🧮 algebra

1. **State the problem:** We need to evaluate the square of the number 0.0033, which means calculating $$(0.0033)^2$$. 2. **Formula used:** The square of a number $x$ is given by $

1. **Stating the problem:** Calculate the value of $1.035^6$ and verify the approximation given as 1.23144, then use the correct value 1.233 to find the final amount RM 61650.

1. **Exercice 1 : Calculer les expressions données.** - Pour toute base $x \neq 0$, $x^0 = 1$.

1. **Problem Statement:** We have a line segment from point $(-8,1)$ to point $(8,-8)$ on the coordinate plane. We need to draw the "rise" and "run" segments and find the slope of

1. The problem involves understanding logarithmic properties and evaluating expressions with exponents. 2. The logarithmic identities given are:

1. **State the problem:** Simplify the expression $$\left(\log \sqrt{27} + \log 8 - \log \sqrt{512}\right) \log \left(\frac{12}{10}\right)$$. 2. **Recall logarithm properties:**

1. The problem is to understand and solve the equation given by the user, which is simply stated as "the equation bud". Since no specific equation is provided, let's clarify the pr

1. **Problem Statement:** A laptop was purchased for RM 3000. Its value decreases each year according to the formula $$3000 \times \left(\frac{9}{10}\right)^n$$ where $n$ is the nu

1. **State the problem:** We are given the function $$f(x) = \frac{\frac{1}{2}x + 1 + \ln x}{x}$$ and we want to simplify and understand it. 2. **Rewrite the function:** The functi

1. **State the problem:** Simplify the expression $$\log \sqrt{27} + \log 8 - \frac{\log \sqrt{512}}{\log \frac{12}{10}}$$. 2. **Recall logarithm properties:**

1. **Problem statement:** Find the remainder when the polynomial $x^3 + x^2 - 14x - 24$ is divided by $x + 3$, and then factorize the polynomial. 2. **Step 1: Use the Remainder The

1. **Problem statement:** We have the function $$f(x) = \frac{1}{2^x + \ln x}$$ defined on $$]0, +\infty[$$.

1. The problem is to solve the equation or expression given by the user. However, no specific equation or expression was provided. 2. To solve an algebraic equation, we typically i

1. **State the problem:** Simplify the expression $\log \sqrt{27} + \log 8 - \log \sqrt{512}$.\n\n2. **Recall logarithm properties:**\n- $\log a + \log b = \log (ab)$\n- $\log a -

1. **State the problem:** Simplify the expression $$\frac{\log(27) + \log(8) - \log(512)}{\log\left(\frac{12}{10}\right)}$$. 2. **Recall logarithm properties:**

1. **State the problem:** Simplify the expression $$\left( \frac{3}{5} + \frac{4}{7} + \frac{2}{7} \right) - \left( \frac{5}{6} - \frac{3}{6} \right) + 2$$. 2. **Combine like terms

1. Let's start by stating the problem: How to take the square root of a number or expression. 2. The square root of a number $x$ is a value $y$ such that $$y^2 = x$$.

1. The problem states that $ (a+b)^2 = 16 $. We need to find the possible values of $ a+b $.\n\n2. Recall the formula for squaring a binomial: $ (a+b)^2 = a^2 + 2ab + b^2 $. Here,

1. **State the problem:** We need to prove that $$\frac{1}{p} + \frac{1}{q} + \frac{1}{x} = \frac{1}{x+p+q}$$. 2. **Analyze the equation:** The left side is the sum of three fracti

1. The problem asks to find the values of the animals (crab, whale, turtle, octopus, fish) based on given equations. 2. For crab: Given equation is $\text{crab} + (225 + 45) = 626$

1. Let's solve each equation step-by-step. 2. For the dragon 🐉: Calculate $992 - (897 - 112)$. Use the rule of subtraction inside parentheses first.