🧮 algebra

1. **State the problem:** We need to find the slope and the y-intercept of the line given by the equation $$3x + 7y = 9$$. 2. **Rewrite the equation in slope-intercept form:** The

1. **State the problem:** Find the intercepts of the graph of the equation $$4x^2 + 16y^2 = 64$$. 2. **Recall the intercepts:**

1. **State the problem:** We need to find an equation relating the number of games $g$ Hakim played to the amount of money $s$ he spent, and then find $g$ when $s=30$. 2. **Assume

1. **State the problem:** Solve the system using Gauss Method: $$

1. The problem is to evaluate the expression $2 - (-9)$. 2. The formula to subtract a negative number is: $a - (-b) = a + b$. This is because subtracting a negative is the same as

1. **State the problem:** Solve the equation $$-\frac{2}{5} x = 10$$. 2. **Identify the goal:** We want to isolate $x$ on one side of the equation.

1. **State the problem:** Simplify the expression $$7m - 17 + 60$$. 2. **Combine like terms:** The terms $$-17$$ and $$+60$$ are constants and can be combined.

1. **State the problem:** We have a geometric sequence with common ratio $7$ and the 4th term is $1029$. We need to find the 3rd term and the 1st term. 2. **Recall the formula for

1. **State the problem:** Determine which of the given sequences are geometric sequences. 2. **Recall the definition:** A geometric sequence is a sequence where each term after the

1. **Problem 4: Expand the volume function** The volume of the open-top box is given by $$V(x) = (7 - 2x)(5 - 2x)(x).$$

1. **State the problem:** We want to find the number of shoppers on the first day given that each day the number of shoppers increases by 20% from the previous day, and the total n

1. **State the problem:** A monkey swings from a tree. The first swing covers an arc length of $20$ m. Each subsequent swing covers $\frac{4}{5}$ of the previous swing's arc length

1. **State the problem:** Cecelia walks $27$ km on the first day. Each subsequent day, she walks $\frac{2}{3}$ of the previous day's distance. We want the total distance walked by

1. **State the problem:** Emma starts with a salary of $39000$ in the first year and receives a 5% raise each subsequent year. We want to find the total amount she earns over the f

1. **State the problem:** Simplify the expression $9rs - 3 + 5 \times 2rs$ fully. 2. **Recall the order of operations:** Multiplication must be done before addition and subtraction

1. **State the problem:** Simplify the expression $-2d \times 7y$. 2. **Recall the multiplication rule:** When multiplying terms, multiply the coefficients (numbers) and then multi

1. **State the problem:** We are given that point $H$ is the midpoint of segment $JK$. The segment $JK$ is divided into two parts: $JH$ and $HK$.

1. **State the problem:** We are given a line segment with points P, M, and O in that order. The segment PM is labeled as $4x - 1$ and the segment MO is labeled as $12x - 17$. We n

1. **State the problem:** We need to solve for $x$ given the distances between points F, G, and H, and the total distance of 10 units. 2. **Understand the setup:** The segment from

1. **State the problem:** Determine if the given examples correctly demonstrate the distributive property. 2. **Recall the distributive property formula:**

1. **State the problem:** Simplify the algebraic expression $$-2(6x - 15) + 5(-x + 9) - 3(-4x + 1)$$. 2. **Apply the distributive property:** Multiply each term inside the parenthe