🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{-3xy^4}{-21x^3y^2}$$. 2. **Write the expression:** $$\frac{-3xy^4}{-21x^3y^2}$$.

1. **State the problem:** We need to solve for $x$ given the formula:

1. **State the problem:** Solve the compound inequality $$x + 9 < 0 \text{ or } 2x > -12$$. 2. **Solve the first inequality:**

1. The problem asks to write the inequality $x \geq 3$ in interval notation. 2. Interval notation expresses the set of all numbers that satisfy the inequality.

1. **State the problem:** Solve the compound inequality $-3x \leq -9$ or $3x - 26 \geq -8$. 2. **Solve the first inequality:**

1. The problem asks for the output of a function when the input is 10 and to plot this point with its coordinates. 2. Since the function is not specified, let's assume a general fu

1. **State the problem:** Simplify the expression $4 \times 3 \times 4 \times 30 - 8xj - 7 - 9 + y + 1r$. 2. **Multiply the constants:** Calculate $4 \times 3 = 12$, then $12 \time

1. **State the problem:** Solve the compound inequality $$x \leq -4 \text{ or } x \geq 10$$ and represent the solution on a number line and in interval notation. 2. **Understand th

1. **State the problem:** We are given a point $P = (7, 27.5)$ and a linear function $y = 2x + 45$. We want to verify the value of $y$ at $x=7$ and understand the graph description

1. We are given the compound inequality $$-14 \leq 7x - 7 \leq 7$$ and need to find the solution set for $x$. 2. The goal is to isolate $x$ in the middle. We start by adding 7 to a

1. **Stating the problem:** Solve the system of equations \(\{x^2 + y^2 = 10, x + y = -1\}\). 2. **Formula and rules:** We can use substitution or elimination. Here, from the linea

1. **State the problem:** Match each quadratic equation with its corresponding graph based on the roots (x-intercepts). 2. **Recall the quadratic formula and factorization:** The r

1. **State the problem:** Match each quadratic equation with its corresponding graph based on vertex and shape. 2. **Recall the vertex formula:** For a quadratic $y = ax^2 + bx + c

1. The problem is to evaluate $4^3$ instead of $2^6$. 2. Recall the definition of exponents: $a^b$ means multiplying $a$ by itself $b$ times.

1. **State the problem:** Simplify the expression $$\sqrt[5]{64x^{9}y^{4}}$$. 2. **Recall the rule for radicals:** $$\sqrt[n]{a^{m}} = a^{\frac{m}{n}}$$.

1. Let's understand the problem: Why use $2^6$ instead of $4^3$? 2. Both expressions represent powers and can be compared by expressing them with the same base.

1. **State the problem:** Simplify the expression $$\sqrt[5]{64x^{9}y^{4}}$$. 2. **Recall the formula:** For any real numbers and variables, $$\sqrt[n]{a^{m}} = a^{\frac{m}{n}}$$.

1. **State the problem:** Solve the quadratic equation $$-4x^2 - x + 4 = 0$$ and find the greatest solution. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c =

1. **State the problem:** We are given a line with slope $m=2$ and an $x$-intercept at $\left(\frac{8}{7},0\right)$. We need to find the $y$-intercept of this line. 2. **Recall the

1. **State the problem:** We are given a triangle with area $x^2$ square centimeters, base length $2x + 22.5$ cm, and height $x - 5$ cm. We need to find the value of $x$. 2. **Form

1. Let's clarify the problem: You are asking about the origin of the number 4 used to subtract 25 in a certain calculation. 2. Typically, in algebraic manipulations, numbers like 4