🧮 algebra

1. Bài 4: Một chiếc thuyền xuôi dòng và ngược dòng trên khúc sông dài 40 km hết 4 giờ 30 phút. Thời gian 4h30phút = 4.5 giờ.

1. **بيان المسألة:** لدينا عددين طبيعيين $a$ و$b$ مُعرفين بدلالة عدد طبيعي $n$ غير معلوم. 2. **تحليل العدد $a$ إلى جداء عوامل أولية:**

1. Problema: Calcular el ingreso promedio por período dado el ingreso total $$I(x)=6x^4-5x^3+2x^2 - x +4$$ y el período $$x+1$$ años. 2. Para encontrar el ingreso promedio por perí

1. State the problem: Express $$\frac{1}{x^{3} - 1}$$ as partial fractions. 2. Factor the denominator using the difference of cubes formula: $$a^{3} - b^{3} = (a - b)(a^{2} + ab +

1. Problema: Indicar cuáles de estas divisiones son exactas usando el Teorema del Residuo. a. Dividir $x^2 - 5x + 1$ entre $x - 2$

1. The AM-GM inequality states that for any list of non-negative real numbers $a_1, a_2, \dots, a_n$, the arithmetic mean (AM) is always greater than or equal to the geometric mean

1. Let's clarify the problem. You seem to be asking about proving an expression involving $2n$ and $n-1$. Please specify the exact statement or equation you want to prove. 2. Assum

1. We need to simplify each algebraic expression by combining like terms. 2. Calculate each:

1. Stated problem: Given the equation $y(x-1)=z$, solve for $x$. 2. Start by isolating $x$ on one side. Divide both sides of the equation by $y$, assuming $y \neq 0$:

1. The problem is to calculate $\frac{1}{2} \times 6 \times 11$. 2. First, multiply $6$ and $11$: $$6 \times 11 = 66$$.

1. The problem is to convert a temperature from Fahrenheit to Celsius. Given the temperature $100.7^\circ F$, we want to find the equivalent in Celsius $^\circ C$. 2. Recall the fo

1. Stating the problem: We want to describe the sequence 144, 72, 36, 18, 9 in mathematical terms. 2. Observe the pattern in the sequence: Each term seems to be divided by 2 to get

1. Start by stating the problem: Simplify and expand the expression $$-2x^2 + 9x - 4 - (-2 - x)(3x - 12)$$. 2. Expand the product $$(-2 - x)(3x - 12)$$ using the distributive prope

1. El problema plantea cambiar la letra \(t\) por otra letra en una expresión matemática o variable. 2. Generalmente, en matemáticas o programación, cualquier letra o símbolo usado

1. The problem is to find the absolute value of $-9$. 2. The absolute value of a number is its distance from zero on the number line, regardless of direction.

1. Problem: Analyze voting data for homework-free day, calculate circle dimensions from circumference, find HCF using prime factorization, and solve wage and profit questions for a

1. We are given that the sales price of the car is 12,590 after a 20% discount. 2. Let the original price be $p$.

1. State the problem: An employee wants to buy a dishwasher originally priced at 450 during a 15% off sale and receives an additional 20% off the lowest price. We need to find the

1. **State the problem:** Sally can paint a house in 4 hours, John can paint the same house in 6 hours. We want to find how long they take together to paint one house. 2. **Find in

1. (a) Problem: A box contains 80 plant seeds. Ben takes $\frac{1}{8}$, Clara takes $\frac{1}{4}$. Find: (i) fraction taken, (ii) number left. Step 1: Calculate fraction taken: $\f

1. **State the problem:** Lynn can type a whole page in $p$ minutes. We want to find out what fraction of the page she can type in 5 minutes. 2. **Understand the rate:** Her typing