🧮 algebra

1. **State the problem:** We need to find three numbers in geometric progression (GP) whose sum is 26 and the difference between the first and third terms is 18. 2. **Set variables

1. **State the problem:** We want to find the maximum value of $ (2x + 3y)^2 $ given the constraint $ x^2 + y^2 = 1 $ where $x$ and $y$ are real numbers.

1. **State the problem:** We have an ellipse $\frac{x^2}{b^2} + \frac{y^2}{25} = 1$ and a hyperbola $\frac{x^2}{16} - \frac{y^2}{b^2} = 1$ with $b < 5$. Their eccentricities are $e

1. **State the problem:** Convert the quadratic function $f(x) = -2x^2 - 4x + 5$ from standard form to vertex form. 2. **Recall the vertex form:** The vertex form of a quadratic is

1. **State the problem:** We are given the quadratic function $f(x) = -2x^2 - 4x + 5$ and want to analyze it. 2. **Formula and rules:** A quadratic function is generally written as

1. **Menyatakan masalah:** Sebuah pesawat memiliki 48 tempat duduk terbagi dalam kelas Bisnis dan Ekonomi.

1. **State the problem:** We need to find the volume of solids formed by multiplying length ($l$), breadth ($b$), and height ($h$) for each given shape. 2. **Formula:** Volume $= l

1. Let's state the problem: You want to understand why one of the $\ln x$ terms disappears when the numerator becomes $3x$ in an expression involving logarithms. 2. Recall the loga

1. **State the problem:** Simplify the expression $n=\frac{250}{100} \times 2$. 2. **Write the formula and rules:** To simplify, first perform the division, then multiply.

1. The problem is to solve the equation $1.80 = \frac{n}{100} \times 30$ for $n$. 2. This equation represents a percentage problem where $n$ is the percentage of 30 that equals 1.8

1. **Problem statement:** We are given a bar graph showing the number of fruits sold in a school's cafeteria for four types of fruits: Oranges, Portugals, Bananas, and Mangoes. - N

1. **State the problem:** We need to solve the equation step by step. Since the user did not specify a particular equation, let's consider a common example: Solve for $x$ in the eq

1. The problem is to understand the Fibonacci sequence given by $x_1=1, x_2=1, x_3=2, x_4=3, x_5=5, x_6=8, x_7=13$. 2. The Fibonacci sequence is defined by the recurrence relation:

1. **State the problem:** Multiply the expression $(z-3)(z-3)$. 2. **Formula used:** This is a product of two identical binomials, which can be expanded using the identity for the

1. **State the problem:** Find the value of $$\frac{10! + 9!}{8!}$$ and express your answer as an integer. 2. **Recall factorial definitions:**

1. **State the problem:** Find the value of the expression $$(3 + \sqrt{3\sqrt{3}})(3 - \sqrt{\sqrt{27}}).$$ 2. **Simplify the radicals:**

1. نبدأ بحل المعادلة الأولى: $$4 - y - x^3 + 4x - 10 + 7 = 0$$ حيث المتغيرات هي $x$ و $y$. 2. نجمع الحدود الثابتة: $$4 - 10 + 7 = 1$$

1. نبدأ بحل المعادلة: $$4|ص-3| - 5(ص - 3) = 7$$ 2. نعرف أن القيمة المطلقة تعني:

1. **State the problem:** Write the ratio 2 feet to 2 yards in simplest form as a fraction. 2. **Understand the units:** 1 yard = 3 feet.

1. The problem asks to write the ratio of 8 skittles to 14 M&M's in simplest form as a fraction. 2. The ratio can be written as the fraction $\frac{8}{14}$.

1. The problem is to simplify the expression $2$. 2. Since $2$ is already a simplified number, there are no further steps needed.