🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n}$$ and evaluate it for $$n = 10$$. 2. **Write the expression clearly:** The numerator is $$n \times n +

1. সমীকরণটি হলো $3x^2 + 8x + 2 = 0$ এবং এর মূলদ্বয় $alpha$ এবং $beta$। 2. বীজগণিতের সূত্র অনুযায়ী, একটি দ্বিঘাত সমীকরণের মূলদ্বয়ের যোগফল এবং গুণফল হলো:

1. সমস্যাটি হলো: কতি, শ্রেয়া এবং মিতা মোট ৬০০০ টাকা দিয়ে ব্যবসা শুরু করেছে। লাভাংশের মধ্যে কতি ৫০ টাকা, শ্রেয়া ১০০ টাকা এবং মিতা ১৫০ টাকা পায়। মিতার ব্যবসায়ের অংশ কত টাকা হতে

1. Problem: Graph the circle given by the equation $x^2 + y^2 = 27$ and find its radius. Step 1: Recall the standard form of a circle centered at the origin is $x^2 + y^2 = r^2$, w

1. Problem: Graph the circle given by the equation $x^2 + y^2 = 27$ and find its radius. Step 1: Recall the standard form of a circle centered at the origin is $x^2 + y^2 = r^2$, w

1. **Problem:** Graph the circle given by the equation $x^2 + y^2 = 27$ and find its radius. 2. **Formula:** The general equation of a circle centered at the origin is $x^2 + y^2 =

1. **Problem Statement:** Find the equation of a circle whose center is at the origin. 2. **Formula:** The general equation of a circle with center at $(h,k)$ and radius $r$ is:

1. The problem is to determine the type of conic section represented by a given equation. 2. Conic sections are curves obtained by intersecting a plane with a double-napped cone. T

1. **State the problem:** We need to analyze and rewrite the equation $$9x^2 + 9y^2 - 6x + 18y + 11 = 0$$ to identify its geometric shape and properties. 2. **Rewrite the equation:

1. **State the problem:** We are given the quadratic equation $$4x^2 + 6xy + 2y^2 - 4x - 2y + 43 = 0$$ and we want to analyze or simplify it. 2. **Identify the type of equation:**

1. **State the problem:** We are given the equation of a circle: $$x^2 + y^2 + 6x - 2y + 9 = 0$$ and we want to find its center and radius. 2. **Formula and rules:** The general fo

1. **State the problem:** We are given the function $f(x) = 1.5x + 4$ and another function $g(x) = f(x) + k$. We need to find the value of $k$ that transforms the graph of $f$ into

1. Simplify $x^{4/3} \cdot x^{2/3}$. Using the rule $a^m \cdot a^n = a^{m+n}$, add the exponents:

1. Masalah: Selesaikan persamaan kuadrat $x^2 - 5x + 6 = 0$. 2. Rumus yang digunakan adalah rumus kuadrat: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ di mana $a$, $b$, dan $c$ adal

1. **State the problem:** Given the variables $a = -3$, $q = 5$, and $t = 6$, we need to solve an algebraic expression involving these values. 2. **Identify the expression:** Since

1. **Problem Statement:** Find the equation of a line parallel to the line given by $$y = -3x + 4$$ and containing the point $$(3, -1)$$. 2. **Recall the formula for the slope-inte

1. The problem is to simplify the expression $17 - 4x^3 + 7x^2$. 2. This is a polynomial expression with terms involving powers of $x$ and constants.

1. The problem is to solve the equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic formula or factorization to solve quadratic equations. The quadratic formula is $$x = \frac{-b \

1. The problem asks us to compare the distance from sea level of the fish and the toad using their elevations on the number line. 2. The elevations given are:

1. The problem asks for the squirrel's vertical distance from sea level. 2. Elevation is given in feet relative to sea level, which is at 0 feet.

1. **Problem Statement:** We are given the elevations of four animals by a lake and need to interpret their positions on a vertical number line. 2. **Given Data:**