🧮 algebra

1. **State the problem:** We are given the function $$y = (x+3)^2 + 2$$ and need to find the function's vertex and describe its graph. 2. **Identify the function type:** This is a

1. The problem is to understand the expansion of the function $$G(s) = s^{v-qr} \left[ 1 - \frac{a}{s^q} \right]^{-r}$$

1. The slope of a line measures how steep the line is. 2. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

1. The problem asks to estimate the number of CDs sold in 2006 based on the trend from 1999 to 2005 shown in a scatter plot. 2. Since the data shows a decreasing trend over time, a

1. **Problem:** Simplify the expression $\frac{1-3s-7}{1-s}$. 2. **Step 1:** Write the numerator clearly: $1 - 3s - 7 = (1 - 7) - 3s = -6 - 3s$.

1. **State the problem:** Factorise the quadratic expression $15x^2 - 16x - 15$. 2. **Identify coefficients:** Here, $a = 15$, $b = -16$, and $c = -15$.

1. The problem is to solve the quadratic equation $$2x^2 - 4x - 6 = 0$$. 2. First, identify the coefficients: $$a = 2$$, $$b = -4$$, and $$c = -6$$.

1. The problem is to solve the quadratic equation $$2x^2 - 4x - 6 = 0$$. 2. First, identify the coefficients: $$a = 2$$, $$b = -4$$, and $$c = -6$$.

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:

1. **State the problem:** We are given total Covid-19 cases in Egypt on two dates: July 24, 2020 (91,072 cases) and August 3, 2020 (94,640 cases). We assume the number of cases cha

1. The problem is to evaluate the square root of 3, written as $\sqrt{3}$.\n\n2. The square root function $\sqrt{x}$ gives the number which, when multiplied by itself, equals $x$.\

1. **State the problem:** We have two lines given by equations: $$2x + ty = -1$$

1. We are asked to find the quadratic function $f(x) = ax^2 + bx + c$ that passes through the points $(3,0)$, $(-2,0)$, and $(1,7)$. 2. Since the points $(3,0)$ and $(-2,0)$ are ze

1. **State the problem:** We are given three points A(2,5), B(9,-2), and J(4,h) that lie on the same straight line. We need to find the value of $h$. 2. **Find the slope of the lin

1. **State the problem:** We have a linear function $f$ such that $f(0) = \frac{1}{2}$ and $f(-3) = -\frac{3}{2}$. We need to find the value of $f(3)$. 2. **Recall the form of a li

1. **State the problem:** Find the equation of the line perpendicular to the line given by $$2x - 3y = -1$$ and passing through the midpoint of segment $$\overline{AB}$$ where $$A(

1. The problem asks us to find which taxi company offers the cheapest total cost for traveling 500 Km. 2. Each taxi company charges a fixed amount plus an additional amount per 25

1. **State the problem:** We are given the equation of a line $$\frac{2}{x} - \frac{3}{y - 1} = 0$$ and need to find its slope. 2. **Rewrite the equation:** Move terms to isolate o

1. **Problem:** Analyze the function $f(x) = \frac{x}{x-1}$. - The function is a rational function with a vertical asymptote at $x=1$ because the denominator is zero there.

1. The problem asks for the slope of the line $m$ passing through points $(2a, a^2)$ and $(2b, b^2)$ where $a \neq b$. 2. Recall the formula for the slope $m$ of a line through two

1. **State the problem:** Find the equation of line $d$ that passes through the origin $O(0,0)$ and is perpendicular to line $k$ which passes through points $A(0,3)$ and $B(2,0)$.\