🧮 algebra

1. **State the problem:** We need to solve the division of two fractions: $\frac{9}{4} \div -\frac{4}{3}$. 2. **Formula used:** Dividing by a fraction is the same as multiplying by

1. **State the problem:** We need to express the last row's expression in radical notation, rational exponents, and evaluate it to two decimal places. 2. **Identify the expression:

1. **State the problem:** We need to determine which statements about radicals and rational exponents are true. 2. **Recall definitions and properties:**

1. **State the problem:** Find the x-intercept, vertical asymptote (VA), horizontal asymptote (HA), hole, y-intercept, domain, and range of the function $$f(x) = \frac{2x^2 + 8x +

1. State the problem. Problem: Solve $194+2p=284$.

1. The problem involves understanding the graph of a line and identifying its equation based on its slope and intercepts. 2. The equation of a line in slope-intercept form is given

1. **State the problem:** We need to select the graph that matches the equation $$y = 4x - 2$$. 2. **Recall the slope-intercept form:** The equation is in the form $$y = mx + b$$ w

1. **State the problem:** We need to identify the graph that matches the equation $$y = -2x - 2$$.

1. **State the problem:** Factor the quadratic expressions and match them with their correct factored forms. 2. **Recall factoring formulas:**

1. The problem gives the equation relating pounds of rice $r$ and beans $b$ with total cost $10$: $$2r + 1.60b = 10$$

1. **State the problem:** Lin has $10 to spend on brown rice and beans. Brown rice costs 2 per pound, beans cost 1.60 per pound. Let $b$ be pounds of beans and $r$ be pounds of ric

1. **State the problem:** We are given a system of two linear equations: $$x + y = 15$$

1. **State the problem:** We are given the total cost function for a home security system: $$C = 80 + 40x$$ where $C$ is the total cost and $x$ is the number of months of service.

1. The problem is to understand why the number 6 can be expressed as the pair (4,1). 2. This likely refers to expressing 6 as a sum of squares or a similar decomposition.

1. **State the problem:** Solve the system of equations using the elimination method: $$\begin{cases} 3x - 2y = 10 \\ 7x + 2y = 30 \end{cases}$$

1. The problem is to solve the equation $$-20 = -10x$$ for $x$. 2. The goal is to isolate $x$ by dividing both sides of the equation by the coefficient of $x$, which is $-10$.

1. **State the problem:** Solve the equation $$x - 5 = -3$$ for $x$. 2. **Recall the goal:** We want to isolate $x$ on one side of the equation to find its value.

1. **State the problem:** Simplify the expression $$\frac{\frac{3}{2} + \frac{3}{x}}{2 + \frac{4}{x}}$$. 2. **Rewrite the expression:** To simplify, first find a common denominator

1. **State the problem:** Solve the rational equation $$\frac{4}{3x+3} = \frac{12}{x^2-1}$$. 2. **Identify the denominators and restrictions:** The denominators are $3x+3$ and $x^2

1. **State the problem:** Expand the expression $$(4x^2 + y^4)^2$$ and write the answer as a polynomial in standard form. 2. **Recall the formula:** The square of a binomial $$(a +

1. **State the problem:** Factor the quadratic expression $x^2 - 12x + 20$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multi