🧮 algebra

1. The problem is to simplify the expression with negative exponents: $m^{-2} n^{-4} p^{3}$. 2. Recall the rule for negative exponents: $a^{-b} = \frac{1}{a^{b}}$ where $a \neq 0$.

1. **State the problem:** We are given the expression $(N + 3)$ and need to understand any restrictions on the variable $N$. 2. **Identify the variable and expression:** The expres

1. The problem is to express $8p^{-3}$ as a fraction without negative exponents. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$.

1. **State the problem:** We are given a table of values for $x$ and $y$: $$\begin{array}{c|ccccc}

1. **State the problem:** Given the expression $(h t u h) = 4 h u + 3 u$ and the term $(n + 3) 3$, we want to understand the restrictions on the variables. 2. **Identify the variab

1. **State the problem:** The total bill for a lawnmower and 15 drawer pulls is within a $400 budget. The lawnmower costs 325. We need to find the maximum cost of each drawer pull.

1. **State the problem:** We need to find the maximum height of the kangaroo's jump modeled by the function $h(t) = -16t^2 + 24t$. 2. **Identify the type of function:** This is a q

1. The problem asks to find the domain of the function $$g(x) = \frac{5x}{x - 5}$$. 2. The domain of a function includes all real numbers except those that make the denominator zer

1. **State the problem:** Solve for $N$ in an equation where $N$ is the unknown variable. 2. **General approach:** To solve for $N$, isolate $N$ on one side of the equation by perf

1. **State the problem:** Solve the equation $$\frac{x}{9} = \frac{7}{15}$$ for $x$. 2. **Formula and rule:** To solve for $x$ in a proportion $\frac{a}{b} = \frac{c}{d}$, cross-mu

1. The problem states: "A number decreased by 7 is at most 13." We need to write an inequality for this. 2. Let the number be $x$. "Decreased by 7" means $x - 7$.

1. **State the problem:** Pet Supply makes a profit of $5.50 per bag of natural dog food. They want to make a profit of no less than 5225. We need to find the minimum number of bag

1. **Problem:** Simplify the expression $-y^{-3}$. 2. **Recall the rule:** Negative exponents mean reciprocal, so $a^{-n} = \frac{1}{a^n}$.

1. The problem gives the arithmetic sequence formula $a_n = 22 + 3(n - 1)$ and asks to find $a_1$ and $a_n$ for the sequence where $a_{13} = 15$ and $d = -7$. 2. Recall the formula

1. **Solve the equation** $-28 = 7 + x$. 2. To isolate $x$, subtract 7 from both sides:

1. We are asked to solve the equations for $x$ in two cases: **Case 3:** $x = -\frac{1}{4}$

1. The problem asks to find the slope $m$ of the linear equation given by $$y = 8x + 2.$$\n\n2. Recall that the slope-intercept form of a linear equation is $$y = mx + b,$$ where $

1. The problem involves finding the first term $a_1$ and the general term $a_n$ of an arithmetic sequence given a specific term $a_{13} = 15$ and common difference $d = 4$. 2. The

1. **State the problem:** Solve the equation $$-9(x + 3) = -18$$ for $$x$$. 2. **Rewrite the equation:** The equation is $$-9(x + 3) = -18$$.

1. **Problem 1: Solve for $t$ in the equation** $$10c = \frac{1}{4} (16p - 8t)$$

1. **State the problem:** We are given the amount of money Francis has in his bank account over several days and need to find a rule for the amount of money $y$ in terms of days $x