🧮 algebra

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

1. **State the problem:** Solve the equation $-3w + 2 = -4$ for $w$. 2. **Isolate the term with $w$:** Subtract 2 from both sides to get:

1. Vamos resolver a expressão $$\frac{(4^{-2})^{5} \times \left(\frac{1}{2}\right)^{10}}{8^{-3}}$$ passo a passo. 2. Primeiro, aplicamos a regra das potências para potências: $$(a^

1. **State the problem:** Solve the literal equation $17n - 20d = 45w + 13n$ for the variable $d$. 2. **Isolate terms involving $d$:** We want to get $d$ alone on one side. First,

1. **State the problem:** Mia earns a base salary of 450 per week plus a 9% commission on sales. She sells 895 worth of beauty supplies in one week. We need to find how much commis

1. Problem: Solve the literal equation $$\frac{2b}{3g} = \frac{s}{4t}$$ for $$t$$. 2. Formula and rules: To solve for $$t$$, we want to isolate $$t$$ on one side of the equation. W

1. **State the problem:** Dane earns a 10% commission on each TV sold. Each TV costs 120. We want to find how much commission Dane makes if 25 TVs are sold. 2. **Formula:** Commiss

1. **State the problem:** Solve the equation $$6 \cdot \frac{| -12g |}{2} + 24 = 48$$ for $g$. 2. **Understand the absolute value:** The absolute value $| -12g |$ is equal to $12|g

1. **State the problem:** Multiply the binomials $$\left(\frac{1}{4}x - 6\right)$$ and $$\left(\frac{4}{3}x - \frac{5}{4}\right)$$ and express the product as a trinomial in simples

1. **State the problem:** Simplify the expression $$\left(\frac{3}{2} u^{-2}\right)^2$$. 2. **Recall the exponent rules:** When raising a product to a power, apply the power to eac

1. The problem is to find the value of $\frac{1}{2}$ divided by 6. 2. Recall that dividing by a number is the same as multiplying by its reciprocal. So, dividing by 6 is the same a

1. **State the problem:** Use the box method to multiply and simplify the expression $(-6x + 3)(-6x + 2)$. 2. **Set up the box:** Create a 2x2 grid. Label the top with the terms of

1. **State the problem:** We need to find the equation of a line in slope-intercept form $y=mx+b$ given the slope $m=1$ and a point $(-1,-7)$ on the line. 2. **Recall the formula:*