🧮 algebra

1. **Problem statement:** A trader mixes 26 kg of rice costing Rs. 20 per kg with 30 kg of another variety costing Rs. 36 per kg and sells the mixture at Rs. 30 per kg. We need to

1. The problem provides several sets of numbers and asks to identify which option (a, b, c, or d) relates correctly to the given sequence. 2. The input sequence is: 16, 26, 56, 36,

1. We are asked to determine whether each inequality or equality statement involving fractions and decimal numbers is True or False. 2. For each item, we convert the fraction to it

1. Let's start by stating the problem: You want complicated math problems solved with detailed steps. 2. Since no specific problem was provided, here is a challenging algebra probl

1. Problem: The sum of the first 10 terms ($S_{10}$) of an A.P is 240 and the 8th term ($a_8$) is 34. Find: a. The common difference ($d$)

1. The problem is to simplify the expression $\sqrt[3]{34} \times \sqrt[3]{2}$. 2. Recall the property of cube roots: $\sqrt[3]{a} \times \sqrt[3]{b} = \sqrt[3]{a \times b}$.

1. **State the problem:** Solve the system of equations: $ (3x - 1) = 2.2x + 2x + 4 $

1. We are given the equation $\frac{1}{14} = \frac{81}{14}x^2 + \frac{20}{7}x^2$ and asked to solve for $x$ step-by-step. 2. First, notice that the right side has two terms involvi

1. The problem involves evaluating and solving multiple absolute value expressions and equations. 2. For the expressions like $|4|, |-3|, |2 - 5|, |6 - 6|, |-1.7|, |-3 \frac{5}{11}

1. **State the problem:** Solve the equation $$\frac{1}{14} = \frac{81}{14x^2} + \frac{20}{7x^2}$$ for $x$. 2. **Find the common denominator:** The denominators are $14x^2$ and $7x

1. **State the problem:** We want to find the value of $a$ such that \(x^2 - 14x + 49 = (x - a)^2\). 2. **Recall the expansion:** The right side is a perfect square trinomial, expa

1. State the problem: Fully factorise the cubic expression $$x^3 - 25x$$. 2. Factor out the common factor: Both terms have a common factor of $$x$$, so factor it out:

1. **Stating the problem:** Solve the equation $8g - 7 = 3$ for $g$. 2. **Add 7 to both sides:**

1. The given system of linear equations is: $$3x_1 - 4x_2 - 2x_3 = 2$$

1. The problem is to expand the expression $(x+8)^2$. 2. Recall the formula for expanding a binomial squared: $$(a+b)^2 = a^2 + 2ab + b^2$$.

1. The phrase "rise over run" refers to the slope of a line, which is usually calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two point

1. **State the problem:** Expand the expression $$(x+8)(x-2)$$. 2. **Apply distributive property (FOIL method):** Multiply each term in the first binomial by each term in the secon

1. It seems you asked, "How did you simplify?" but did not provide a specific expression or problem to simplify. 2. To assist you effectively, please provide the exact algebraic ex

1. **Stating the problem:** The first three terms of an arithmetic progression (A.P) are given as $2x$, $(3x - 1)$, and $(x + 4)$. We need to find: i. The value of $x$

1. Problem: The sum of the first 10 terms of an arithmetic progression (A.P.) is 240 and the 8th term is 34. a. Find the common difference.

1. The user asked about the variable "a" which was not mentioned previously. 2. Without specific context, "a" can represent a constant, coefficient, or variable in an equation.