🧮 algebra

1. The problem is to graph the function $y = x^2$, which is a quadratic function. 2. The general form of a quadratic function is $y = ax^2 + bx + c$. Here, $a=1$, $b=0$, and $c=0$.

1. **Problem statement:** Solve the inequality $-7z \geq 14$ in the set of real numbers. 2. **Formula and rules:** To solve inequalities, isolate the variable on one side. Remember

1. The problem is to analyze the function $$S_{xx}(\omega) = \frac{\omega^2 + 9}{\omega^4 + 5\omega^2 + 4}$$ and understand its behavior. 2. The formula given is a rational functio

1. **Problem 42:** Find the value of $k - a$ given that the line $y = kx - 7$ and the parabola $y = ax^2 - 13x + 17$ intersect at points with abscissas 4 and 2. 2. **Step 1:** Sinc

1. The problem is to graph a quadratic function that produces a U-shaped curve with a vertex (lowest point) around $y=6$ and x-values roughly between $-1.5$ and $1.5$. 2. The gener

1. **State the problem:** Simplify the expression $$\frac{f-1}{e g} \div \frac{f g}{g+2} = \frac{g}{g}$$. 2. **Recall the division of fractions rule:** Dividing by a fraction is th

1. **Problem Statement:** Find the prime factorisation of the numbers 72, 756, 187, and 630, expressing each answer in index notation. 2. **Formula and Rules:** Prime factorisation

1. **Stating the problem:** We are given a piecewise function $$R(\tau)$$ defined as: $$R(\tau) = \begin{cases} \lambda^2, & |\tau| > \lambda^2 \\ \lambda(1 - 3|\tau|), & |\tau| \l

1) Solve $\frac{x - 7}{x - 1} < 0$. Step 1: Identify critical points where numerator or denominator is zero: $x=7$ and $x=1$.

1. **Problem 34:** Find $q$ for the parabola $y = x^2 + px + q$ given that it touches the $x$-axis at $x=5$. 2. Since the parabola touches the $x$-axis at $x=5$, it means $x=5$ is

1. **State the problem:** We want to understand how to graph the function $f(x) = x^2 - 2x + 1$. 2. **Formula and rules:** This is a quadratic function of the form $f(x) = ax^2 + b

1. **Masala bayoni:** 21-masala: $y = -6x^2 + 7x - 2$ kvadrat funksiyaning nollari yig'indisini toping. 2. **Formulalar va qoidalar:** Kvadrat tenglama $ax^2 + bx + c = 0$ ning ild

1. **State the problem:** We need to find the value of $x$ such that $f(x) = 1 - e^x = 0$. 2. **Set the equation to zero:**

1. **Problem:** Solve and analyze the quadratic equation $x^2 - 25 = 0$. 2. **Formula and rules:** The quadratic equation is $ax^2 + bx + c = 0$. The axis of symmetry is $x = -\fra

1. **Problem Statement:** Find the axis of symmetry, vertex, y-intercept, and x-intercepts of the quadratic function $y = ax^2 + bx + c$. Also, show how to find the x-intercepts an

1. Solve $x^2 - 25 = 0$. - This is a difference of squares: $a^2 - b^2 = (a-b)(a+b)$.

1. **State the problem:** Calculate the volume $V$ given by the formula $V = (3.1416)(5)(9)$. 2. **Formula used:** This is a simple multiplication problem where volume $V$ is the p

1. The problem is to understand what arithmetic and geometric sequences are. 2. An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is co

1. Let's start by understanding what a sequence is. A sequence is an ordered list of numbers following a specific pattern. 2. For example, the sequence $2, 4, 6, 8, \dots$ increase

1. **State the problem:** Solve for $x$ in the equation $$8.6 + 5.6x - 1.5 = 40.7.$$\n\n2. **Simplify the equation:** Combine like terms on the left side: $$8.6 - 1.5 = 7.1,$$ so t

1. **بيان المسألة:** حل المثال الأول (3.5):