🧮 algebra

1. The problem asks to arrange a set of items in ascending order, but the specific items are missing from the question. 2. To solve such a problem, you would typically compare the

1. **State the problem:** We have a rectangular garden with length $x+4$ metres and width $x-4$ metres. The area is given as 180 m². We need to find the value of $x$ and then calcu

1. The problem asks to arrange a given set of items in ascending order. However, the specific items to be ordered are not provided in the question. 2. To solve an ascending order p

1. The problem asks to find the equation of a parabola given its vertex and x-intercepts. 2. The vertex is at $ (2, -1) $ and the x-intercepts are at $ x = -2 $ and $ x = 6 $.

1. **State the problem:** We need to find the values of constants $m$ and $c$ in the linear equation $y = mx + c$ given two points: when $x=3$, $y=20$ and when $x=4$, $y=40$. 2. **

1. Let's start by defining what a sequence and a series are. 2. A sequence is an ordered list of numbers, for example, $a_1, a_2, a_3, \dots, a_n$.

1. Problem 45 asks for the rate of depreciation. 2. Problem 46 asks for the original cost of the car.

1. The problem is to understand or interpret the expression "Y 1.75?" which seems incomplete or unclear. 2. If you meant to ask about the value of a variable Y equal to 1.75, then

1. Planteamos el problema: Encontrar el vértice, foco, directriz y eje de simetría de la parábola dada por la ecuación $$(y - 1)^2 = -5(x + 3)$$ 2. Identificamos la forma estándar

1. **Problem Statement:** Solve a system of two linear equations using three methods: Cramer's Rule, Inversion Method, and Gauss Elimination Method. Provide two examples for each m

1. Problem 41: We analyze the depreciation of values over time given the drop every 6 years. - For each item, the value drop rate per year is calculated by dividing the drop amount

1. **State the problem:** We are given the number pattern 698, 683, 670, 659, 650 and need to find the next two numbers. 2. **Identify the pattern:** Look at the differences betwee

1. **Problem Statement:** Verify the correctness of matrix operations and determinant calculations given in the problem. 2. **Matrix B calculation:** Given matrices

1. Problem 41: Find the rate of change for the resale value of a refrigerator given the data points from (0, 600) to (15, 0). Step 1: Identify two points on the line: $(0,600)$ and

1. Problem 38: Compare the rate of change of profits of companies A and B. - The rate of change of profit is the slope of the profit vs. year graph.

1. The problem is to solve the quadratic equation $$2x^2 + 5x - 18 = 0$$ by completing the square. 2. First, divide the entire equation by 2 to make the coefficient of $x^2$ equal

1. The problem asks for the axis of symmetry of the curve given by the quadratic function $y = 3x^2 - x - 4$. 2. Recall that the axis of symmetry for a parabola in the form $y = ax

1. **State the problem:** We have a sequence of tile patterns where the number of tiles increases by the same amount each time. We want to find an expression for the number of tile

1. **State the problem:** We have a sequence of patterns made from tiles. Each pattern adds the same number of tiles as the previous one. We want to find an expression for the numb

1. The problem is to solve the equation $$2x + 3 = 7$$ for $x$. 2. Start by isolating the variable term on one side. Subtract 3 from both sides:

1. The problem is to solve the equation $$2x + 3 = 11$$ for $x$. 2. Start by isolating the variable term on one side. Subtract 3 from both sides: