🧮 algebra

1. **Problem:** Find the domain and range of the function $y = x + 4$. 2. **Formula and rules:** For linear functions $y = mx + b$, the domain is all real numbers because $x$ can b

1. The problem is to analyze and understand the given functions: 2. The functions are:

1. The problem asks to find the domain and range of the numbers. 2. The domain of a function or set of numbers is the set of all possible input values (x-values) for which the func

1. The problem is to evaluate the expression $\sqrt[]{}$, which is an incomplete square root notation. 2. The square root symbol $\sqrt{}$ requires a number or expression inside th

1. The problem states that the relationship between $y$ and $x$ is given by the formula $$y = \frac{k}{x^2}$$ where $k$ is a constant. 2. We are given that when $y = 8$, the equati

1. The problem is to find the minimum value of the parabola shown in the graph. 2. The parabola is U-shaped and opens upward, which means it has a minimum point at its vertex.

1. **State the problem:** We are given a parabola opening upward with vertex at about $(0, -2)$ and x-intercepts at about $(-2, 0)$ and $(2, 0)$. We need to find the minimum value

1. El problema nos pide encontrar cuántas sillas debe vender la empresa para maximizar sus ingresos dados por la función $$R(x) = 50x - 0.5x^2$$ donde $x$ es el número de sillas ve

1. The problem is to analyze the function $y=|x|$. 2. The absolute value function $|x|$ is defined as:

1. **Problem:** Find the distance between the pair of parallel lines given by the equations: $$y = 7$$ and $$y = -1$$

1. **State the problem:** We are given two expressions:

1. **State the problem:** Evaluate the division of fractions $$\frac{2}{7} \div \frac{8}{3}$$. 2. **Recall the rule for dividing fractions:** To divide by a fraction, multiply by i

1. **State the problem:** Evaluate the division of fractions $\frac{4}{3} \div \frac{7}{8}$. 2. **Recall the rule for dividing fractions:** To divide by a fraction, multiply by its

1. **State the problem:** Evaluate the division of fractions $$\frac{3}{5} \div \frac{1}{9}$$. 2. **Recall the rule for dividing fractions:** To divide by a fraction, multiply by i

1. **State the problem:** We need to evaluate the division of two fractions: $$\frac{5}{4} \div \frac{3}{5}$$. 2. **Recall the rule for dividing fractions:** To divide by a fractio

1. The problem asks which expression is equal to $\frac{6}{7}$.\n\n2. Let's analyze each option:\n\n- A: $6 - 7 = -1$, which is not equal to $\frac{6}{7}$.\n- B: $6 \times 7 = 42$,

1. **State the problem:** Add the fractions $\frac{4}{6}$ and $\frac{4}{8}$. 2. **Formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ wh

1. The problem is to multiply the mixed number $2 \frac{3}{4}$ by the fraction $\frac{4}{5}$. 2. First, convert the mixed number to an improper fraction.

1. **State the problem:** Yoko's Coffee Shop makes a blend of two types of coffee: Type A costs 4.05 per pound, Type B costs 5.80 per pound. The total blend is 158 pounds and costs

1. **State the problem:** We are given a proportional relationship between the size of Tammy's garden $x$ (in square feet) and the number of carrots $y$ she can grow, modeled by th

1. **State the problem:** We are given a proportional relationship between the size of Tammy's garden $x$ (in square feet) and the number of carrots $y$ she can grow.