🧮 algebra

1. The word "inclusive" in a math or interval context means including the boundary points or endpoints. 2. If a problem says something like $x \in [a,b]$, it means $x$ can be equal

1. The first problem is to list and provide set builder form for even integers between 60 and 73. 2. First, list even integers between 60 and 73. Even integers are multiples of 2.

1. **Understanding Vertical Lines:** The equation of a vertical line is $x = c$, where $c$ is a constant.

1. **State the problem:** We need to find the value of $\frac{1}{4} - \left(-\frac{3}{7}\right)$. 2. **Rewrite the expression:** Subtracting a negative number is the same as adding

1. Problem: Calculate $16 - \frac{1}{4} - \left(- \frac{3}{7}\right)$. Subtracting a negative is addition, so rewrite as:

1. The problem is to simplify the expression: $$2\left(\frac{10 - y}{3}\right)^2$$. 2. Start by understanding that the square applies to the entire fraction \(\frac{10 - y}{3}\). T

1. **State the problem:** We are given that the sum of a father's and his son's current ages is 56.

1. Problem i: Evaluate $$6^9 \left( \frac{3}{2} - 4^3 \right) 8^3 \times 16 \times 2$$. 2. Calculate powers:

1. **State the problem:** A student scores 36% and gets 24 marks.

1. **State the problem:** We are given two numbers $\alpha$ and $\beta$ such that their sum is $\alpha + \beta = -6$ and their product is $\alpha \beta = 1$. 2. **Interpretation:**

1. The request is to expand an algebraic expression, but the exact expression to expand is not provided. 2. Please provide the specific algebraic expression (for example, $(a+b)^2$

1. The problem is to expand the expression $\left(x-\frac{\alpha}{\beta}\right)\left(x-\frac{\beta}{\alpha}\right)$. 2. Use the distributive property (FOIL method) to expand:

1. The given expression is $\left(x-\frac{\alpha}{\beta}\right)\left(x-\frac{\alpha}{\beta}\right)$. 2. This is equivalent to squaring the binomial: $\left(x-\frac{\alpha}{\beta}\r

1. The problem is to simplify the expression $$(x-\frac{\alpha}{\beta})(x-\frac{\alpha}{\beta}).$$ 2. Recognize that this is a product of two identical binomials, so it can be rewr

1. The problem is to simplify the ratio 2:7. 2. A ratio represents the relationship between two numbers, here 2 and 7.

1. مسئله: نحوه رسم نمودار تابع $y=f(x-1)$ از روی نمودار تابع $y=f(x)$ را بیان کنید. 2. برای رسم $y=f(x-1)$ کافی است نمودار $y=f(x)$ را یک واحد به راست انتقال دهیم زیرا تغییر $x$ به

1. **Problem 1: Calculate total sales revenues for Kamukamu and Tweziimbe groups** 1. Given:

1. **State the problem:** We are given a rectangle with length $(x + 2)$ cm and width $(x - 5)$ cm, and the area is 120 cm$^2$. We need to find the value of $x$. 2. **Write the are

1. **State the problem:** We want to find the combined advertising revenue for Television and Internet in 2011, assuming the same absolute trends (changes) from 2009 to 2010 contin

1. The problem states that the Internet advertising forecast for 2011 is divided into mobile and display advertising in a ratio of $1:4$. 2. This means for every 1 part of mobile a

1. Stating the problem: Simplify the expression $$24 - 7 \left[-5^2 - 4(3 - 9) - \frac{49}{-7}\right]$$. 2. Simplify inside the brackets step-by-step.