🧮 algebra

1. **State the problem:** We are given the sum of 5 consecutive integers is 265, and we need to find the fifth number in this sequence. 2. **Define variables:** Let the first integ

1. **State the problem:** We need to find the first of three consecutive even numbers whose sum is 270. 2. **Define variables:** Let the first even number be $x$. Since the numbers

1. **State the problem:** We need to find the second number in a sequence of 4 consecutive odd numbers whose sum is 40. 2. **Define variables:** Let the first odd number be $x$. Si

1. Problem statement: Solve the equation $$\frac{n^2 + n}{n} = 10$$. 2. Formula and rules: We simplify the rational expression by dividing each term in the numerator by $n$, which

1. **State the problem:** We need to find the fourth number in a sequence of 6 consecutive even numbers whose sum is 126. 2. **Define variables:** Let the first even number be $x$.

1. **State the problem:** We need to find Shobhit's present age given that 11 years from now, his age will be 3 times what it was 3 years ago. 2. **Define variables:** Let Shobhit'

1. نبدأ بكتابة الدالة المعطاة: $$f(x) = \frac{1}{3}x^{3} - \frac{1}{2}x^{2} - 6x + 1$$

1. The problem involves analyzing the function given previously (assumed to be $y=\frac{a}{b}$ or similar) and showing its graph. 2. To graph a function, we plot points $(x,y)$ tha

1. **State the problem:** Kriti has 20 coins consisting of 1-rupee, 2-rupee, and 5-rupee coins totaling 41 rupees. The number of 2-rupee coins is three times the number of 5-rupee

1. **Problem Statement:** We are given the cubic function $$f(x) = \frac{1}{3}x^{3} - \frac{1}{2}x^{2} - 6x + 1$$ and asked to evaluate or approximate the value of $$f\left(\frac{2

1. **State the problem:** We have two numbers, one is positive and is 3 times the other. If we add 2 to the larger number and 5 to the smaller number, then one of the resulting num

1. Le problème concerne la compréhension des coefficients dans le développement d'un binôme au cube, par exemple $ (a+b)^3 $.\n2. La formule utilisée est le développement du cube d

1. **State the problem:** We have two positive numbers where one is 3 times the other. If we add 2 to the larger number and 5 to the smaller number, then one of these new numbers b

1. **State the problem:** Solve for real $x$ in the equation $$\arctan\left(\frac{1}{n^2+n+1}\right) = \arctan\left(\frac{1}{n}\right) - \arctan(x).$$ 2. **Recall the formula for d

1. **Find the interval of $x$ satisfying:** $$| |x - 3| - 2 | \geq 1$$

1. The problem is to solve the equation: $\text{first}'$. Since the input is incomplete or unclear, please provide the full equation or expression to solve. 2. Generally, to solve

1. Let's solve a typical algebraic equation from class 8: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. The formula or rule we use here is to isolate the variable $x$ by perfor

1. **State the problem:** Solve the equation as a normal equation in 3 steps. 2. **Step 1: Identify the equation and isolate the variable term.** For example, if the equation is $a

1. The problem asks to make the Latin the subject of the formula in given cases. 2. To make a variable the subject of a formula means to isolate that variable on one side of the eq

1. **Problem statement:** We have two numbers, 3090 and 1854, and we want to find their greatest common divisor (GCD) and least common multiple (LCM). 2. **Formula and rules:**

1. The problem is to express the variables $h$ and $k$ as the subject of an equation. 2. To do this, we need a specific equation involving $h$ and $k$. Since the user did not provi