🧮 algebra

1. **State the problem:** Evaluate the expression $$\frac{\sqrt{900 - \left(\frac{30}{14}\right)^2}}{13}$$. 2. **Recall the formula and rules:** The square root function is defined

1. The problem is to simplify the expression $$3\sqrt{6} - 6$$. 2. Recall that $$\sqrt{a}$$ means the square root of $$a$$, and it cannot be simplified further unless $$a$$ is a pe

1. **Stating the problem:** We are given the expression \(\frac{\frac{2x}{9}}{1 - 2x} \div (1 - x - 3)\) and asked to solve it or simplify it.

1. The problem asks to find the difference between the values obtained by rounding 4.82 to one significant figure and to one decimal place. 2. **Rounding to one significant figure:

1. **Stating the problem:** We need to find which number from the list rounds to the same value when rounded to one significant figure and when rounded to one decimal place. 2. **U

1. **State the problem:** We need to find which number among 0.1245, 0.0255, 0.255, and 0.1255 rounds differently when rounded to two significant figures versus when rounded to two

1. **Stating the problem:** We are given two fractions, $\frac{1}{2}$ and $\frac{9}{14}$, and we want to compare their values and understand their positions on the number line. 2.

1. **Problem Statement:** Given the function $$f(x) = \frac{1}{x+2}$$ 2. **Find the domain of definition:** The function is defined for all real numbers except where the denominato

1. The problem involves understanding the relative positions of the points $-\frac{1}{2}$, $\frac{1}{6}$, and $\frac{5}{12}$ on a number line. 2. To compare these fractions, we fin

1. **State the problem:** Calculate $\frac{1}{5} - \frac{3}{5}$. 2. **Formula and rules:** To subtract fractions with the same denominator, subtract the numerators and keep the den

1. **State the problem:** Calculate the value of the expression $2 \times (4+5)$. 2. **Recall the order of operations:** According to the order of operations (PEMDAS/BODMAS), we fi

1. The problem is to simplify the expression $-)(4+4(3$. 2. First, we need to clarify the expression. Assuming the expression is $- (4 + 4 \times 3)$, we follow the order of operat

1. The problem is to simplify the expression $-2 + 2$. 2. The expression involves simple addition and subtraction of integers.

1. **State the problem:** We are given the function $y = 3 - \sqrt{x}$ and want to understand its behavior. 2. **Recall the formula and domain:** The function involves a square roo

1. **Stating the problem:** We need to make $x$ the subject of the equation. However, the equation is not provided in your message. 2. **Next steps:** Please provide the equation i

1. সমস্যাটি হলো: বার্ষিক ৪% সুদে ৮০০০ টাকা ৫ বছর ব্যাংকে জমা রাখা হয়েছে। (ক) ৮০০০ টাকার ৪% কত টাকা? (খ) ৫ বছরে মোট মুনাফা কত হবে? (গ) ৫ বছরে মোট মুনাফা কত টাকা হলো? 2. সূত্র: বার্

1. The problem is to solve a system of linear equations using the Vienna method (also known as Cramer's rule). 2. The Vienna method uses determinants to find the solution of a syst

1. **Stating the problem:** Find the roots of the polynomial $$x^4 + 15x^3 + 70x^2 + 120x + 64$$ using the grouping method (GP). 2. **Recall the grouping method:** Group terms to f

1. **Problem a:** Solve the quadratic equation $$-3x + \frac{6}{7} = 9x^2$$ and find its roots. 2. **Step 1:** Rearrange the equation to standard quadratic form $$ax^2 + bx + c = 0

1. **State the problem:** Harry and Joe together can mop a warehouse in 8 hours. Harry alone takes 12 hours. We need to find how long Joe alone would take. 2. **Formula and concept

1. **State the problem:** Simplify the expression $$2 - \left[1 - \left(\frac{1}{2} \times \frac{2}{3} \div 1\right)\right] \times (-0.75)^2$$. 2. **Recall the order of operations: