🧮 algebra

1. The problem is to evaluate the expression: $4 \times 7 - 3 \times \left(8 \times 1 \div 2 + 5\right) + 10$. 2. Use the order of operations (PEMDAS/BODMAS): Parentheses first, th

1. **State the problem:** Calculate the value of the expression $1 + \frac{8}{2} \times 2$. 2. **Recall the order of operations (PEMDAS/BODMAS):**

1. **State the problem:** Francesca has one-third of her babysitting earnings left after spending $14.65 on a movie and popcorn and $1.35 on a pen. We need to find how much she ear

1. **State the problem:** We are given a line passing through points $(-1, -2)$ and $(1, -4)$ and need to find its slope $m$ and y-intercept $b$. 2. **Formula for slope:** The slop

1. Το πρόβλημα ζητά να λυθεί ένα σύστημα γραμμικών εξισώσεων. 2. Ένα γραμμικό σύστημα αποτελείται από δύο ή περισσότερες γραμμικές εξισώσεις με κοινές μεταβλητές.

1. **Stating the problem:** We want to understand and solve problems using the reciprocal law, which states that the reciprocal of a number $x$ is $\frac{1}{x}$. 2. **Formula and e

1. Το πρόβλημα ζητά να βρούμε το παρεμβολικό πολυώνυμο $p(x)$ βαθμού το πολύ 4 που περνά από τα σημεία $(-2,-3)$, $(-1,1)$, $(0,0)$, $(1,1)$, $(2,3)$. 2. Το γενικό πολυώνυμο βαθμού

1. The problem is to understand and apply the Reciprocal Law, which states that the reciprocal of a number $x$ is $\frac{1}{x}$, provided $x \neq 0$. 2. The formula for the recipro

1. **Problem:** Given $f(x) = 3x + 1$, find which expression equals $g(x)$ from options: A) $3|x - 1|$, B) $|x| - 3$, C) $3|x| - 1$, D) $|x - 3|$. Since $f(x)$ is linear and no abs

1. **Problem statement:** Find the equation of a parabola in standard form that passes through points $(-5, 2)$ and $(-2, 2)$ and has a maximum value of 20. 2. **Recall the standar

1. Masala: Berilgan $f(x) = 3x - 7$ va $g(x) = 4x + 3$ funksiyalar uchun $g(f(x))$ ni toping va teskari funksiyasini aniqlang. Formulalar: Kompozitsiya funksiyasi $g(f(x)) = g(f(x)

1. Problem: Given functions and piecewise definitions, find expressions and values for g(x), f(g(11)), and solve functional equations. 2. For the first problem, f(x) = 3x + 1 and g

1. Muammo: Berilgan funksiyalar va ifodalar asosida turli algebraik masalalarni yechish. 2. Masala: $f(x) = 3x + 1$ bo'lsa, $f(x)$ ning qiymatlarini topish va boshqa berilgan funks

1. Problem: Find $f(g(x))$ given piecewise functions $f(g(x)) = \begin{cases} -3x + 10, & x < 3 \\ 3x - 8, & x \geq 3 \end{cases}$. Explanation: This is a piecewise function define

1. The problem asks to find the simplified expression for the perimeter of a triangle with side lengths given by the expressions: Left side: $9x - 6w$

1. The problem is to solve for $h$. 2. Since no equation is given, we need an equation involving $h$ to solve it.

1. Given $f(x) = (2x + \frac{1}{2})(3x - 5)$, find $\int_{5/6}^6 f(x) \, dx$. 2. Given $f(x) = \frac{x + 2}{x - 3}$ and $f(g(x)) = 4x - 5$, find $g(f(5.5))$.

1. Masala: $g(f(x))$ funksiyaning teskari funksiyasini toping, bunda $f(x) = 3x - 7$ va $g(x) = 4x + 3$. 2. $g(f(x)) = g(3x - 7) = 4(3x - 7) + 3 = 12x - 28 + 3 = 12x - 25$.

1. Masala: $f(x) = (2x + \frac{1}{2})(3x - 5)$ berilgan. $\int \frac{5}{6}$ ni toping. Bu yerda $\int \frac{5}{6}$ ifodasi aniq emas, ehtimol $f(\frac{5}{6})$ ni topish kerak.

1. Masala: $f(x) = \left( 2x + \frac{1}{2} \right)(3x-5)$ berilgan. $\int \left( \frac{5}{6} \right)^6$ ni toping. Bu yerda $\int \left( \frac{5}{6} \right)^6$ ifodasi integral ema

1. Topish: $f(x) = (2x + \frac{1}{2})(3x - 5)$ va $\int_{5/6}^1 f(x) dx$ ni hisoblash. 2. Avval $f(x)$ ni ochamiz: