🧮 algebra

1. We are given the quadratic function $f(x) = 2x^2 + 6x - 5$ and asked to analyze it. 2. The general form of a quadratic function is $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c

1. **Problem Statement:** We have five cards, each with two three-digit numbers. Some digits are obscured by ink. We need to find the card where the sum of the digits of both numbe

1. The problem states that a player scores one goal in every match, including the final, in a FIFA World Cup tournament. 2. The tournament structure is: 3 group matches followed by

1. **State the problem:** We have three scales balanced as follows: - Scale 1: 3 circles + 2 triangles = 9 squares

1. **Problem Statement:** Given that A and B together can complete a work in 12 days, and B alone can complete the same work in 30 days, find how many days A alone will take to fin

1. Problem: When $y$ varies directly as $x$, and $y=21$ when $x=16$, find $y$ when $x=8$. 2. Formula: Direct variation means $y=kx$ where $k$ is a constant.

1. **Problem Statement:** (a) Factorize completely:

1. The problem is to find the value of $(\frac{2}{3})^{-1}$. 2. Recall the rule for negative exponents: For any nonzero number $a$ and integer $n$, $a^{-n} = \frac{1}{a^n}$.

1. The problem asks to write the expression $$\sqrt[3]{x^5}$$ as a rational exponent. 2. Recall the rule that a radical expression $$\sqrt[n]{x^m}$$ can be written as $$x^{\frac{m}

1. The problem is to evaluate the expression $$\sqrt[4]{81y^{8}x^{4}}$$. 2. Recall the rule for radicals: $$\sqrt[n]{a^{m}} = a^{\frac{m}{n}}$$. This means the fourth root of a pow

1. Problem (c): A dining room set is advertised with a 20% discount, and the discounted price is 75000. Calculate the original price before discount. 2. Formula: The discounted pri

1. Problem: Evaluate the function $f(x) = -3x + 4$ at $x=4$. 2. Formula: To find $f(a)$, substitute $x$ with $a$ in the function.

1. **State the problem:** Given the equation $$x^2 = 3^{2/3} + 3 - 2/3$$, prove that $$3x^2 + 9x = 8$$. 2. **Rewrite the given equation:**

1. The problem is to evaluate the expression $$(36x^4)^{\frac{1}{2}}$$. 2. We use the rule of exponents: $$(a^m)^n = a^{mn}$$ and the property of square roots: $$\sqrt{a} = a^{\fra

1. **State the problem:** Evaluate the expression $$ (36x^4)^{\frac{1}{2}} $$. 2. **Recall the rule:** The square root of a product is the product of the square roots, and the powe

1. The problem involves calculating the total price for a surface area given the dimensions and price per square meter. 2. First, calculate the area in square centimeters: $$\text{

1. The problem is to solve the first question from Class 7, Chapter 7, Exercise 7a, which typically involves algebraic expressions or equations. 2. Since the exact question is not

1. The problem is to find the value of $x$. 2. Since no equation or expression is given, we cannot solve for $x$ directly.

1. **State the problem:** A building is valued at 241000. Its value increases by 4.5%. We need to find the new value after the increase. 2. **Formula used:** To find the new value

1. **State the problem:** Solve the inequality $x + 5 > 7$. 2. **Formula and rules:** To solve inequalities, we isolate the variable on one side. Adding or subtracting the same num

1. Let's understand the expression $x=\pm \frac{2}{1}$. This means $x$ can be either positive or negative $\frac{2}{1}$.\n\n2. The symbol $\pm$ means "plus or minus," indicating tw