🧮 algebra

1. **State the problem:** Solve the system of equations: $$\frac{x+1}{3} - \frac{y-1}{2} = 1$$

1. Diberikan soal: Hitung nilai dari $\log_3 9 + \log_3 8 - \log_3 12$. 2. Kita gunakan sifat logaritma: $\log_b m + \log_b n = \log_b (mn)$ dan $\log_b m - \log_b n = \log_b \left

1. **State the problem:** Calculate the value of the expression $344 + 56(153 - 95)$.\n\n2. **Apply the order of operations:** According to the order of operations (PEMDAS/BODMAS),

1. **State the problem:** Ludek has two payment options for 8 days of work. Option 1 pays a fixed $40 per day. Option 2 pays doubling amounts starting at $2 on day 1, $4 on day 2,

1. **State the problem:** Calculate the value of the expression $$(1239+601)(1521-1481)$$. 2. **Apply the order of operations:** First, solve the expressions inside the parentheses

1. **State the problem:** Solve the system of inequalities: $$|3x - 2| < 7$$

1. **State the problem:** Find the expression for the perimeter of a square table whose area is given by $$9x^4 - 24x^2 + 16$$.

1. **State the problem:** A couple is arranging flowers for a wedding. The bride finishes one arrangement in $x$ minutes, and the groom finishes his arrangement 8 minutes later, i.

1. **State the problem:** A bride and groom are arranging flowers. The bride finishes one arrangement in $x$ minutes, and the groom finishes one arrangement 8 minutes later, i.e.,

1. Find the domain and range of $f(x) = 1 + x^2$. - Domain: Since $x^2$ is defined for all real $x$, domain is all real numbers: $(-\infty, \infty)$.

1. Énoncé du problème : Réduire les expressions algébriques données en combinant les termes semblables. 2. Rappel de la règle : Pour réduire une expression algébrique, on additionn

1. **State the problem:** We are given the function $f(x) = 5 - 2x$ and want to understand its properties. 2. **Formula and rules:** This is a linear function of the form $f(x) = m

1. **State the problem:** Fully factorise the quadratic expression $2x^2 + 13x + 15$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers

1. The user requested graphs of functions but did not specify which functions to graph. 2. To provide graphs, please specify the functions you want to see plotted.

1. **Problem Statement:** Find the natural domain and analyze the functions given in exercises 15 to 20. 2. **Function 15: $f(x) = 5 - 2x$**

1. **State the problem:** Fully factorise the quadratic expression $$3t^2 + 16t + 5$$. 2. **Recall the factoring method:** For a quadratic $$at^2 + bt + c$$, we look for two number

1. **Problem 15: Find the natural domain and graph of** $f(x) = 5 - 2x$. - This is a linear function.

1. **State the problem:** Solve the equation $$|x| = x^2 + x - 3$$. 2. **Recall the definition of absolute value:**

1. **State the problem:** Solve the equation $$\sqrt{7} \cdot \frac{\log n}{\log 2} - \frac{\log 2n}{\log 2} = 1$$ for $n$. 2. **Recall logarithm properties:**

1. **Problem statement:** The mass of a radioactive substance decreases exponentially at a rate of 3% each day. We need to find the overall percentage decrease after 10 days. 2. **

1. Let's start by understanding what percentage increase and decrease mean. 2. Percentage increase is used when a value goes up. The formula is: