🧮 algebra

1. **State the problem:** Simplify the expression $$\sqrt{\frac{4x^2}{9y^4}}$$ and verify if it equals $$\frac{8}{3xy}$$. 2. **Recall the formula:** The square root of a fraction i

1. **State the problem:** We need to solve the given word problem. Since the user did not specify the exact problem, please provide the problem statement for a detailed solution. 2

1. **State the problem:** We know the price of an 8-minute phone call is 1.20. We want to find the price of a 17-minute phone call. 2. **Identify the formula:** The price is propor

1. **State the problem:** We have two docks, A and B, with an initial ratio of crates 4:9. Both docks are loaded at a constant rate of 8 crates per hour combined. After 8 hours, th

1. **State the problem:** 9 years ago, the ratio of Miko's age to her sister's age was 5:7. This year, the ratio is 4:5. We need to find Miko's current age. 2. **Define variables:*

1. The problem asks to redo problem 3, but since the original problem 3 is not provided here, I will assume it involves solving an algebraic equation or expression. 2. To proceed,

1. **Determine whether the equation represents an exponential function.** The general form of an exponential function is:

1. Stating the problem: Simplify and solve the equation $$\frac{0.3x^{0.7}y^{-0.7}}{0.7x^{-0.3}y^{0.3}}=4$$ for $x$ and $y$. 2. Use the property of exponents for division: $$\frac{

1. **State the problem:** Solve the compound inequality $-4a < 20$ and $-9 > a - 6$. 2. **Solve the first inequality:**

1. **State the problem:** Solve the system of inequalities $$-4a < 20$$ and $$-9 > a - 6$$. 2. **Solve the first inequality:** $$-4a < 20$$.

1. **State the problem:** Given the quadratic function $f(x) = -5x^2 + 11x + 5$, we need to find the vertex, determine if the graph opens up or down, find the axis of symmetry, and

1. The problem asks to find the y-intercept of a function or equation. 2. The y-intercept is the point where the graph crosses the y-axis.

1. **State the problem:** A snail climbs a 30-foot wall. Each hour, it climbs 3 feet but slips down 2 feet. We need to find how long it takes to reach the top. 2. **Understand the

1. El problema pide realizar la tabla de valores y la gráfica de la función $f(x)=3x+5$. También pide indicar el dominio y rango de esta función. 2. La función es una función linea

1. El problema pide realizar la tabla de valores y la gráfica de varias funciones, y luego indicar su dominio y rango. 2. Nos enfocaremos en la primera función: $f(x) = 3x + 5$.

1. **State the problem:** We need to find the difference in cost between 300 g of potatoes and 300 g of carrots using the graph. 2. **Read the costs from the graph:**

1. The problem asks to find the difference in cost between 300 g of potatoes and 300 g of carrots using the graph. 2. From the graph description:

1. **State the problem:** Solve the equation $5(X-5)^2=25$ for $X$. 2. **Isolate the squared term:** Divide both sides by 5 to simplify.

1. The problem is to simplify the expression $\sqrt{27}$. 2. Recall that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, which allows us to break down the radicand into factors.

1. **State the problem:** Simplify and solve the equation $\frac{r+r}{r} = 7$ for $r$. 2. **Write the formula and rules:** The expression $\frac{r+r}{r}$ means the sum of $r$ and $

1. **State the problem:** Solve the equation $r + \frac{r}{r} = 7$ for $r$. 2. **Understand the equation:** The term $\frac{r}{r}$ simplifies to 1 for all $r \neq 0$ because any no