📘 algebra, geometry

1. **Problem 1:** Find the equation of the line through $P = (2, 2)$ parallel to the line $y = 3x$. 2. The slope of the given line $y = 3x$ is $3$.

1. Problem 38: Identify which expressions describe the pattern 8, 12, 16, 20, ... 2. The pattern increases by 4 each time, starting at 8.

1. **Problem Statement:** Solve the algebraic expressions given for the odd-numbered problems (29, 31, 33, 35, 37, 39, 41, 43, 45, 47). 2. **Problem 29:** Simplify and analyze the

1. **State the problem:** We need to write and solve an equation to find $b$, the number of bags each club needs to sell so that the amount raised is the same for both clubs.

1. **Statement of the problem:** Create a similar question for each of the three given images involving algebraic expressions, area calculation, and perimeter calculation.

1. **Problem Statement:** (a) Calculate the total amount to be returned on a loan of 48.52 million at 0.5% simple interest per month after 1.5 years.

1. Evaluate: $\frac{6}{11} \div \left(-\frac{3}{5}\right)$. Use the rule: dividing by a fraction is the same as multiplying by its reciprocal.

1. Problem: Find the results for each set and algebra question. (a) $Q \cup Q = Q$ because the union of a set with itself is the set.

1. **Problem:** Calculate the area of a rectangle with dimensions $(4 + \sqrt{3})$ cm and $(4 - \sqrt{3})$ cm. 2. **Formula:** Area of a rectangle = length $\times$ width.

1. **Problem 1: Prove that $3 - 2\sqrt{5}$ is irrational given $\sqrt{5}$ is irrational.** 2. We start by assuming the contrary: suppose $3 - 2\sqrt{5}$ is rational.

1. **Stating the problem:** Solve the equation $8x + 75 = 180$ for $x$. 2. **Isolate the variable term:** Subtract 75 from both sides:

1. **State the problem:** We need to evaluate $\log_9 0.48$ given $\log_2 2 = 0.3010$, $\log_3 3 = 0.4771$, and $\log_5 5 = 0.6990$. Also, we have a right triangle with sides 3 cm

1. **Problem 1:** Three identical machines take 6 hours to empty a reservoir together. We need to find how long it takes for one machine to empty it alone. 2. The rate of work for

1. Solve the simultaneous equations: Given the system:

1. Solve the simultaneous equations: $$\begin{cases} 2x + 3y = 12 \\ x - y = 3 \end{cases}$$ 2. Simplify the algebraic fraction: $$\frac{3x^2 - 12}{6x}$$

1. **State the problem:** (a) Write down the inequality shown on the graph.

1. **State the problem:** a. Write down the inequality shown on the number line with an open circle at -3 and a closed circle at 2 connected by a solid line.

1. முதலில், முதல் கேள்வியைப் புரிந்து கொள்வோம்: மின்சார மோட்டார் சைக்கிளின் பெறுமதி 360000 ஆகும். 2. அதன் 2/3 பகுதியை முதலில் செலுத்த வேண்டும். அதாவது:

1. **Calculer les expressions données :** - $A = \sqrt{2} + \sqrt{49} = \sqrt{2} + 7$

1. **Problem 1:** Find the equation of a line passing through $(-2,5)$ and parallel to the line $6y + 2x = 10$. 2. **Step 1:** Rewrite the given line in slope-intercept form $y = m

1. **Simplify the algebraic expression:** Given expression: $-3 - x^2 - 6x - 5x^2 + 3x - 1$