🧮 algebra

1. Let's start by recalling the point-slope form of a line: $$y - y_1 = m(x - x_1)$$ where $(x_1,y_1)$ is a point on the line and $m$ is the slope. 2. The standard form of a line i

1. The problem asks us to find the standard form equation of the line passing through points $ (25,34) $ and $ (35,50) $.\n\n2. First, calculate the slope $ m $ of the line using t

1. Let's clarify your question: it seems you are asking about when to move numbers to the other side of an equation. 2. In algebra, to isolate a variable, we often move terms (incl

1. Given points are $(2, -5)$ and $(-1, 1)$ which lie on a line. We need to find the equation of this line in standard form. 2. First, calculate the slope $m$ using the formula $$m

1. Let's denote the three consecutive natural numbers as $n$, $n+1$, and $n+2$. 2. The problem states that their sum is 63, so we write the equation:

1. Consider the instruction to write math in full form, not in English. 2. Since no specific math problem is given, no equations or expressions to convert.

1. Stated problem: Simplify the expression $$2r\cdot\cos\left(\frac{a}{2}\right)\cdot \frac{\sin(a)}{\sin\left(\frac{a}{2}\right)\sin\left(\frac{3a}{2}\right)}.$$\n\n2. Use the dou

1. The problem is to simplify the expression $$\sqrt[4]{64m^{6}n^{12}}$$. 2. Start by expressing each part inside the fourth root separately: $$\sqrt[4]{64} \times \sqrt[4]{m^{6}}

1. **Stating the problem:** Solve the equation $x + 4 = 6$ for $x$. 2. **Isolating the variable:** To find $x$, subtract 4 from both sides of the equation.

1. The user requests content appropriate for class 6 level. 2. Since no specific math problem was provided, I'll provide a simple algebra problem example.

1. **State the problem:** Simplify the given expression \((a_-b)^{m+1}[8b^2(a_-b)^2]^2 + m4b^m[b(a_-b)^3]^{m+2}\). 2. **Rewrite the expression:**

1) Given the function $f(x) = 2x - 5$: 1. a) Find $f'(x)$, the derivative of $f(x)$.

1. The problem appears to be an empty set of brackets $\left[\;\right]$, which means there is no mathematical expression provided. 2. Since there is no expression or equation, ther

1. **State the problem:** Simplify the expression $$\frac{-9b^2 (a + 3b)^{m+2} (2b - 4c)^{2+m}}{4(3a + 9b)^{2m+2} (b^2 - 2cb)^{2-m}}$$

1. Let's analyze the sets and terms given: - Set A = odd numbers.

1. Stating the problem: Simplify arithmetic and algebraic expressions involving polynomials, variables, and fractions from exercises 29 to 40. 2. Exercise 29: Simplify $29\, 1\, \f

1. **State the problem:** Simplify the rational expression $$\dfrac{x^2 - 7x + 12}{x^2 - 6x + 9}$$ to its lowest terms and determine which values of $$x$$ must be excluded from its

1. State the problem: Simplify the expression $$-9b^2 (a+3b)^{m+2} (2b-4c)^2 + m / 4 (3a+9b)^{2m+2} (b^2 - 2cb)^{2 - m}$$. 2. Factor expressions where possible:

1. Problem: Identify the composite number. - Composite numbers have factors other than 1 and itself.

1. The average of $a,b,$ and $e$ is 16, so $$\frac{a+b+e}{3} = 16 \implies a+b+e = 48.$$ 2. The average of $c,d,$ and $e$ is 26, so $$\frac{c+d+e}{3} = 26 \implies c+d+e = 78.$$

1. **State the problem:** We have a studio apartment costing 64000, divided into labour, materials, and contractor's charges in ratio 12:15:5. 2. **Express individual costs:** Let