🧮 algebra

1. **Stating the problem:** Simplify the expression $3 - 2\sqrt{5} + 6\sqrt{5}$ and find its equivalent form. 2. **Combine like terms:** The terms $-2\sqrt{5}$ and $6\sqrt{5}$ are

1. **State the problem:** Evaluate the composite functions (g \circ f)(-1), (g \circ f)(0), (f \circ g)(-1), and (f \circ g)(4) using the given graphs of y = f(x) and y = g(x). 2.

1. **State the problem:** Divide the polynomial $$4x^2 - 6x + 8$$ by the binomial $$2x + 3$$ using polynomial long division. 2. **Recall the formula and rules:** Polynomial long di

1. **State the problem:** Simplify the radical expression $\sqrt{24}$. 2. **Recall the rule:** To simplify a square root, factor the number inside into perfect squares and other fa

1. **State the problem:** Simplify the expression $$\sqrt{144m^{16}n^{20}}$$. 2. **Recall the formula and rules:** The square root of a product is the product of the square roots:

1. **State the problem:** Solve for $x$ and $y$ in the equation $$\frac{635}{10} = \left(63 \cdot \frac{x}{100}\right) + \left(65 \cdot \frac{y}{100}\right).$$ 2. **Rewrite the equ

1. The problem states: Simplify the fraction $\frac{635}{10}$ and check if it equals 63. 2. The formula for division of numbers is $\frac{a}{b} = a \div b$.

1. **State the problem:** We need to compare the transaction fees for cash withdrawals at Freedom Bank and Choice Bank. 2. **Given:**

1. **Planteamiento del problema:** Se nos da una tabla con alturas de postes (x) y longitudes de sus sombras (y). Debemos identificar la gráfica que corresponde a esta relación, en

1. State the problem: Find two possible degree 4 polynomials with negative leading coefficient, exactly 3 real zeros, one zero of order 2, and positive between two zeros. 2. Given

1. **State the problem:** We need to identify which lists contain only irrational numbers. 2. **Recall definitions:**

1. **State the problem:** Evaluate the expression $$\frac{1}{2} - \frac{1}{5} \div \frac{2}{3}$$ and write the answer as a fraction. 2. **Recall the division rule for fractions:**

1. **State the problem:** Evaluate the expression $$\frac{2}{5} + \frac{3}{5} \times \frac{3}{4}$$ and write the answer as a fraction. 2. **Recall the order of operations:** Multip

1. **State the problem:** Solve the linear equation $16 - 2t = 5t + 9$ for $t$. 2. **Write the formula and rules:** To solve for $t$, we need to isolate $t$ on one side of the equa

1. **State the problem:** Solve the equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the formula and rules:** To solve for $t$, we need to isolate $t$ on one side of the equati

1. **State the problem:** Find 22% of 180. 2. **Formula:** To find a percentage of a number, use the formula:

1. **State the problem:** Solve for $c$ in the equation $Bc - 3c = 15$. 2. **Identify the formula and rules:** We can factor out $c$ from the left side since it is common in both t

1. **State the problem:** Solve for $w$ in the equation $13w - 10w = 6$. 2. **Combine like terms:** Since both terms on the left side contain $w$, subtract the coefficients:

1. **State the problem:** Solve for $r$ in the equation $$4r - 3r = 20$$. 2. **Combine like terms:** Since both terms on the left side contain $r$, subtract the coefficients:

1. **State the problem:** Solve for $v$ in the equation $2v - v = 11$. 2. **Use the formula and rules:** Combine like terms on the left side. When subtracting or adding terms with

1. **State the problem:** Solve for $B$ in the equation $$R=100-\frac{100}{\left(\frac{\frac{E(L-1)+(B-A)}{L}}{\frac{F(L-1)}{L}}+1\right)}.$$ 2. **Rewrite the equation:** Start by