🧮 algebra

1. The problem gives us pairs of numbers that combine into a result. We need to find how the two numbers combine to produce the number in the box. 2. For the top-left graph: two nu

1. Stating the problems: - Problem 1: Solve the equation $$\frac{1}{x} + \frac{1}{x+1} = \frac{1}{x(x+1)}$$.

1. **State the problem:** Calculate the annual salary at the end of the 3rd year given a starting salary and raises every 6 months. 2. **Step 1:** Identify the starting salary: Bir

1. **Problem Statement:** Convert the recurring decimals to fractions. 2. **Part (a):** Convert $0.\overline{4}$ to a fraction.

1. Le problème demande de résoudre un système d'équations linéaires dans \(\mathbb{R}\) en utilisant la méthode de Cramer. 2. Supposons un système 2x2 donné par:

1. The first expression is $\frac{6^{14}}{6}$. 2. Using the property of exponents $\frac{a^m}{a^n} = a^{m-n}$, simplify:

1. The problem asks which expressions are equivalent to $$\frac{12^6}{3^6}$$. 2. We can start by simplifying the expression using properties of exponents:

1. **State the problem:** We want to find which expressions are equivalent to $$\frac{10^3}{5^3}$$. 2. **Simplify the original expression:**

1. **Stating the problem:** We are given several equations and need to analyze and solve each one. 2. **Problem a)** Equation: $x^2 - 4x + y^2 - 8y = 0$

1. We are asked to expand and understand the expression $(3x - y^2)^6$. 2. This is a binomial raised to the sixth power, which can be expanded using the Binomial Theorem.

1. The problem is to expand the expression $$(2x - 5)^5$$ using the Binomial Theorem. 2. Recall the Binomial Theorem: $$(a - b)^n = \sum_{k=0}^n \binom{n}{k} a^{n-k} (-b)^k$$. Here

1. Problem: For $f(x) = \frac{(1+2x)^2}{(1-x)^2}$, find (i) the first 4 terms in its power series expansion, and (ii) state when the expansion is valid. (i) First, rewrite the func

1. First, understand the problem: Calculate $\sqrt{7164} \times 0.082$ without using logarithms, using a tabular method. 2. Estimate $\sqrt{7164}$. Since $85^2 = 7225$ and $84^2 =

1. **State the problem:** We need to find the value of $\sqrt{0.7164 \times 0.082}$ using logarithms. 2. **Calculate the product inside the square root:**

1. The problem is to find the value of $\sqrt{0.7164 \times 0.082}$ using logarithms. 2. First, calculate the product inside the square root:

1. نبدأ بملاحظة المسألة: نحتاج لإثبات أن التعبير $$2 - \sqrt{27} + (12a^1 b^3)^{-1} \times (\sqrt{3} ab)^3 / (4^{-1}) a \times (2025)^0 = 2 - 2 \sqrt{3}$$

1. **State the problem:** We have two shops offering discounts on the same phone. We need to find which shop has the lower offer price and the difference in prices. 2. **Calculate

1. Stating the problem: We have a total hire cost of 600, which is shared among 90 students, with 10% of the total cost intended perhaps as a discount or additional fee. We want to

1. The problem is to understand and interpret the inequality $X \geq 0$. 2. This inequality states that the variable $X$ is greater than or equal to zero.

1. Start by stating the problem: Expand and simplify the expression $ (2x - 3)(3x + 5) $. 2. Use the distributive property (FOIL) to expand the product:

1. Við skulum byrja á að segja að þú ert að vísa til punktanna sem hafa ekki sama $x$-gildi eða sama $y$-gildi. Þetta þýðir að punktarnir eru ekki þar sem línurnar skerast eða fall