🧮 algebra

1. **Problem:** Calculate the capacity of a tank that is 50 dm long, 3 dm wide, and 20 dm deep, when it is \(\frac{3}{5}\) full. 2. **Formula:** Volume of a rectangular tank is giv

1. The problem is to find the missing numerator $x$ in the equation $$8 \times \frac{x}{6} = \frac{20}{3}$$. 2. The formula used here is to solve for $x$ in a proportion or equatio

1. مسئله: مقدار عبارت $\frac{\sqrt{1}}{\sqrt{3}}$ را بیابید. 2. فرمول‌ها و قوانین مهم:

1. **Problem statement:** We have a cubic polynomial $p(x)$ such that for $j=1,2,3,4$, $p(\frac{1}{j})=2j-1$. We need to find $p(-1)$. 2. **Understanding the problem:** Since $p(x)

1. **State the problem:** We have a cubic equation $$x^3 + 3x^2 - 24x + 1 = 0$$ with roots $$a, b, c$$. We want to find the value of

1. **Stating the problem:** We analyze the function $f_1: y = x - 3$. 2. **Domain and range:** The function $y = x - 3$ is a linear function defined for all real numbers, so the do

1. **State the problem:** Solve the equation $x + 3 = 2 \left( \frac{1}{3} x - 1 \right) + 4^3$. 2. **Recall the order of operations and distributive property:** First, calculate p

1. **State the problem:** Solve the exponential equation $$9^x - 10 \cdot 3^x + 9 = 0$$. 2. **Rewrite the bases:** Note that $$9 = 3^2$$, so we can write $$9^x = (3^2)^x = 3^{2x}$$

1. Let's start by stating the problem: We want to find the values of $x$ such that $f(x) = 0$. 2. The equation $f(x) = 0$ means we are looking for the roots or zeros of the functio

1. Let's clarify the problem: you want to find the value, domain, and range of a function, but the function is not specified. 2. The **domain** of a function is the set of all poss

1. نبدأ ببيان المشكلة: لدينا المتباينة أو المعادلة $$\frac{x - y}{\sqrt{x}} = \frac{x - y}{\sqrt{y}}$$ حيث $$x > 0$$ و $$z > 0$$ (لكن $$z$$ غير مستخدم في المعادلة المعطاة). 2. نلاح

1. **State the problem:** Expand the expression $4(5r + t + u)$. 2. **Formula used:** Use the distributive property of multiplication over addition:

1. **State the problem:** Expand and simplify the expression $$3(5b - 2) - 4(3b + 5)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the facto

1. **Problem statement:** Given the inequality $16 > |12 - 4x|$, find the solution set. 2. **Recall the definition of absolute value inequality:** For $a > |b|$, this means $-a < b

1. **State the problem:** Find the value of $y$ given the equation $y + 5 - x$ and $x = -3$. 2. **Rewrite the equation:** The expression $y + 5 - x$ can be interpreted as $y + 5 -

1. **State the problem:** We need to find the value of $y$ given the equation $y + 5 - x$ and the value $x = -3$. 2. **Rewrite the equation:** The expression $y + 5 - x$ can be int

1. **Problem Statement:** Find the local maxima and minima of the function $$f(x) = |x^4 - 256|$$ and determine the intervals where the function is increasing or decreasing.

1. The problem is to solve for $x$ given the equation or context, but no specific equation was provided. 2. To solve for $x$, we need an equation involving $x$.

1. **State the problem:** Solve the equation $13 - 9(x+1) = 2x - 9$ for $x$. 2. **Apply the distributive property:** Expand $-9(x+1)$ to get $-9x - 9$.

1. **State the problem:** Simplify the expression $$\frac{\sqrt{8}}{3} + \frac{\sqrt{32}}{24}$$. 2. **Recall the rules:**

1. The problem is to simplify and evaluate the expression $\left(\sqrt{3} + 1.2\right)^2$. 2. The formula for squaring a binomial is $$(a+b)^2 = a^2 + 2ab + b^2$$ where $a = \sqrt{