🧮 algebra

1. **State the problem:** We are given three parallel segments AD, BE, and CF with lengths expressed as algebraic expressions: $AD = 3x + 20$, $BE = 2x + 14$, and $CF = x + 25$. Si

1. Plantea el problema: Un fabricante vende tres modelos de coches A, B y C con precios 1.5, 2 y 3 millones respectivamente. 2. Define variables: Sea $x$, $y$, $z$ el número de coc

1. **State the problem:** Determine which systems of equations are equivalent to the system: $$\begin{cases} y = -5x - 8 \end{cases}$$

1. The problem states that a pie chart represents three uniform units: Scouts (Pengakap), Police Cadets (Kadet Polis), and KRS, with given numbers for Scouts (45) and KRS (115). We

1. The problem involves calculating the speed given the time and distance. 2. We know the formula for speed is $$\text{speed} = \frac{\text{distance}}{\text{time}}$$.

1. The problem gives a number sequence: $$150, m, 126, 114, 102, n$$ and asks to find the value of $$m - n$$. 2. To solve this, we first identify the pattern in the sequence. The s

1. Diberikan persamaan $3^n \times 3^2 = 27^{n+1}$. Kita diminta mencari nilai $n$. 2. Ingat bahwa $27$ dapat ditulis sebagai $3^3$, sehingga persamaan menjadi $3^n \times 3^2 = (3

1. The problem asks: What number is 65% of 840? 2. To find a percentage of a number, use the formula:

1. **State the problem:** We need to find the number for which 36 is 30% of it. 2. **Formula:** To find a number when a percentage of it is given, use the formula:

1. **State the problem:** Calculate the total pay for 8 overtime hours at a rate of $13.50 per hour with time and a half. 2. **Formula:** Overtime pay rate = Regular pay rate \time

1. **State the problem:** Calculate the total pay for 35 regular hours at a rate of 8.81 per hour. 2. **Formula used:** Total pay = hourly rate \times number of hours

1. The problem asks to find the pay for a given condition, but the specific condition is not provided. 2. To solve pay-related problems, we typically use the formula: $$\text{Pay}

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} 5x - 2y + 3z = 6 \\ -4x + 6y - 7z = -3 \\ 3x + 2y - z = 6 \end{cases}$$

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + 4y + z = 9 \\ -x + 2y + 2z = 0 \\ 2x + 2y - z = 9 \end{cases}$$

1. **State the problem:** Daniel has two income options: hourly pay at 10 per hour and a salary of 110 per day. We need to write equations for each, graph the relations, and decide

1. The problem is to find the equation representing the table of values and verify if the given equations and graphs are correct. 2. The general form of a linear equation is $$y =

1. The problem is to solve a quadratic equation using the grade 10 quadratic formula. 2. The quadratic formula is given by $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ where $a$, $b$, and

1. **State the problem:** We have a rectangle with surface area 60 cm², length $x+9$, and width $x-8$. We need to find $x$ and the dimensions. 2. **Formula:** Area of rectangle = l

1. **Problem Statement:** We are asked to draw sets of counters representing given ratios and find how many different ways these can be done.

1. The problem is to find the value of $k$ for which the quadratic equation $$x^2 + (k+8)x + 9k = 0$$ has a real double root. 2. A quadratic equation $$ax^2 + bx + c = 0$$ has a re

1. **Problem statement:** Determine the condition on $k$ such that the quadratic equation $kx^2 + 3x + 6 = 0$ has two unique real roots. 2. **Formula used:** For a quadratic equati