🧮 algebra

1. The problem is to rewrite the expression $$\sqrt[3]{x^7}$$ using rational exponents. 2. Recall the rule for radicals and exponents: $$\sqrt[n]{a^m} = a^{\frac{m}{n}}$$ where $n$

1. **State the problem:** Solve the quadratic equation $4x^2 + 4x - 5 = 0$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, th

1. **State the problem:** Solve the inequality $$|5 - 7x| + |2x + 3| \geq 10x + 1$$. 2. **Identify critical points:** The expressions inside the absolute values change sign at poin

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by the denominator to e

1. **State the problem:** We have the infinite series $$\sum_{n=1}^\infty 2 \left(-\frac{1}{2}\right)^{n-1}$$ and we want to find the first term $a_1$, the common ratio $r$, and th

1. **State the problem:** Calculate the value of the expression $4(2.5 - 17)$.\n\n2. **Apply the order of operations:** First, solve the expression inside the parentheses.\n\n3. Ca

1. **State the problem:** Simplify and evaluate the expression $$4(x - 1) + 8x^2$$ when $$x = 2.5$$. 2. **Write the expression:** $$4(x - 1) + 8x^2$$.

1. **State the problem:** Simplify the expression $$\frac{y^2 - 2ps + 2s}{2y - 4p + 4}$$. 2. **Identify the numerator and denominator:**

1. The problem is to find the 7th row of Pascal's triangle. 2. Pascal's triangle rows are numbered starting from 0, where the 0th row is [1]. The nth row contains the binomial coef

1. **State the problem:** Complete the table illustrating the distributive property by expanding and simplifying the given expressions. 2. **Recall the distributive property formul

1. **State the problem:** Solve the system of equations: $$x = y + 7$$

1. **State the problem:** Solve for $y$ in the equation $X = y + 7$. 2. **Formula and rules:** To isolate $y$, subtract 7 from both sides of the equation.

1. **State the problem:** Simplify the expression $$\frac{(q r p^{-2})^{-2} p^{-2} q^{5} r^{0}}{q r}$$ and verify if the result is $$\frac{1}{q^{4} r^{3} p^{6}}$$. 2. **Recall the

1. **State the problem:** Simplify the expression $\frac{(q r p^{-2})^{-2} p^{-2} q^{5} r^{0}}{q r}$.\n\n2. **Recall exponent rules:**\n- $(a^m)^n = a^{m \cdot n}$\n- $a^{-m} = \fr

1. The problem is to simplify or understand the expression $\frac{1}{q^4 r^3 p^6}$.\n\n2. This expression is a fraction with variables $q$, $r$, and $p$ raised to powers 4, 3, and

1. **State the problem:** Solve the system of equations by elimination. For example, consider the system: $$\begin{cases} 2x + 3y = 8 \\ 4x - y = 2 \end{cases}$$

1. **State the problem:** Simplify the expression $\frac{(q r p^{-2})^{-2} p^{-2} q^{5} r^{0}}{q r}$. 2. **Recall the rules:**

1. The problem is to find the reciprocal of a given number or expression. 2. The reciprocal of a number $x$ is defined as $\frac{1}{x}$, provided $x \neq 0$.

1. **Problem:** Determine if the graphs of the given equations are parallel, perpendicular, or neither for problems 7-17, then write equations of lines perpendicular to given lines

1. **State the problem:** Simplify the expression $$\left(\frac{x^{-3} y^{3} z^{0}}{x^{4} y^{0} z^{-4} (y^{0})^{3}}\right)^{4}$$. 2. **Recall the rules:**

1. **Problem statement:** Find the perimeter of each figure given the side lengths. 2. **Formula for perimeter:** The perimeter $P$ of a polygon is the sum of the lengths of all it