🧮 algebra

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:

1. **Problem Statement:** Solve the exponential equation and convert it into an algebraic expression. 2. **General Formula:** Exponential equations often have the form $a^{f(x)} =

1. **State the problem:** Solve the equation $$\frac{x^2 - 3x + 2}{x - 1} = 0$$ for $x$. 2. **Recall the rule:** A fraction equals zero if and only if its numerator is zero and the

1. **State the problem:** We are given the expression $$\frac{x^2 - c}{x - b}$$ where $b$ and $c$ are positive integers. It is stated that this expression is equivalent to $$x + b$

1. **State the problem:** Simplify the expression $$\frac{x^2}{x-3} - \frac{x+15}{2x-6}$$ and express it in the form $$ax + b$$ for all $$x \neq 3$$. Find the value of $$b$$. 2. **

1. **State the problem:** We need to find the value of $k$ such that $$(4\sqrt{10})(3\sqrt{10}) = 100^k.$$\n\n2. **Rewrite the expression:** Recall that $\sqrt{10} = 10^{1/2}$. So,

1. **State the problem:** We are given that the value of $k^{-5}$ is twice the value of $4k^{-2}$. We need to find the value of $k$. 2. **Write the equation:** According to the pro