🧮 algebra

1. **Stating the problem:** Solve the system of equations: First system:

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} y + 1 = 2x \\ y = 3x + 2 \end{cases}$$

1. The problem is to solve the equation given by the user. However, no specific equation was provided, so I will demonstrate solving a simple algebraic equation as an example: $2x

1. Simplify the polynomial expression $a(4a + 3)$. 2. Use the distributive property: $a(b + c) = ab + ac$.

1. **State the problem:** Simplify the expression for the area of the shaded region, which is the area of the larger rectangle minus the area of the smaller rectangle inside it. 2.

1. **State the problem:** Bill's remaining distance to Philadelphia is a linear function of his driving time. Given two points: after 35 minutes, distance is 45 miles; after 53 min

1. The problem asks to state the degree of each function and classify it as linear or quadratic. 2. Recall the definitions:

1. The problem asks which expression can be factored to $$3xy(2x + 1)(x - 4)$$. 2. To check, we expand the factored form using the distributive property:

1. **State the problem:** Solve the system of equations: $$x^2 + y^2 = 9$$

1. **State the problem:** Subtract the mixed numbers $7 \frac{2}{3} - 3 \frac{5}{12}$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** We are given two equations:

1. **State the problem:** We are given a table of heights $y$ (in feet) at different times $x$ (in seconds) and asked to predict the height after 5 seconds. 2. **Analyze the data:*

1. **State the problem:** We have a table showing the height $y$ of a baseball at different times $x$ seconds after it was hit. We want to predict the height after 5 seconds using

1. The problem is to analyze and understand the function $$y = -3|x - 2| + 4$$ and its key features such as vertex and points. 2. The formula involves an absolute value function, w

1. **State the problem:** Simplify the expression $$\frac{4^3 \div 2^2}{2^0 \times (2^3)^3}$$. 2. **Recall the exponent rules:**

1. **State the problem:** We are given two functions $g$ and $f$ with their domains and ranges, and we need to find the domain and range of the composition $f \circ g$. 2. **Recall

1. **State the problem:** Simplify the expression $$\frac{512^3 \times 2^{-9} \div 2^8}{9^2 \div 9 - 5^0}$$. 2. **Rewrite the expression:**

1. Problem A: Complete the perfect square trinomial $x^2 - 30x + \_\_\_$. 2. The formula for a perfect square trinomial is $$a^2 - 2ab + b^2 = (a - b)^2$$.

1. **State the problem:** Solve the equation $-16 + 3n = -8 - 5n$ for $n$. 2. **Write down the equation:**

1. **State the problem:** We are given a recursive sequence defined by $a_1 = 5$ and $a_n = -2a_{n-1}$ for $n \geq 2$. We need to find the value of $a_6$. 2. **Understand the formu

1. **State the problem:** Simplify the expression $$\left( \frac{p^2 t^7}{10} \right)^3$$. 2. **Recall the exponent rule:** When raising a quotient to a power, apply the power to b