🧮 algebra

1. The expression $iv + 7u$ represents a linear combination of two variables $i$ and $u$, where $v$ and $7$ are coefficients multiplying $i$ and $u$ respectively. 2. The expression

1. The problem is to define the tensor product of modules. 2. The tensor product of modules is a construction in abstract algebra that combines two modules over a commutative ring

1. Let's clarify the problem: You asked if $x.y$ gives the length of $x+y$. 2. Typically, $x.y$ denotes the product of $x$ and $y$, while $x+y$ denotes their sum.

1. **State the problem:** Solve the equation $$3^x - 2^{2+4} = 10$$ for $x$. 2. **Rewrite the equation:** The term $2^{2+4}$ can be simplified using the exponent addition rule $a^{

1. **State the problem:** Solve the equation $3^x - 2^{4} + 2 = 10$ for $x$. 2. **Recall the formula and rules:** We need to isolate the term with the variable $x$, which is $3^x$.

1. Diberikan dua persamaan kuadrat: Persamaan 1: $x^2 + 5x + a = 0$

1. **State the problem:** Solve the equation $3^x - 2^4 + 2 = 10$ for $x$. 2. **Recall the formula and rules:** We will isolate the exponential term $3^x$ and then solve for $x$ us

1. **State the problem:** Solve the equation $$3^{2x} - 30(3^x) + 81 = 0$$ for $x$. 2. **Rewrite the equation:** Notice that $3^{2x} = (3^x)^2$. Let $y = 3^x$. Then the equation be

1. **State the problem:** Solve the inequality $g - 5 \leq 10g - 6$ for $g$. 2. **Write the inequality:**

1. **Find the slope of the line through (2, 3) and (5, 9).** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$

1. **State the problem:** Find the slope of the line passing through the points $(2,3)$ and $(5,9)$. 2. **Formula for slope:** The slope $m$ of a line through two points $(x_1,y_1)

1. **State the problem:** Solve the equation $2^{2x} - 9(2^{2x}) + 20 = 0$ for $x$. 2. **Rewrite the equation:** Let $y = 2^{2x}$. The equation becomes $y - 9y + 20 = 0$.

1. Let's start by understanding the problem: You asked for a detailed answer, but no specific math problem was provided. 2. Since no specific problem is given, I will explain how t

1. Factorise the following expressions: **i)** $2b(3a - c) + 12ac - b^2$

1. Let's clarify what "is it really equal?" means by considering an example or expression you want to verify. 2. To check equality between two expressions, we use algebraic manipul

1. **State the problem:** We are given the linear equation $$y = \frac{2}{5}x + 2$$ and need to understand its graph and key features. 2. **Formula and rules:** This is a linear fu

1. The problem is to understand and analyze the four given linear equations in point-slope form: $$y - 18 = -\frac{5}{6}(x - 5)$$

1. The problem is to solve the equation $$y - 18 = -\frac{5}{6}(x - 5)$$ correctly. 2. This is a linear equation in point-slope form: $$y - y_1 = m(x - x_1)$$ where $m$ is the slop

1. Solve for $x$: $$2x + 3 = 7$$ 2. Find the roots of the quadratic equation: $$x^2 - 5x + 6 = 0$$

1. The problem asks to identify the correct point-slope form equation representing the combination of homeroom groups: 18 groups of 10 students and 5 groups of 12 students. 2. Reca

1. **State the problem:** Find the slope $m$ of the line passing through points $(-2,5)$ and $(0,2)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1,y_1)$ and $(x