🧮 algebra

1. **Problem statement:** Find the domain and range of the given relations. 2. **Part (a): Relation with points (-3, 2.8) and (1.3, -2.1) and a wavy curve passing through (-5,0), (

1. The problem asks for the capacity of one bottle. 2. To find the capacity of one bottle, we need the total capacity and the number of bottles.

1. Simplify each of the following expressions: (a) Simplify $\frac{4x^4}{12x^5}$:

1. **State the problem:** Solve the quadratic equation $$x^2 + x - 2 = 0$$. 2. **Identify coefficients:** Here, $$a = 1$$, $$b = 1$$, and $$c = -2$$.

1. **State the problem:** Simplify the expression $$\frac{3}{2} + \frac{4}{5} - \frac{2}{3} \times \frac{3}{4} + \frac{5}{6} \div \frac{5}{2} - \frac{1}{2} + \frac{3}{6} \times \fr

1. **Problem (a):** Find the rates for a quarter for a house with an assessed annual value of 65000 and an annual rates percentage of 8%. Step 1: Calculate the annual rates.

1. **State the problem:** Factorise the polynomial expression $$3x^4 - 48$$ fully. 2. **Factor out the greatest common factor (GCF):**

1. The problem asks to find how many games City FC lost using the data from the table. 2. From the table, the total games lost by all teams combined is 35.

1. **Problem statement:** We have a group of people who participated to get a vehicle licence.

1. **State the problem:** Rohan ordered 5 kg of premium coffee and some quantity $x$ kg of ordinary coffee. The price per kg of premium coffee is three times the price per kg of or

1. **State the problem:** Rohan ordered 5 kg of premium coffee and some ordinary coffee. The price per kg of premium coffee is three times that of ordinary coffee. When the quantit

1. **State the problem:** Rohan ordered 5 kg of premium coffee and some quantity $x$ kg of ordinary coffee. The price per kg of premium coffee is three times the price per kg of or

1. **Problem statement:** Given an arithmetic progression (AP) with first term $a_1=5$ and 25th term $a_{25}=25$, find: (i) the common difference $d$,

1. Problem statement: Rohan ordered 5 kg of premium coffee and some additional kilograms of ordinary coffee. The price per kg of premium coffee is three times that of ordinary coff

1. The problem gives parametric equations: $$y = t^6 - 5$$ and $$x = 4^3 - 1$$. 2. First, simplify the expression for $$x$$ since it does not depend on $$t$$: $$4^3 = 64$$, so $$x

1. نبدأ بكتابة التعبير الرياضي المعطى: $$77^{10} \times 26^{8} \times 52 \div (20^{9} \times 91^{8} \times 7) - 40$$

1. **Problem statement:** A drum contains chemicals P, Q, and R in the ratio 3:5:2. After removing 30 litres of the blend, 12 litres of P and 8 litres of Q are added. The final qua

1. **Problem statement:** A drum contains chemicals P, Q, and R in the ratio 3:5:2. Let the initial total quantity be $x$ litres. 2. The quantities of P, Q, and R initially are:

1. The problem asks to expand the logarithm $\log_2 5x$. 2. Recall the logarithm product rule: $\log_b (MN) = \log_b M + \log_b N$.

1. **State the problem:** We need to calculate $$\frac{2.37 \times 10^{8}}{6.83 \times 10^{-3}}$$ and express the answer in standard form to 3 significant figures. 2. **Rewrite the

1. **State the problem:** We need to calculate $$\frac{7.45 \times 10^{-12}}{2.12 \times 10^{-5}}$$ and express the answer in standard form to 3 significant figures. 2. **Divide th