🧮 algebra

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:

1. **State the problem:** Solve the equation $$\frac{3^x \cdot 27^{x+3}}{9^x} = \left(81^x\right)^{2x-1}$$ for $x$. 2. **Rewrite all terms with base 3:**

1. **State the problem:** A phone plan costs 40 flat plus 0.20 per minute over 500 minutes. Last month the bill was 52. We need to find how many extra minutes were used. 2. **Set u

1. **State the problem:** Solve the system of inequalities: $$3x \geq 2$$

1. **State the problem:** Solve the inequality $$-3x + 12 > 27$$. 2. **Isolate the variable term:** Subtract 12 from both sides to get $$-3x > 27 - 12$$.

1. **State the problem:** Solve the system of inequalities: $$3x - 7 < -16$$

1. **State the problem:** We need to find the equation of a line that passes through the point $(0, 2)$ and is parallel to the line given by $$y = -2x + 5.$$ 2. **Recall the formul

1. The problem asks which line is perpendicular to the line given by the equation $y = 5x + 1$. 2. Recall that the slope of a line in the form $y = mx + b$ is $m$. Here, the slope

1. **State the problem:** We need to find which line is parallel to the line given by the equation $y = 4x - 7$. 2. **Recall the rule for parallel lines:** Two lines are parallel i

1. **Problem Statement:** A family needs at least 350 points to win the Thanksgiving game night prize. Each board game played gives 60 points, and each card game gives 25 points. T

1. **State the problem:** We are given two inequalities: $x < -5$ and $x \geq -2$. We want to understand the solution set for these combined conditions. 2. **Analyze each inequalit

1. **State the problem:** We have a rectangle with a perimeter of 44 cm. The length ($L$) is 6 cm more than the width ($W$). We need to find the length. 2. **Formula for perimeter

1. **State the problem:** We are given two numbers whose sum is 18 and their difference is 4. We need to find the larger number. 2. **Set variables:** Let the two numbers be $x$ an

1. **State the problem:** A chemist wants to mix a 10% acid solution and a 25% acid solution to get 60 liters of a 15% acid solution. We need to find how many liters of each soluti

1. نبدأ بحل التعبير الجبري المعطى: $1 - 8 \times 2 + 4 + 5 - 3$ 2. نطبق قاعدة ترتيب العمليات: نبدأ بالضرب ثم الجمع والطرح من اليسار إلى اليمين.

1. The problem asks for the slope of the line given by the equation $y = -5x + 8$. 2. Recall that the slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$

1. **State the problem:** Convert the equation $y - 5 = 3(x - 2)$ to slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. **Recall the