🧮 algebra

1. We are asked to solve the equation $$\frac{x - 3}{5} + \frac{3x + 1}{10} = 0$$. 2. To solve this, we first find a common denominator for the fractions, which is 10.

1. সমস্যাটি হলো একটি আয়তাকার বাগানের দৈর্ঘ্য প্রস্থের থেকে ৫ মিটার কম এবং বাগানের পরিসীমা ৩০ মিটার। 2. আমরা দৈর্ঘ্যকে $x$ মিটার এবং প্রস্থকে $y$ মিটার ধরে নিচ্ছি।

1. **State the problem:** Solve the system of equations using Gaussian elimination method: $$\begin{cases} 2x - 3y + 5z = 2 \\ x + 4y - 2z = 1 \\ 4x + 5y + z = 4 \end{cases}$$

1. **State the problem:** You have a total project cost of $2050$ for hardware and $350$ for Proteus software.

1. **Problem:** Given the polynomial function $p(x) = (3x+2)(1-5x)(1-x^2)$, determine which statement about $p(x)$ is correct. 2. **Step 1: Find the constant term of $p(x)$.**

1. **State the problem:** Simplify the expression $12a^2b + 18ab^2 - 30ab$. 2. **Identify the common factors:** Each term contains the variables $a$ and $b$, and the coefficients 1

1. **Stating the problem:** Calculate the value of $$\sqrt{5(3 + \sqrt{3})} + \sqrt{28 + 6\sqrt{3}}$$. 2. **Formula and rules:** We will simplify each square root expression by try

1. **Problem:** Resolve the fraction $$\frac{3x - 2}{2x^2 - x}$$ into partial fractions. 2. **Step 1: Factor the denominator.**

1. **State the problem:** Simplify or solve the expression $$\frac{\sqrt{3}x + 2 + \sqrt{x}}{\sqrt{3}x + 2 - \sqrt{x}}$$. 2. **Identify the structure:** This is a fraction with a n

1. The problem is to simplify the expression $3\sqrt{282}$. 2. Recall that the square root of a product can be written as the product of the square roots:

1. **State the problem:** Simplify the expression $\frac{2x}{6x}$. 2. **Recall the rule:** When dividing fractions or terms with the same variable, you can divide the coefficients

1. **Stating the problem:** We have two functions $f(x) = x^2$ and $g(x) = 2x + 1$. We need to find the following combined functions: $(f+g)(x)$, $(f-g)(x)$, $(fg)(x)$, and $\frac{

1. **State the problem:** Factorise the quadratic expression $6x^2 + 7x - 20$. 2. **Recall the formula and method:** To factorise a quadratic $ax^2 + bx + c$, we look for two numbe

1. **State the problem:** Factorise the expression $$4b^4 + 6b^3 + 2b^2$$. 2. **Identify common factors:** Each term contains a factor of $$b^2$$, so we can factor that out first.

1. **State the problem:** Factorise the expression $$4b^4 + 6b^3 + 2b^2$$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in all terms. Each term contain

1. **State the problem:** Factorise the expression $$4b^4 + 6b^3 + 2b^2$$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in all terms. Each term contain

1. **State the problem:** Expand and simplify the expression $$(x^2+6)(x^2+5)$$. 2. **Formula used:** To expand two binomials, use the distributive property (FOIL method for binomi

1. **State the problem:** Simplify the expression $-3(x + y) + 5(x - y)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. The problem asks to find the function $g(x,y,z)$ given that $g(x,y,2) = |x + 2z + \sqrt{1 - 2y}|$. 2. Notice that the function is given with the third variable fixed as 2, so we

1. The problem asks for the additive inverse of $-\frac{3}{7}$. 2. The additive inverse of a number $x$ is the number that, when added to $x$, results in zero. Mathematically, if $

1. The problem asks for the additive inverse of $-\frac{3}{7}$. 2. The additive inverse of a number $x$ is the number that, when added to $x$, results in zero. Mathematically, if $