🧮 algebra

1. The problem asks to create an equation in point-slope form using a simplified slope and a point from a table. 2. The point-slope form of a line equation is given by:

1. **State the problem:** Calculate the value of the fraction with numerator $-30 - (-16)$ and denominator $12 - 5$. 2. **Write the expression:**

1. **State the problem:** Add the fractions $\frac{2}{3}$ and $\frac{1}{4}$. 2. **Formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ wh

1. Stating the problem: Simplify the expression $\frac{9}{10} - \frac{3}{5}$.\n\n2. Find a common denominator: The denominators are 10 and 5. The least common denominator (LCD) is

1. The problem asks to simplify the expression $3t \cdot 3(-t)$. 2. The expression involves multiplication of terms. Recall the rule: when multiplying, multiply coefficients (numbe

1. **Problem:** Find the traits algebraically for the function $y = x^3 - x^2 - 9x + 9$ (problem 2). 2. **Formula and rules:** To analyze a cubic function, find:

1. **State the problem:** Marko originally filled out 8 more applications than Henry.

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

1. **State the problem:** Meya and Eric's combined ages equal Sam's age, which is 69 years.

1. Problem: Find the factors of $11x^2y$. Factors are numbers or variables multiplied together to get the expression. Here, the factors are $11$, $x$, $x$, and $y$.

1. Problem: Find the common difference in the arithmetic sequence 5, 7, 9, 11, ... The common difference $d$ in an arithmetic sequence is found by subtracting any term from the nex

1. Problem: Find the answers to the given arithmetic expressions involving integers. 2. Formula and rules:

1. **State the problem:** We are given the sequence $35, \frac{35}{3}, \frac{8}{9}, \frac{17}{27}, \ldots$ and asked to find: (a) the common difference or common ratio,

1. **Problem Statement:** Alex needs to rent a minivan for a week. Two companies offer different pricing schemes: - Easyvans charges a flat fee of 230 plus 0.10 per kilometer.

1. **State the problem:** Simplify and analyze the function $$r(z) = z^{-8} - z^{\frac{1}{2}}$$. 2. **Recall the rules:**

1. **State the problem:** Factor the trinomial $$h^2 + 3h - 40$$ into the form $$(h + a)(h - b)$$ where $a$ and $b$ are numbers to be found. 2. **Recall the factoring rule:** For a

1. **Problem:** Multiply the rational expressions \(\frac{2a^2 b}{b^2 c} \times \frac{b}{a}\). 2. **Formula and rules:** When multiplying rational expressions, multiply numerators

1. The problem describes a parabola with points labeled a, b, and c, where c is the vertex, b is on the same y-coordinate as the dock but on the opposite side of the parabola, and

1. **State the problem:** Simplify the expression $$(2x^2 - 2x + 5)(x + 4)$$ and write it in the form $$ax^3 + bx^2 + cx + d$$. 2. **Use the distributive property (FOIL for polynom

1. **Problem statement:** Linda is water-skiing and the boat follows a parabolic path with vertex at the origin $(0,0)$. The dock is at $(30,30)$ and the boat starts at $(-30,60)$.

1. **State the problem:** Solve the inequality $5 - x \leq 3$ and express the solution in interval notation. 2. **Write the inequality:**