🧮 algebra

1. The problem asks for the end behavior of the function $y = f(x)$ based on its graph. 2. End behavior describes how the function behaves as $x$ approaches positive infinity ($x \

1. Factorise the quadratic expression $x^2 + 5x + 6$. 2. Factorise the difference of squares $9y^2 - 16$.

1. The problem asks to approximate $\pi + \sqrt{50}$ to the nearest hundredth. 2. Recall that $\pi \approx 3.14159$ and $\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$. Since $\sqrt{2

1. Stating the problem: Simplify the expression $3 - 3 \times 3 - 3^2$. 2. Recall the order of operations (PEMDAS/BODMAS):

1. **State the problem:** Simplify the expression $ (8y)^2 $ and write the answer without parentheses. 2. **Recall the power of a product rule:** For any numbers or variables $a$ a

1. **State the problem:** Simplify the expression $ (2u)^3 $ and write the answer without parentheses. 2. **Recall the power of a product rule:** For any numbers or variables $a$ a

1. **State the problem:** Simplify the given algebraic expressions by multiplying out the numerators and combining like terms. 2. **Recall the distributive property:** To multiply

1. The problem is to simplify the expression given above (though the exact expression is not provided, we will demonstrate the simplification process for a general algebraic expres

1. **State the problem:** We need to rewrite the sum of two algebraic fractions with different denominators by finding a common denominator and expressing both fractions with that

1. **State the problem:** We have 4.5 cups of trail mix with ingredients given as percentages and fractions: - Peanuts: 25%

1. **State the problem:** Solve the inequality $$(3x + 1)(1 - 3x) + 2(1 - 3x) \geq (x - 1)^3 - x^2(6 + x).$$ 2. **Expand and simplify each side:**

1. **State the problem:** Simplify the expression $2p(q-3)^2 + 12pq$. 2. **Recall the formula:** The square of a binomial $(a-b)^2 = a^2 - 2ab + b^2$.

1. **State the problem:** We want to find the value of $n$ such that the polynomial $x^3 + 22x + n$ becomes a perfect square trinomial. 2. **Understand the form of a perfect square

1. **State the problem:** We are given the cubic expression $x^3 + 22x + n$ and need to analyze or solve it depending on the context (e.g., find roots, factor, or determine $n$ for

1. **State the problem:** Solve the equation $$\frac{x}{4} - 2 = 5$$ for $x$. 2. **Add 2 to both sides** to isolate the term with $x$:

1. **State the problem:** We are given the cubic expression $x^3 + 22x + n$ and need to analyze or solve it depending on the context (e.g., find roots, factor, or determine $n$ for

1. **State the problem:** Simplify the expression $-(-2 \frac{1}{5}) - \left(-\frac{13}{5}\right) - 3 \frac{3}{5}$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Solve the system of inequalities: $$ (x + 3)(2 - x) \leq 0 $$

1. **State the problem:** Hillary collects three times more bottles than Morgan, which is expressed as the equation $h = 3m$. 2. **Given:** $m = 6$ (Morgan collected 6 bottles).

1. **Stating the problem:** Solve for $x$ in the proportion $\frac{x}{12} = \frac{5}{10}$. 2. **Formula used:** For proportions $\frac{a}{b} = \frac{c}{d}$, cross-multiply to get $

1. The problem asks to create an equation in point-slope form using a simplified slope and a point from a table. 2. The point-slope form of a line equation is given by: