🧮 algebra

1. The problem involves the equation $(\varepsilon + Kt) = 1 + (xt) t$ and the relation $-xt- = -et$ with $t (2)t t$ given. 2. First, clarify the expressions: assume $xt$ and $et$

1. مسئله را بیان می‌کنیم: چرا در تقسیم $$\frac{13}{26}$$ به $$\frac{1}{2}$$ رسیدیم؟ 2. ابتدا کسر $$\frac{13}{26}$$ را داریم. این کسر به معنای تقسیم عدد 13 بر عدد 26 است.

Problem: In a class of 40 students the number of students who study French is 10 more than the number of students who study history. If 8 students study both subjects, how many stu

1. Stating the problem: Decompose the expression $$\frac{x^2 + x - 3}{x(x-1)}$$ into simpler parts or partial fractions. 2. Factor the numerator if possible: The numerator is $$x^2

1. Reduce each numerical fraction to lowest terms: (a) $\frac{13}{26} = \frac{13 \div 13}{26 \div 13} = \frac{1}{2}$

1. **State the problem:** We are given the equation

1. The problem is to solve the equation using properties of equality or algebraic properties. 2. Since the user did not specify the exact equation, let's consider a general example

1. Let's first state the problem: We want to know if the numbers 7, 8, and 9 can be related or solved using the properties called componendo, alternendo, and invertendo. 2. These p

1. نبدأ بكتابة العدد المعطى: $\frac{6\sqrt{}}{42\sqrt{}}$. 2. نلاحظ أن المقام هو عدد ناطق، أي يمكن كتابته على شكل كسر بسيط.

1. **Problem 6:** The polynomial is $3x^3 + 8x^2 - 15x + k$ and $(x - 1)$ is a factor. Find $k$ and factorise the polynomial completely. Step 1: Since $(x - 1)$ is a factor, substi

1. The problem is to expand and simplify the expression $ (b + 5)(b - 10) $. 2. Use the distributive property (FOIL method) to expand:

1. The question asks if the interval for 3 is $(-\infty,0) \cup \{0\} \cup (0,+\infty)$. 2. This notation means all real numbers except possibly how 0 is treated (open or closed).

1. The problem is to solve the equation $\log 4 + \log p^2 = 2$ for $p$. 2. Use the logarithm property that $\log a + \log b = \log (ab)$ to combine the terms:

1) Problem: Determine the domain and range of the cubic curve with one local maximum and one local minimum crossing the x-axis near the origin. Step 1. A cubic function is generall

1. The problem is to expand and simplify the expression $$(m + 5)(m + 2)$$. 2. Use the distributive property (FOIL method) to expand:

1. **State the problem:** Thuto runs 6 km in 24 minutes at a constant speed. We need to find how long it will take him to run 10 km at the same speed. 2. **Convert time to hours:**

1. Given expression: $2ax + 4bx + 8cx + 6dx$ Method: HCF

1. The problem is to expand and simplify the expression $$(x + 2)(x + 7)$$. 2. Use the distributive property (FOIL method) to expand:

1. Problem 15: Volume of gas tank and cost to fill the tank. The cost to fill the tank is directly proportional to the volume of the gas tank.

1. **State the problem:** Expand and simplify the expression $$(7b - 3)(2b - 1)$$. 2. **Apply the distributive property (FOIL method):**

1. **State the problem:** Thuto runs 6 km in 24 minutes. We want to find how long it will take him to run 10 km at the same constant speed. 2. **Convert time to hours:** 24 minutes