🧮 algebra

1. **Problem statement:** A farmer has 24 meters of fencing to enclose a garden along the walls of an L-shaped house. The garden is divided into three equal sections for carrots, t

1. **State the problem:** Simplify the expression $$(5a - 9b - 2c) + (c + 7b + 3a)$$ by adding the opposite and gathering like terms. 2. **Recall the rule:** When adding expression

1. **Problem statement:** (i) Find the quadratic polynomial $p(x)$ given that $(2x+1)$ is a factor and the remainders when $p(x)$ is divided by $(x-1)$ and $(x-2)$ are $-6$ and $-5

1. **State the problem:** Simplify the algebraic expression by combining like terms: $$6x + 7a - 3x - 2a$$ 2. **Identify like terms:** Like terms have the same variable raised to t

1. The problem is to match each given function with its corresponding graph based on the description of the curves. 2. The functions are:

1. The problem is to match each given function with its corresponding graph based on the description of their shapes. 2. The functions are:

1. **State the problem:** We need to find the expression for the top base $B$ of a trapezoid given the area $A = 12x^2 - 29x + 14$, the bottom base $b = x - 5$, and the height $h =

1. **State the problem:** Calculate the value of the expression $$80 \div (|(-4)^3 + 10| - 14) + 12$$. 2. **Recall the order of operations:** Parentheses and absolute value first,

1. **State the problem:** Evaluate the expression $$12 + \left(\frac{2^5}{-8}\right) \times |12 - 15| + 5$$. 2. **Recall the order of operations:** Parentheses, Exponents, Multipli

1. **State the problem:** We are given the trapezoid area formula $$A = \frac{(B + b) \cdot h}{2}$$ and expressions for $$A$$, $$b$$, and $$h$$ in terms of $$x$$. We need to find t

1. **State the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} -x + 3, & x > 0 \\ 2x + 3, & x \leq 0 \end{cases}$$

1. **State the problem:** Solve the equation $$\frac{2x + 1}{4} + \frac{6x + 2}{5} = \frac{1}{4}$$ to find the value of $x$. 2. **Identify the formula and rules:** To solve equatio

1. **State the problem:** We have a vehicle whose value $D$ in dollars depreciates over time $t$ in years according to a function (not explicitly given in the prompt). We want to f

1. **State the problem:** Anon runs a snowboard business charging 12 per snowboard with 36 rentals per day. For each 0.50 decrease in price, rentals increase by 2. We want to find

1. Write an equation to find the number of oranges in each basket if there are 25 oranges in total and 4 baskets plus 3 extra oranges: 4x + 3 = 25 2. Solve for x by undoing operati

1. **State the problem:** Given the linear function $y = 2x + 3$, find the value of $y$ when $x = 2$. 2. **Formula used:** The function is already given as $y = 2x + 3$.

1. Stwierdźmy problem: Rozwiążemy równanie $$(2 - \sqrt{2})(3\sqrt{3} - x) = 4 - 2\sqrt{2}$$. 2. Użyjemy własności mnożenia i rozkładu wyrażeń algebraicznych oraz uprościmy obie st

1. **State the problem:** We are given the function $f(x) = 5(x-8)(x+2)$ and asked to analyze or simplify it. 2. **Formula and rules:** This is a quadratic function in factored for

1. **Problem Statement:** Find the zeros of a quadratic function, which are the values of $x$ where the function equals zero. 2. **Formula:** The quadratic function is generally wr

1. **State the problem:** Simplify the expression $3x(-1)x^8$. 2. **Recall the rules:** When multiplying terms with the same base, add the exponents: $x^a \cdot x^b = x^{a+b}$.

1. The problem is to understand what matrices are and how they work. 2. A matrix is a rectangular array of numbers arranged in rows and columns.