🧮 algebra

1. مسئله: رسم نمودار تابع $y = x^2 - 1$ است. 2. فرمول: این تابع یک تابع درجه دوم است که به شکل $y = ax^2 + bx + c$ با $a=1$, $b=0$, و $c=-1$ است.

1) Schreibe mit dem Wurzelzeichen: Gegeben ist $a^{\frac{2}{7}}$.

1. **State the problem:** We need to graph the function $y=2(x-4)^2-7$. 2. **Identify the type of function:** This is a quadratic function in vertex form $y=a(x-h)^2+k$ where $(h,k

1. The problem is to express 30 as a product of three numbers: $30 = \_ \times \_ \times \_$. 2. We want to find three factors of 30 such that their product equals 30.

1. The problem asks to express 24 as a product of four numbers. 2. We start by finding the prime factorization of 24.

1. **Problem:** Expand $\sqrt{9 - 4x}$ in ascending powers of $x$ up to $x^3$ and state the range of $x$ for validity. 2. **Formula:** Use binomial expansion for fractional powers:

1. The problem is to simplify the square roots given: a) $\sqrt{52}$ and b) $\sqrt{170}$.\n\n2. The formula to simplify square roots is to find the prime factors and take out pairs

1. **State the problem:** Convert the quadratic function $y = -\frac{1}{2}(x + 6)^2 + 2$ into vertex form, zero form, and standard form. Find the vertex coordinates, zeros, max/min

1. **State the problem:** We are given a parabola with vertex at $(-6, 2)$ and a point $(-8, -4)$ on the parabola. We want to find the equation of the parabola in vertex form, zero

1. **Problem:** Daisy has 200 and wants to buy T-shirts costing 25 each. Find the possible number of T-shirts she can buy. 2. **Formula:** Number of T-shirts $n$ must satisfy $25n

1. **State the problem:** Add the fractions and mixed numbers: $1 \frac{2}{6} + \frac{5}{6} + \frac{7}{6}$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Solve the equation $4 - \frac{3}{5}m = \frac{6}{5}m + 2$ for $m$. 2. **Isolate the variable terms:** Move all terms involving $m$ to one side and constant

1. **State the problem:** Solve for $m$ in the equation $$\frac{4-3}{5}m = \frac{6}{5}(m+2).$$ 2. **Write the equation clearly:**

1. **State the problem:** Solve the equation involving absolute values: $|2 - x| + |3 + x| = 5$. 2. **Understand absolute values:** The absolute value $|a|$ equals $a$ if $a \geq 0

1. Problema: Išspręskite lygtį $$\sqrt{2A - 56} = 200$$. 2. Naudojama formulė: Jei $$\sqrt{x} = y$$, tai $$x = y^2$$.

1. **Problem statement:** A student bought five online courses with durations 131, 46, 31, 22, and 15 hours, totaling 245 hours. He watches exactly 3 or 4 hours per day of some cou

1. Problem: Solve the inequality $x^2 + 3 > 0$. 2. Formula and rules: For any real number $x$, $x^2 \geq 0$. Adding 3 makes it strictly positive.

1. **State the problem:** Calculate the value of the expression $$\frac{2.75}{0.35+0.15} \times 2$$. 2. **Add the numbers in the denominator:**

1. **State the problem:** Calculate the value of $2.75(0.35+0.15)\times 2$. 2. **Apply the order of operations:** First, solve the expression inside the parentheses.

1. Problem 22 asks for a description of the algebraic expression $\frac{e}{d} - 15$. 2. This expression means you divide $e$ by $d$, then subtract 15 from the result.

1. **State the problem:** Solve the algebra problem given (no specific problem stated, so let's consider a general algebraic equation example: Solve for $x$ in $2x + 3 = 7$. 2. **F