🧮 algebra

1. **State the problem:** Find the explicit form of the function $y$ from the equation

1. Énoncé du problème : La largeur d'un rectangle est 1 cm de plus que la moitié de sa longueur. Le périmètre est de 86 m. Trouvons les dimensions du rectangle. 2. Formule du périm

1. **State the problem:** Solve the inequality $8 < 2 - 2(3x - 1) + \frac{4}{5}x$. 2. **Apply distributive property:** Expand $-2(3x - 1)$ to get $-6x + 2$.

1. **State the problem:** Solve the inequality $-x - \frac{5}{2} \geq -8 + \frac{1}{2}(-x + 1)$.\n\n2. **Write down the inequality:** $$-x - \frac{5}{2} \geq -8 + \frac{1}{2}(-x +

1. Stwierdzenie problemu: Rozwiążmy równanie tożsamościowe $$4mn \times x = mn + x + \frac{1}{2}$$ dla zmiennej $x$. 2. Przepiszmy równanie: $$4mnx = mn + x + \frac{1}{2}$$

1. **Planteamiento del problema:** Resolver la ecuación $2(x+1)-3(x-2)=5(x+4)$. 2. **Expansión y simplificación:** Aplicamos la distributiva:

1. **Problem:** Solve the quadratic equation $3x^2 - 5x - 9 = 0$ using the quadratic formula and give answers correct to 2 decimal places. 2. **Formula:** The quadratic formula is

1. **Problem:** Solve the quadratic equation $3x^2 - 5x - 9 = 0$ using the quadratic formula and give answers correct to 2 decimal places. 2. **Formula:** The quadratic formula is

1. The problem is to draw the graphs of the two linear equations: $$x - 5y = 6$$

1. **Problem Statement:** Find the inverse of an exponential function, typically given as $y = a^x$ where $a > 0$ and $a \neq 1$. 2. **Formula and Important Rules:** The inverse of

1. Let's start by understanding what an exponential function is. An exponential function has the form $$y = a^x$$ where $a$ is a positive constant not equal to 1, and $x$ is the ex

1. **State the problem:** Expand and simplify the expression $$(c - 4)(c + 6) - (c + 2)(c - 3)$$. 2. **Recall the distributive property:** To expand products of binomials, use the

1. The problem is incomplete as only "A=[" is provided without further information. 2. To solve or analyze a matrix or set, we need the full elements or context.

1. **State the problem:** We have a binary operation defined as $a * b = a + b - 2$. We are asked to find the inverse of 5 under this operation, given that the identity element is

1. **State the problem:** We are given the quadratic function $f(x) = 3x^2 + 5x - 7$. 2. **Express $f(x)$ in the form $a(x+h)^2 + k$ (completing the square):**

1. **State the problem:** Orlando missed 5 out of 40 questions on the test. We need to find the percentage of questions he got right. 2. **Formula:** Percentage of correct answers

1. **Problem:** Factorize completely the expressions given. 2. **Part a:** Factorize $6y^2 - 18xy$.

1. Masala: Parabolaning uchi $(-1, -4)$ nuqtada joylashgan. $f(x) = ax^2 + bx + c$ tenglamada $a - b + c$ ni toping. Parabola uchi koordinatalari $x_0 = -\frac{b}{2a}$ va $y_0 = f(

1. Muammo: Parabolani $b(-3;4)$ vektor bo'yicha parallel ko'chirish natijasida hosil bo'lgan parabolaning tenglamasini toping. Formulasi: Agar $y=f(x)$ parabola $b(h;k)$ vektor bo'

1. The problem is to analyze and graph the piecewise function: $$Y = \begin{cases} -2x^2 + x - 5 & \text{if } x < -2 \\ |x - 4| & \text{if } x \geq 2 \end{cases}$$

1. مسئله را بیان می‌کنیم: الف) ضابطه جبری تابع داده شده را بیابید.