🧮 algebra

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.

1. The user's message "For the first A.p" is ambiguous and does not specify a clear math problem to solve. 2. "A.p" often stands for Arithmetic Progression (Arithmetic Sequence), a

1. The substitution method is used to solve systems of equations by expressing one variable in terms of the other and substituting it into the other equation. 2. Since the user men

1. The problem states that the sum of the first 10 terms of an arithmetic progression (A.P.) is 240 and the 8th term is 34. Step 1: Recall the sum formula for the first n terms of

1. Solve each equation for the variable step-by-step. **7a.** Solve $2(x - 1) = 18$

1. Solve for $x$ in equations: a. Given $\frac{x + 1}{3} = 4$, multiply both sides by 3:

1. Evaluate expression 13: $24 - 7 [ -5^2 - 4(3 - 9) - 49 \div (-7) ]$ - Calculate inside brackets:

1. Solve for $x$ in each equation: a. Given $\frac{x}{2} + 1 = 3$

1. The problem gives three numbers on cards: 3, 11, and 6. We are asked to find the number on Jeff's fourth card. 2. Without additional context, we assume a pattern or relationship

1. Solve each equation for $x$ by isolating $x$ on one side. a. $2x + 1 = 5$

1. Stating the problem: Solve the quadratic equation $$5x^2 - 7x - 6 = 0$$ by factoring. 2. Multiply the coefficient of $x^2$ (which is 5) by the constant term (which is -6):

1. The problem asks to find the solution set, but no specific equation or inequality is given. 2. To find a solution set, typically we need an equation, inequality, or expression t