🧮 algebra

1. The problem is to convert a decimal or number into a fraction. 2. To convert a decimal to a fraction, write the decimal number as the numerator (top number) and use a power of 1

1. **State the problem:** We are given that quantities $x$ and $y$ are proportional, and we have pairs of values: $(9, 4.5)$, $(14, 7)$, and $(30, 15)$. We need to find the constan

1. **Stating the problem:** Solve the equation $$\frac{x-5}{3} = \frac{x-3}{3} + \frac{6x+1}{21}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, find a comm

1. **Problem statement:** Solve the equation $$\frac{x-5}{3} - \frac{x-3}{3} = \frac{6x+1}{21}$$. 2. **Formula and rules:** To solve equations with fractions, first find a common d

1. **Problem statement:** We have several sequences $(u_n)$ defined by different formulas and recurrence relations. We need to analyze their properties such as bounds, monotonicity

1. The problem is to solve the equation $8^z = -7$ for $z$. 2. Recall that for any real number base $a > 0$ and $a \neq 1$, the exponential function $a^x$ is always positive. This

1. **State the problem:** Convert and calculate various time-related quantities. 2. **Find the number in 4 1/2 hours:**

1. The problem is to evaluate the expression $-5 + 8$. 2. The operation involved is addition of integers.

1. **Problem Statement:** Determine all intervals where the function $f(x) \leq 0$ based on the given graph description. 2. **Understanding the problem:** The function $f(x)$ is le

1. **State the problem:** We have a shape ABCDEF made from two rectangles with given side lengths in terms of $x$. The total area is 342 cm$^2$. We need to show that $x^2 + x - 72

1. The problem asks us to determine if the equation $4x + 2y - 10 = 0$ represents a straight line and explain why. 2. The general form of a linear equation in two variables $x$ and

1. **Problem statement:** Find the equation of the straight line passing through the points $(1,4)$ and $(-2,-2)$ in the form $y = mx + c$. 2. **Formula used:** The slope $m$ of a

1. Problem: Find the value of the function $f(x) = 2x^2 - 3x + 1$ at $x=3$. 2. Formula: To find the value of a function at a specific point, substitute the value of $x$ into the fu

1. **State the problem:** Rewrite the equation $$\frac{1}{2}x - \frac{3}{4}y = \frac{5}{6}$$ in the form $$y = mx + c$$ and find the gradient $$m$$. 2. **Formula and rules:** The s

1. **State the problem:** Find the value of the limit $$\lim_{x \to +\infty} \frac{2^{-x}}{2^x}$$. 2. **Recall the properties of exponents:**

1. **State the problem:** We are given two functions:

1. **State the problem:** We want to find the number of days $t$ it takes for the video views $y$ to reach 2500, given the exponential growth function $$y = 80e^{0.2t}.$$ 2. **Writ

1. **Problem Statement:** Find the roots of the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula Used:** The roots of a quadratic equation $$ax^2 + bx + c = 0$$ are given by t

1. Masalah ini menanyakan berapa banyak titik potong grafik fungsi dengan sumbu x. 2. Titik potong pada sumbu x terjadi ketika nilai fungsi sama dengan nol, yaitu $y=0$.

1. The problem involves analyzing three quadratic functions: $$f(x) = -3x^{2} + 4x + 1$$

1. **State the problem:** We are given the number of boys in a school as 120 and the ratio of boys to girls as 5:7. We need to find the total number of students in the school. 2. *