🧮 algebra

1. Stating the problem: Solve the equation $$-48 + 36 = -\frac{x}{0.04} - 80x$$. 2. Simplify the left side: $$-48 + 36 = -12$$.

1. **State the problem:** We are given the equation $$\frac{K+K}{K} = 6$$ and need to find the value of $K$. 2. **Write the formula and simplify:** The numerator $K+K$ can be combi

1. **State the problem:** We want to estimate the number of chickens on a farm after 15 years, given an initial population of 20,000 and an annual increase of 3.6% using simple int

1. **State the problem:** We want to find the height of an apple tree after 2 years, given it grows at an average compound rate of 1.6% per month and is currently 1 meter tall. 2.

1. **State the problem:** Solve the quadratic equation $$x^2-(k+1)x+4k-3=0$$ for $x$ in terms of the parameter $k$. 2. **Recall the quadratic formula:** For an equation $$ax^2+bx+c

1. **State the problem:** A bucket initially contains 25 litres of water. It loses 12% of its water every minute due to a leak. We need to find the amount of water left after 10 mi

1. **Problem statement:** The population of Town X is currently 56,000 and is expected to increase by 5% per annum with simple interest. We need to find the population after 3 year

1. **State the problem:** Solve the quadratic equation $$(k+2)x^2 - 2kx + k - 1 = 0$$ for $x$. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solut

1. The first expression is $-1^{ro}$. Assuming $ro$ is a variable or exponent, the expression means the negative of $1$ raised to the power $ro$. Since $1$ raised to any power is $

Let's clear that up! 🎉 **Step 1:** We said Group 1 is $(x - 4)$, so it has 4 toys: <span style='font-size: 2em;'>🧸 🧸 🧸 🧸</span> (4 toys)

Let's factor $x^2 - 16$ step by step! 🎉 **Step 1:** Notice that $x^2 - 16$ is a difference of squares because $16 = 4^2$.

Let's solve step by step! 🎉 1. First, find $g(3)$.

1. **Problem statement:** Determine all the sub-lattices of $D_{30} = \{1,2,3,5,6,10,15,30\}$ that contain at least four elements. 2. **Background:** $D_{30}$ is the set of divisor

1. **State the problem:** We need to find the value of $f(-2 - g(3))$ given the functions $f(x) = \frac{3}{4}x + 10$ and $g(x) = x^2 - 3$. 2. **Calculate $g(3)$:** Substitute $x=3$

1. **State the problem:** Solve the inequality $$(x - 2)(x - 4)(x - 1) < 0$$ 2. **Identify the roots:** The expression equals zero at $x=1$, $x=2$, and $x=4$. These points divide t

1. **Problem Statement:** Find the number of pairs of letters in the word "STREAMING" that have the same number of letters between them as in the English alphabetical series, consi

1. Let's try another example with two machines again! 🎉 **Box 1:**

1. Imagine you have two machines: one called $g$ and one called $f$. Each machine changes a number. 2. First, you put a number into machine $g$, and it gives you a new number.

1. Let's start by defining the terms. 2. The **domain** of a function is the set of all possible input values (usually $x$ values) for which the function is defined.

1. Diberikan persamaan $\log(x^2 - 5x + 6) = \log 4$. Kita diminta mencari himpunan penyelesaian $x$. 2. Aturan penting: Jika $\log a = \log b$, maka $a = b$, dengan syarat $a > 0$

Masalah: Tentukan himpunan penyelesaian dari $\log(x^2 - 5x + 6) = \log 4$. 1. Aturan: Jika $\log A = \log B$ dan kedua argumen positif, maka $A = B$.