find

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 2x + 6y - z = 6 \\ 4x - 3y + 5z = -5 \\ 6x + 9y - 2z = 11 \end{cases}$$

1. **State the problem:** Simplify the algebraic expression $5w^2 + 3w + 2w^2 - 2w$. 2. **Group like terms:** Combine terms with $w^2$ and terms with $w$ separately.

1. **State the problem:** Simplify the expression $6(3n + 8)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by 6. The distributive property state

1. **State the problem:** A boat travels 336 miles downstream and back upstream. The downstream trip takes 12 hours, and the upstream trip takes 14 hours. We need to find the speed

1. **State the problem:** Matt and Ming sold small and large boxes of oranges at a fundraiser. We know:

1. **State the problem:** We have the profit function $$P(x) = 5x^2 - 5x + 9$$ and need to find the average rate of change of profit between certain values of $x$, and the instanta

1. **State the problem:** We need to find which expressions are equivalent to $$3^{-9} \cdot 3^{-3}$$. 2. **Use the property of exponents:** When multiplying powers with the same b

1. The problem asks to evaluate the expression $$\sqrt{-9} - 6\sqrt{-2}$$ and write the result in the form $a + bi$ where $a$ and $b$ are real numbers. 2. Recall that for any negat

1. **State the problem:** We need to identify the linear inequality represented by a graph with a solid line of slope $\frac{1}{3}$ and y-intercept $-1$, with the region shaded bel

1. **State the problem:** We are given a function $f(x) = x$ and a graph of another function $g(x)$ which is a transformation of $f(x)$. We need to find the equation for $g(x)$ fro

1. **State the problem:** We have multiple linear equations of the form $h = mx + b$ with slopes $3$, $-3$, and $1$, and intercepts $1$ and $7$. We want to identify which pairs of

1. **State the problem:** We have a car traveling a distance $d$ as a function of time $t$. The car travels 425 miles at a speed of 50 miles per hour. We need to find the domain an

1. **State the problem:** We have a vehicle traveling 315 miles over 6 hours. The distance traveled as a function of time is $d(t)$, where $t$ is in hours.

1. **State the problem:** Jeremy has an $8 gift card and wants to buy comic books costing $5.25 each. The function $f(x) = 5.25x - 8$ gives the cash needed to buy $x$ comic books.

1. **State the problem:** The band wants to earn 500 by selling posters. The number of posters sold depends on the price per poster $p$ and is given by the expression $-3.5p + 85$.

1. The problem asks to identify the domain of a function from given options. 2. The domain of a function is the set of all possible input values (usually $x$) for which the functio

1. The problem asks for the total cost to join a gym for one year, given a monthly fee of 45 and a one-time starting fee of 75. 2. The total cost for one year includes paying the m

1. **State the problem:** We are given the sequence 3, 7, 11, 15, 19, … and need to determine which given explicit or recursive definitions correctly describe the n-th term of this