🧮 algebra

1. **State the problem:** Order the numbers $4 \frac{2}{5}$, $\frac{35}{8}$, $4.49$, and $4.461$ from least to greatest. 2. **Convert all numbers to decimals for easy comparison:**

1. **State the problem:** We need to order the numbers 6 7/11, 6.18, 53/8, and 6.635 from least to greatest. 2. **Convert all numbers to decimals for easy comparison:**

1. **State the problem:** We want to find the unknown time $t$ (in days) it takes for 18 meters of snow to fall, given a proportion relating time and snow depth. 2. **Set up the pr

1. **State the problem:** We need to find the unknown amount of tuna $A$ (in kilograms) using a proportion with the given values $A$, 36, 8, and 9. 2. **Set up the proportion:** Th

1. **State the problem:** A satellite travels 350 kilometers in 56 seconds. We want to find how far it travels in 8 seconds at the same rate. 2. **Set up the proportion:** Let $d$

1. **Stating the problem:** We need to find the distance a satellite travels in 8 seconds using a proportion from part (a). 2. **Understanding proportions:** A proportion states th

1. **State the problem:** We are given two functions $f(x) = x - 5$ and $g(x) = \frac{1}{x} - 1$. We need to find the composition $fg(x)$, which means $f(g(x))$. 2. **Recall the co

1. El problema es entender por qué la ecuación $x + \sqrt{3} y = 2$ se transforma en la forma pendiente-intersección $y = -\frac{1}{\sqrt{3}} x + \frac{2}{\sqrt{3}}$. 2. Para despe

1. The problem is to continue simplifying or operating with the given expressions. 2. Let's start with the first fraction: $$\frac{x^2 - 1}{x^2 - 3x}$$.

1. **Stating the problem:** We are given that the cost $C$ of registering for an examination is partly constant and partly varies with the number of subjects $N$. We know:

1. **State the problem:** Simplify the expression $3x^3 + 2 - x(5xy^2)(-\frac{1}{5}x)$.\n\n2. **Recall the rules:** When multiplying terms with the same base, add exponents: $x^a \

1. **State the problem:** Express the repeating decimal $0.21\overline{21}$ as a fraction using the sum of an infinite geometric series. 2. **Recall the formula for the sum of an i

1. **Problem statement:** Find possible function equations for the given graphs based on their properties.

1. **State the problem:** Simplify the expression $x \cdot x^{-3}$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the same base, ad

1. **State the problem:** Solve the equation $$0 = 2x - 32x^{-3}$$ for $x$. 2. **Rewrite the equation:** The equation is $$0 = 2x - 32x^{-3}$$.

1. **State the problem:** Simplify the expression $\frac{-3x+4}{2x+3}$. 2. **Identify the expression:** This is a rational expression, a fraction where both numerator and denominat

1. The problem is to simplify the expression $6x^0$. 2. Recall the rule that any nonzero number raised to the power of zero equals 1, i.e., $x^0 = 1$ for $x \neq 0$.

1. **State the problem:** Solve the equation $x^2 - x2 = 36$. 2. **Rewrite the equation:** The term $x2$ is ambiguous, but it likely means $2x$. So the equation becomes:

1. **State the problem:** Simplify the expression $10x^2 - 8x^2$. 2. **Recall the rule:** When subtracting like terms, subtract their coefficients and keep the variable part unchan

1. **State the problem:** Simplify the expression $a^4 \cdot a^3$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the same base, add

1. **Problem Statement:** We are given population data for an animal over years 0 to 5 and need to find an exponential model that fits this data and then predict the population at