🧮 algebra

1. **State the problem:** We are told that $y$ is directly proportional to $x^3$, and that $y=20h$ when $h=x$. We need to find $y$ in terms of $h$ and $x$. 2. **Write the proportio

1. The problem is to evaluate the expression \(6 \div \frac{2}{8}\) using modulo arithmetic. 2. First, understand the division of fractions: dividing by a fraction is the same as m

1. The problem states that $y$ is directly proportional to $x$ cubed. This means we can write the relationship as: $$y = kx^3$$

1. The problem is to factor the cubic polynomial $$x^3 - 6x^2 + 11x + 6$$ and find its roots. 2. We use the Factor Theorem and synthetic division to find factors. The Factor Theore

1. **Menyatakan masalah:** Diketahui kemasan berbentuk balok dengan panjang $p$ cm, lebar $5$ cm lebih pendek dari panjangnya, dan volume kemasan $V(p) = p^3 - 22p^2 + 85p - 900$ c

1. **Problem Statement:** Solve the equation involving exponents and logarithms: $$2^{x} = 8$$ and find $x$.

1. Let's start by stating the problem: We want to understand how to solve algebraic equations using examples. 2. The general formula or approach for solving linear equations is to

1. **Stating the problem:** Understand the relationship between exponents and logarithms. 2. **Definition of exponents:** Exponents represent repeated multiplication. For example,

1. **Stating the problem:** We want to understand how to solve algebraic equations with examples. 2. **Formula and rules:** The main goal in algebra is to isolate the variable (usu

1. The problem is to understand the relationship between exponents and logarithms. 2. Exponents represent repeated multiplication. For example, $a^x = b$ means multiplying $a$ by i

1. The problem is to simplify the expression $\sqrt{8}$.\n\n2. Recall the property of square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$. This allows us to break down the

1. Let's start by stating the problem: We want to understand the difference between an arithmetic sequence and a geometric sequence. 2. An arithmetic sequence is a list of numbers

1. **Problem Statement:** An airplane travels 1400 km in the same time a car travels 560 km. The car's speed is 200 kph less than the airplane's speed. Find the rate of each vehicl

1. **State the problem:** An airplane travels 1400 km in the same time a car travels 560 km. The car's speed is 200 kph less than the airplane's speed. We need to find the speed of

1. **State the problem:** A man is three times as old as his daughter. In twelve years, he will be twice as old as his daughter. We need to find their present ages. 2. **Define var

1. **Problem Statement:** When divided by $x - 3$, the polynomials $x^3 - px^2 + x + 6$ and $2x^3 - x^2 - (p + 3)x - 6$ leave the same remainder. Find the value of $p$. 2. **Formul

1. **State the problem:** Philip takes 9 hours longer than Jane to paint a car alone. Together, they paint the car in 6 hours. We need to find how long Jane takes to paint the car

1. **State the problem:** Solve the equation $$2^{x+7} - 2^{x+6} = 1$$ for $x$. 2. **Recall the properties of exponents:**

1. **State the problem:** Find all numbers $x$ such that the difference of the number and 3 equals half of the quotient of thrice the number and the sum of the number and two.

1. **State the problem:** Find all numbers $x$ such that the difference of the number and 3 equals half of the quotient of thrice the number and the sum of the number and two.

1. **State the problem:** A heptagon has a perimeter of 77 feet. Four sides are equal in length, and the remaining three sides are half as long as those four. We need to find the l