🧮 algebra

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

1. **State the problem:** Determine if 8 and 21 are solutions to the equation $3x = 24$. 2. **Recall the equation:** $3x = 24$ means multiply $x$ by 3 to get 24.

1. The problem is to identify the equation corresponding to a graph that shows a sinusoidal wave with decreasing amplitude as $|x|$ increases, oscillating around $y=0$ with a perio

1. **State the problems:** We need to express and graph the piecewise functions:

1. **State the problem:** Solve the equation $$10x = 2.5x$$ and determine how many solutions it has. 2. **Write the equation:** $$10x = 2.5x$$

1. **State the problem:** We want to understand how to determine if an equation has no solution or infinitely many solutions. 2. **Recall the types of solutions for linear equation

1. The problem is to graph the linear equations: $$y = -\frac{1}{3}x - 3$$

1. The problem is to graph the linear equation $$y = -\frac{1}{3}x - 3$$. 2. The formula for a linear equation in slope-intercept form is $$y = mx + b$$, where $m$ is the slope and

1. **State the problem:** Determine whether the two expressions $$\frac{3x^3}{2}$$ and $$\frac{6x^4}{4}$$ are equivalent. 2. **Recall the rule for equivalence:** Two expressions ar

1. **State the problem:** We are given the function $$f(x) = \frac{3x^2 - 14x - 5}{3x^3 - x - 2}$$ and need to analyze its domain, vertical asymptotes, and horizontal asymptote.