🧮 algebra

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

1. The problem asks to find the intersection and union of given intervals using graphs. 2. Recall the definitions:

1. **State the problem:** Solve for $c$ in the equation $3c = 0$. 2. **Formula and rules:** To isolate $c$, divide both sides of the equation by 3. The rule is that dividing both s

1. **State the problem:** Arthur is seven times as old as his son Nelson. Three years ago, Arthur was sixteen times as old as Nelson. We need to find their present ages. 2. **Defin

1. **State the problem:** Rashid starts with 45 wristbands and gives 3 wristbands to each group of students. He needs to return for more wristbands when he has fewer than 9 left. W

1. **State the problem:** Solve the equation $$\left(\frac{1}{125}\right)^x - \left(25^{\frac{3}{4}}\right)^{-1} = 0$$ for $x$. 2. **Rewrite the equation:** We want to find $x$ suc