📘 algebra, geometry

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: $-3 - x^2 - 6x - 5x^2 + 3x - 1$

1. نبدأ بحل المعادلة: $$0 = 3(x - 2)$$ 2. نوزع 3 على القوس: $$0 = 3x - 6$$

1) **حل المسألة الأولى: العمليات على المجموعات باستخدام خط الأعداد** ① لدينا المجموعتين $[-1,4]$ و $[2,5]$ ونريد اتحادهما $[-1,4] \cup [2,5]$.

1. **Problem 1: Find the median length of the leaves given the frequency distribution.** We have the length intervals and the number of leaves in each interval:

1. **Stating the problem:** Simplify and evaluate the expressions for $X$, $Y$, $A$, $B$, and $C$, and solve the geometric problem involving triangle $ABC$ with given segment ratio

1. نبدأ بحل المعادلة الجبرية المعطاة: $$س - 3س - 1 = 0$$. 2. نجمع الحدود المتشابهة: $$س - 3س = -2س$$، إذن المعادلة تصبح:

1. Problem 65: A miller takes 1/10 of the flour he grinds as his fee. A customer has exactly one bushel left after the fee. How much flour did the miller grind? 2. Let the total am

1. **Problem 6:** Given that $y$ varies directly as the square of $(x+1)$, and $y=200$ when $x=4$, find the equation connecting $y$ and $x$. 2. **Step 1:** Write the direct variati

1. **Problem statement:** We have several algebraic expressions and geometric questions to solve.

1. Problem 1: The total cost of a tablet device is divided into material, labour, and overheads in the ratio 3:4:1. The cost of material is given as 315.

1. **Factorize** $25 - 16x^2$. This is a difference of squares: $a^2 - b^2 = (a - b)(a + b)$.

1. **Problem:** Identify the graph type for each polynomial function given. 2. **Step 1:** Understand the shape of polynomial graphs based on degree and leading coefficient.