🧮 algebra

1. **Problem statement:** We have a parabola $y=f(x)$ opening downwards passing through the origin and peaking near $(0.5,7)$. A point $P(-2,11)$ lies outside the parabola. We want

1. **State the problem:** Find the product of the radicals in the expression $3\sqrt{2}(5\sqrt{12} - \sqrt{18} + 4\sqrt{24})$. 2. **Recall the formula and rules:**

1. Problem. Solve the quadratic equation $2x^2 - 3x - 5 = 0$.

1. **State the problem:** Find the point $(a,b)$ on the line $2x - 3y + 6 = 0$ that is closest to the point $(3,1)$, then find $a+b$. 2. **Formula and concept:** The closest point

1. The problem asks to find the values of $b$, $c$, and $d$ in the cubic function $y = x^3 + bx^2 + cx + d$ given its graph, and to find the coordinates where the curve crosses the

1. **Stating the problem:** Simplify and evaluate the expression $$12 - (-3) \times \left\{ \frac{1}{4} \div \left[-\frac{1}{2}\right]^2 \right\}$$. 2. **Recall the order of operat

1. **Problema:** Determinare dominio, segno, limiti agli estremi del dominio e asintoti della funzione $$f(x) = \frac{1 - x^3}{4x^2 - 1}$$. 2. **Dominio:** Il denominatore non può

1. **State the problem:** We are given two functions: $$f(x) = \frac{3}{x^2}$$

1. **Problem statement:** Given $a=3.0$, $b=4.24$, and $c=3.654$, find the percentage error of the expression $$\frac{a+b}{c+a}$$. 2. **Formula and explanation:** Percentage error

1. **Problem:** Complete the table by finding the missing values for percentage profit or loss and cost prices. 2. **Formula:** Percentage profit or loss is calculated as $$\text{P

1. **State the problem:** Solve the simultaneous equations using the matrix method: $$2n + 3m = 12$$

1. **State the problem:** A truck contains 15 boxes, each either red or blue. Red boxes weigh 3 kg each, blue boxes weigh 2 kg each. The total weight is 36 kg. We need to find the

1. **Problem:** Simplify the expression $$\sqrt[4]{\sqrt{2}} \cdot \sqrt[3]{4} \cdot \sqrt[5]{32}$$. 2. **Rewrite each radical as an exponent:**

1. **Stating the problem:** Simplify the expression $$\frac{2}{3} \sqrt{18} + 2 \sqrt{27} - \sqrt{108} + 0.3 \sqrt{200}$$. 2. **Recall the rule:** Simplify square roots by factorin

1. **Problem statement:** Given two functions $f(x) = x^2$ and $g(x) = 2x + 1$, find the following combined functions: $(f+g)(x)$, $(f-g)(x)$, $(fg)(x)$, and $\frac{f}{g}(x)$. 2. *

1. Diberikan pertidaksamaan: $$2x^{2} + 5x + 15 \leq 3x^{2} + 5x - 1$$ 2. Langkah pertama adalah memindahkan semua suku ke satu sisi agar pertidaksamaan menjadi nol di sisi lain:

1. The problem asks to find the solution set of the inequality $$x^{2} - 5x - 14 < 0$$ where $$x \in \mathbb{R}$$. 2. To solve quadratic inequalities, we first find the roots of th

1. The user asked for Year 10 math questions. 2. Since the request is for questions and not a specific problem to solve, I will provide a sample Year 10 math question.

1. Masalah: Pak Musa memiliki kebun berbentuk persegi panjang dengan luas $1728\,m^2$ dan selisih panjang dan lebarnya adalah $12\,m$. Di sekeliling kebun dibuat jalan dengan lebar

1. The problem is to solve the equation or expression given by the user, but since no specific problem was provided, I will explain how to approach a general algebraic problem. 2.

1. The problem is to find the sum of the first 3 terms of an arithmetic progression (AP). 2. The formula for the sum of the first $n$ terms of an AP is: