🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{2^2 \times 2^{\frac{1}{2}}}{2^{-3}}$$. 2. **Recall the exponent rules:**

1. The problem is to simplify the fraction $\frac{30}{6}$. 2. The formula for simplifying a fraction $\frac{a}{b}$ is to divide both numerator and denominator by their greatest com

1. The problem is to express the number 2.74 x 10^{-5} in decimal form. 2. The number is given in scientific notation, which is a way to express very large or very small numbers.

1. The problem is to find the least common multiple (LCM) of given numbers. 2. The LCM of two or more integers is the smallest positive integer that is divisible by each of the num

1. **State the problem:** Solve the expression $$xy(k^2+1) + k(x^2 + y^2)$$ for simplification or factoring. 2. **Identify the formula and rules:** We want to simplify or factor th

1. The problem asks to find the ratio in its simplest form. 2. A ratio compares two quantities and is simplified by dividing both terms by their greatest common divisor (GCD).

1. The problem involves understanding ratios and proportions. 2. We are given a ratio of 7:4 and quantities 44 litres and 8 litres.

1. The problem asks us to find the inverse function $g^{-1}(x)$ of the given function $g(x) = \frac{x - 10}{8}$.\n\n2. To find the inverse, we start by replacing $g(x)$ with $y$: $

1. **State the problem:** We are given the function $f(x) = \frac{x}{7} + 5$ and asked to find the inverse function $f^{-1}(x)$. 2. **Recall the formula and rules:** To find the in

1. **State the problem:** Find the inverse function $f^{-1}(x)$ of the function $f(x) = \frac{x}{7} + 5$ and expand any brackets in the answer. 2. **Recall the formula and rules:**

1. **State the problem:** Divide $\left(1\frac{1}{2} + \frac{1}{4}\right)$ by $\left(1\frac{1}{2} - \frac{1}{4}\right)$. 2. **Convert mixed numbers to improper fractions:**

1. **Problem statement:** Forecast the future sales for the years 2016, 2017, and 2018 given that sales in 2015 were 345000 and sales increase by 10% per annum.

1. **State the problem:** A car travels 11 kph faster than a bus. The car covers 152 km in the same time the bus covers 110 km. We need to find the speed of each vehicle. 2. **Defi

1. The problem is to simplify the expression $\log 10 - \log 5$. 2. We use the logarithm subtraction rule: $\log a - \log b = \log \left( \frac{a}{b} \right)$. This rule states tha

1. **State the problem:** Simplify the expression $\frac{6x}{12}$. 2. **Formula and rules:** To simplify a fraction, divide the numerator and denominator by their greatest common d

1. Masalah: Tentukan bayangan fungsi linear $k \equiv 5x - y + 2 = 0$ setelah didilatasi horizontal dengan skala 4 dan dilanjutkan dengan refleksi terhadap garis tegak $x=3$. 2. Fu

1. Masalah: Diberikan fungsi kuadrat $y = f(x) = x^2$ dan dilakukan translasi oleh vektor $T = (0, -b)$. Tentukan persamaan kurva hasil translasi. 2. Formula translasi: Jika sebuah

1. समस्या: 9 और 10 बजे के बीच घड़ी की घंटे और मिनट की सुइयाँ कब एक दूसरे से समकोण (90°) बनाएंगी, यह ज्ञात करें। 2. सूत्र और नियम:

1. The problem is to draw the number line for the set $\mathbb{Q}_1$, which typically refers to the set of rational numbers with a certain property or subset. 2. Since the user did

1. **Problem (a):** Given that $231_x - 143_x = 44_x$, find the value of $x$. 2. **Understanding the problem:** The numbers are in base $x$. We need to convert each number from bas

1. **State the problem:** Solve the quadratic equation $$x^2 + x - 12 = 0$$ for $x$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solu