🧮 algebra

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:

1. **State the problem:** Rationalise the denominator of $$\frac{15 + \sqrt{5}}{6\sqrt{5}}$$ and simplify the expression. 2. **Formula and rule:** To rationalise a denominator cont

1. **State the problem:** We need to find the number of rhinos at the safari park given relationships between the numbers of rhinos, chimps, and alpacas. 2. **Define variables:** L

1. **State the problem:** We are given the formula $$h\frac{a+b}{2}$$ and need to find a formula for $a$ in terms of $h$, $b$, and the expression. 2. **Rewrite the expression:** Th

1. The problem is to find the formula for a given variable $a$. 2. To find a formula for $a$, we need more context or an equation involving $a$.

1. The problem is to simplify and understand the expression $h \frac{a+b}{2}$ and the term "einangra a" which seems unclear but we focus on the algebraic expression. 2. The express

1. **State the problem:** Solve the equation $a+b+2ab=8$ for the expression $a+b$. 2. **Analyze the equation:** The equation is $a+b+2ab=8$. We want to find $a+b$ in terms of known

1. The problem is to solve the equation $5(3^{1-x}) = x$ for $x$. 2. We start by rewriting the equation:

1. **State the problem:** Express the equation $2^x + 7 = 57$ in logarithmic form. 2. **Rewrite the equation:** Subtract 7 from both sides to isolate the exponential term:

1. **Énoncé du problème :** Déterminer des bases et les dimensions des sous-espaces vectoriels $E_1$, $E_2$, et $E_1 \cap E_2$ dans $\mathbb{R}^3$ où: