🧮 algebra

1. **State the problem:** We have two equations representing the total cost of bags of popcorn and plates of nachos purchased by Jeremy and Kendrick: $$4p + 2n = 18.50$$

1. **State the problem:** Simplify the expression $2\sqrt{18} \times 18 - 3 \sqrt{50} \div \sqrt{32} \div 2$. 2. **Recall important rules:**

1. **State the problem:** Simplify the expression $$2\sqrt{18} \times \sqrt{6} - 3 \sqrt{50} + \sqrt{32} \times 2$$. 2. **Recall the properties of square roots:**

1. **State the problem:** We have a polynomial function $$f(x) = x^4 + x^3 + 2x^2 + ax + b$$ where $$a$$ and $$b$$ are constants. 2. **Given:** When $$f(x)$$ is divided by $$(x - 1

1. **State the problem:** Solve the system of equations using the substitution method: $$\begin{cases} 5x + 4y = 37 \\ x = 2y - 1 \end{cases}$$

1. **State the problem:** Simplify the expression $$\left[\frac{1 + a^{2} \sqrt{(a^{2} + a) a + a^{-1}}}{\sqrt[a]{1 + a^{2} \sqrt{a}} \cdot \left(1 + a^{2} \sqrt[a]{a^{a}}\right)}\

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} 6x - 5y = -14 \\ y = 4x \end{cases}$$

1. **State the problem:** Solve the system of equations by substitution: $$y = 3x - 13$$

1. **State the problem:** Solve the equation $7w = 35$ for $w$. 2. **Formula and rule:** To solve for $w$, divide both sides of the equation by 7, because dividing both sides by th

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} y = 2x + 9 \\ y = 5x + 10 \end{cases}$$

1. **State the problem:** Solve the system of equations using the substitution method: $$\begin{cases} y = 3x + 1 \\ 3y - 5x = 11 \end{cases}$$

1. **State the problem:** Solve the equation $6w = -12$ for $w$. 2. **Formula and rules:** To solve for $w$, we use the rule of equality which states that if you perform the same o

1. **State the problem:** Solve the equation $-2 = -2t$ for the variable $t$. 2. **Recall the formula and rules:** To solve for $t$, we want to isolate $t$ on one side of the equat

1. **State the problem:** Solve the equation $-5y = -10$ for $y$. 2. **Formula and rules:** To solve for $y$, we need to isolate $y$ on one side of the equation. Since $y$ is multi

1. **State the problem:** Solve the equation $-12r = 12$ for $r$. 2. **Formula and rules:** To solve for $r$, we need to isolate $r$ on one side of the equation. Since $r$ is multi

1. Stating the problem: Calculate the value of $7 \times \left( \frac{3}{4} \right) - \left( \frac{2}{5} \right)$.\n\n2. Use the distributive property and order of operations. Firs

1. **State the problem:** We are given the expression $5(7 + 2x)$ and its transformations in subsequent lines. We need to identify the property that justifies each step. 2. **Step

1. **State the problem:** Find the equation of the tangent line to the curve defined by $$ (x^2 + x^2)^3 = 8x^2y^2 $$ at the point $(-1, 1)$. 2. **Simplify the equation:** Note tha

1. **State the problem:** We are asked to find the matrix $A$ given by $$A = \begin{pmatrix} 3 & 9 \\ 4 & 3 \end{pmatrix} - \begin{pmatrix} 5 & 5 \\ 4 & 3 \end{pmatrix}$$

1. The problem states: "Three more than 7 times a number is the same as 208 more than twice the number." We need to write an equation using $x$ to represent this sentence and then

1. **State the problem:** Calculate $20^2$. 2. **Formula used:** The expression $a^b$ means $a$ multiplied by itself $b$ times.