🧮 algebra

1. Diketahui m \neq 0 dan n \neq 0. Sederhanakan ekspresi $$\left(\frac{125^{-1} m^{-4} n^{-6}}{\frac{1}{5} mn^4}\right)^{-1}$$

1. The problem asks to analyze the sum notation $\sum u_n$ and the expression $S_n = u_2 + u_3 + \cdots + u_{n+2}$.\n\n2. The summation $\sum u_n$ typically means the sum of terms

1. **State the problem:** Write each given function in the standard quadratic form $ax^2 + bx + c$ and identify the values of $a$, $b$, and $c$. 2. **Recall the standard form:** A

1. **State the problem:** Solve the equation $Y(3+y)=0$ for $y$. 2. **Formula and rules:** The product of two factors equals zero if and only if at least one of the factors is zero

1. **State the problem:** Solve the equation $y(3 + y) = 0$. 2. **Use the zero product property:** If a product of two factors equals zero, then at least one of the factors must be

1. **Stating the problem:** We are given the equation $$\frac{2x+3}{x-1} = 4$$ and need to solve for $x$. 2. **Formula and rules:** To solve rational equations like this, multiply

1. The problem is to solve the sums provided, but since no specific sums are given, I cannot solve any particular problem. 2. Please provide the sums or equations you want to solve

1. The question asks: What is the easiest function to solve? 2. In mathematics, the easiest functions to solve are typically linear functions because they have the form $$y = mx +

1. The problem involves calculating the weighted total score from given marks and coefficients. 2. The formula for weighted total is $$\text{Total} = \sum (\text{mark} \times \text

1. The problem is to multiply the expressions $(2\sqrt{2} - \sqrt{5}) \cdot (\sqrt{2} + \sqrt{5})$ using the difference of squares formula. 2. Recall the difference of squares form

1. Represent the following as integers: 1. Rising 5 units means moving up 5 steps, so the integer is $+5$.

1. **State the problem:** Simplify the algebraic expression $54x^3 + 27x^3 - 10x - 4a$. 2. **Combine like terms:** The terms $54x^3$ and $27x^3$ are like terms because they both co

1. **State the problem:** Solve the inequality $4x + 4y \le 24$ for $y$ in terms of $x$. 2. **Rewrite the inequality:** We want to isolate $y$ on one side.

1. Problem: Factorise the following expression using the cross method: $d(d - 5) - 84$. 2. Expand to standard quadratic form.

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Formula and rules:** To simplify a rational expression, factor the numerator and denominator and the

1. Problem: Divide the polynomial $6x^5 - x^4 + 4x^3 - 5x^2 - x - 15$ by $2x^2 - x + 3$. 2. Formula and rules: Use polynomial long division: repeatedly divide the leading term of t

1. **State the problem:** Solve for $x$ in the equation $$(6 - \sqrt{35})^x + (6 + \sqrt{35})^x = 142.$$\n\n2. **Recognize the form:** Let $a = 6 - \sqrt{35}$ and $b = 6 + \sqrt{35

1. Problem: Simplify the expression $\frac{1}{y^2+3y+2} \div \frac{2}{y^2-4}$. 2. Formula and rule: To divide fractions use the rule $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cd

1. **State the problem:** Simplify the expression $$\frac{1}{y^{2} + 3y + 2} \div \frac{2}{y^{2} - 4}$$. 2. **Recall the division rule for fractions:** Dividing by a fraction is th

1. **State the problem:** Solve the system of equations using the substitution method: $$4x + y = 17 \quad (1)$$

1. **State the problem:** Solve the system of linear equations using the substitution method: $$4x + y = 17 \quad (1)$$