🧮 algebra

1. **Stating the problem:** We are given three points (0, 3), (1, 0), and (3, 0) that define the boundary of a flower planting area. We need to determine which statements about the

1. Soal menyatakan lintasan semprotan air mancur mengikuti fungsi kuadrat $$f(x) = -x^2 + 8x$$. 2. Fungsi kuadrat ini berbentuk parabola yang membuka ke bawah karena koefisien $$x^

1. **State the problem:** We need to graph the region defined by the inequalities: $$y - x < 2$$

1. Soal 1: Diberikan fungsi lintasan air mancur $f(x) = -x^2 + 8x$. Kita diminta untuk menggambar sketsa lintasan dan menentukan ketinggian maksimum. 2. Sketsa lintasan air mancur

1. The problem asks to define the region bounded by the parabola, the vertical lines $x=-1$ and $x=5$, and the $x$-axis. 2. From the description, the parabola opens upwards with ve

1. **State the problem:** We need to define the region bounded by the curve $$y^2 = 4x$$, the line $$y = 4$$, the y-axis $$x=0$$, and the vertical line $$x=4$$. 2. **Analyze the cu

1. **State the problem:** We are given a system of inequalities: $$y - x < 2$$

1. **Problem:** Determine between which two integers the number $\sqrt{3}$ lies. Step 1: Identify perfect squares around 3. The perfect squares near 3 are $1 = 1^2$ and $4 = 2^2$.

1. Problem: Determine if $\sqrt{196}$ is rational or irrational. Step 1: Calculate $\sqrt{196}$. Since $196 = 14^2$, $\sqrt{196} = 14$.

1. Simplify $\sqrt[3]{1}$: Since $1^3 = 1$, $\sqrt[3]{1} = 1$.

1. **State the problem:** We need to analyze and graph the region defined by the system of inequalities: $$y - x < 2$$

1. The problem states there is a linear relationship between the number of people in tens of millions living in urban areas in the US and the number of years since 1960. 2. We are

1. Stating the problem: Simplify the expression $\left(\frac{3-7}{5}+\frac{3}{10}\right)-\left(\frac{7}{12}-\frac{1}{3}\right)$.\n\n2. Simplify inside the first parentheses:\nCalcu

1. The problem gives the equation $$y = -9x + 1830$$ where $x$ is the number of years since 1950 and $y$ is the average number of working hours per worker. 2. The Y-intercept is th

1. **State the problem:** We are given a linear relationship between the number of years since 2009, $X$, and the price per box of oranges, $Y$. We need to find the slope and the Y

1. Stating the problem: Simplify the expression $\left(\frac{7}{3}+\frac{9}{4}\right)-\left(\frac{1}{2}+1\right)$.\n\n2. Find a common denominator for the fractions inside the firs

1. Factoriser A = (x + 4)(6x - 1) + (x + 4)(7x - 2) On remarque que (x + 4) est un facteur commun.

1. Factoriser chaque expression donnée. 2. Pour A = (x + 4)(6x - 1) + (1 + x)(4 + 4)(7x - 2) :

1. The problem is to simplify the expression $ (1 + i)(2 + 3i)(4 - 3i) $ where $i$ is the imaginary unit with $i^2 = -1$. 2. First, multiply the first two complex numbers:

1. **State the problem:** Ellie and Colette are typing research papers. Ellie types 1 page per hour and already has 15 pages done. Colette types 3 pages per hour and has 3 pages do

1. **تمرين 1** 1.1. فكك العددين $x=154$ و $y=140$ إلى جداء عوامل أولية: