🧮 algebra

1. **State the problem:** Multiply the polynomials $\left(5x^2 + 2x + 8\right)\left(7x - 6\right)$. 2. **Recall the distributive property:** To multiply two polynomials, multiply e

1. **State the problem:** We are given a rectangular box with dimensions Length = $3x + 4$, Width = $3x$, and Height = $3x - 1$. The volume is given by $3x(3x + 4)(3x - 1)$. We nee

1. The problem is to simplify the expression $\frac{2\sqrt{3} - 3\sqrt{2}}{6}$.\n\n2. The formula used here is to simplify fractions by dividing numerator and denominator by common

1. The problem is to solve the equation $$\sqrt{x^2} = \sqrt{80}$$ for $x$. 2. Recall that $$\sqrt{x^2} = |x|$$, which means the square root of $x^2$ is the absolute value of $x$.

1. **State the problem:** Calculate the sum of the fractions $$\frac{1}{2} + \frac{1}{4} + \frac{1}{14}$$. 2. **Formula and rules:** To add fractions, find a common denominator, th

1. **State the problem:** Simplify the expression $$y = \sqrt[4]{x^5} - \frac{1}{\sqrt{x}}$$. 2. **Recall the rules:**

1. **State the problem:** Kyle invests money in a simple savings fund where the amount increases at a constant rate. We know the amount after 3 years is 16500 and after 6 years is

1. **State the problem:** We need to graph the solution to the system of inequalities: $$-5x + 2y \leq 2$$

1. The problem is to analyze the system of inequalities: $$-5x + 2y \leq 2$$

1. **State the problem:** We are given a function with vertical asymptotes at $x = -3$ and $x = 2$. We want to find a possible expression for the function $y$ that matches these ch

1. **State the problem:** Simplify the expression $-4\sqrt{100} + 10\sqrt{16}$. 2. **Recall the square root values:**

1. **State the problem:** Simplify the expression $$\left(\sqrt[4]{10v}\right)^5$$. 2. **Recall the rule for radicals and exponents:** The fourth root of a number is the same as ra

1. **State the problem:** Simplify the expression $$\frac{4x^{2}y^{-3} \cdot x^{4}y^{4}}{3xy^{2}}$$. 2. **Recall the rules:**

1. The problem is to solve the equation and find the correct answer from the given options. 2. Since the user did not specify the equation, I will assume a generic example: Solve f

1. **State the problem:** Simplify the expression $$\left(2y^{-4} \cdot 2y^2\right)^3$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $$-\frac{1}{2} = -\frac{1}{2}a + \frac{3}{4}$$ for the variable $a$. 2. **Isolate the term with $a$:** Subtract $\frac{3}{4}$ from both

1. **State the problem:** Solve for $c$ in the equation $2.5 + \frac{c}{0.4} = 11$. 2. **Isolate the term with $c$:** Subtract 2.5 from both sides:

1. **State the problem:** We need to find the weight of each red block and each green block given two conditions: - 3 red blocks and 4 green blocks weigh 20 lbs.

1. The problem is to solve a system of linear equations using the elimination method. 2. The elimination method involves adding or subtracting the equations to eliminate one variab

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

1. **State the problem:** We are given the equation $x + y = z$ and values $x=4$, $y=7$, and $z=47$. We need to check if the equation is true with these values. 2. **Substitute the