🧮 algebra

1. Problem: Find the price of 1 book and 1 notebook given two purchases: Let $x$ be the price of 1 book and $y$ be the price of 1 notebook.

1. **State the problem:** We are given the volume of a rectangular box as $x^3 + 3x^2 + 2x - 5$ cubic centimeters and the height as $x + 1$ centimeters. We need to find the area of

1. Stated problem: Find the sum of $\frac{3}{8}$ and $-\frac{5}{8}$.\n\n2. Since the denominators are the same, we can add the numerators directly:\n$$\frac{3}{8} + (-\frac{5}{8})

1. The question asks what step should always be done first when dividing polynomials. 2. When dividing polynomials, the first step is typically to arrange both the dividend and div

1. El usuario pide resolver una ecuación, pero no se especifica la ecuación a resolver. 2. Por favor, proporciona la ecuación completa para que pueda ayudarte a resolverla paso a p

1. The problem asks for the number of one-digit nonnegative integers $x$ such that the sum $$S = x! + \sum_{i=0}^{2013} i!$$ is divisible by 4. 2. Note that the sum $$\sum_{i=0}^{2

1. The problem is to simplify the fraction $-6/4$. 2. First, find the greatest common divisor (GCD) of 6 and 4, which is 2.

1. The formula used to calculate the roots of a quadratic equation $ax^2 + bx + c = 0$ is called the Quadratic Formula. 2. The formula is:

1. Masalah yang diberikan adalah menentukan nilai pintasan-y bagi garis lurus JK dengan kecerunan (gradien) $\frac{-3}{-5}$ dan titik pada garis $(10,0)$. 2. Kecerunan $m$ diberika

1. The problem is to simplify the number $-\frac{3}{4}$. 2. Since $-\frac{3}{4}$ is already in its simplest fractional form (a negative fraction where numerator is 3 and denominato

1. **State the problem:** Simplify the expression $-8/4$. 2. **Perform the division:** Divide 8 by 4.

1. Determina su mínima expresión para $$\frac{x+1}{x^2-4} \cdot \frac{x^3 + 5x + 6}{4x + 12} \div \frac{x+1}{4x - 8}$$

1. **Problem 1**: Given a polynomial $P(x) = 3x^3 + ax^2 + bx - 9$, it leaves a remainder of $-7$ when divided by $x+1$ and a remainder of $23$ when divided by $x-2$. We need to fi

1. The problem asks to evaluate the expressions when $y = e$ and $x = e$. 2. Since both $y$ and $x$ are equal to the constant $e$, which is approximately 2.718,

1. Factor the expression $7 - 3x^2 - 8z^3$. This is a simple polynomial expression with three terms; it cannot be factored easily as a product. So, it remains as is. 2. Factor $p^3

1. **Problem 1:** Given polynomial $$P(x) = 3x^3 + ax^2 + bx - 4$$ leaves remainder -7 when divided by $$x + 1$$ and remainder 23 when divided by $$x - 2$$. By the Remainder Theore

1. Masalah: Cari persamaan garis lurus yang melalui titik E (-3,8) dan F (5,-2). 2. Mula-mula kita cari kecerunan (gradien) $m$ garis lurus menggunakan formula:

1. Planteamos el problema: utilizar el método de Ruffini para dividir el polinomio $$f(x)=x^4-8x^2+16$$ por un binomio de la forma $$x-r$$, donde $$r$$ es una raíz del polinomio qu

1. The problem is to simplify the expression $-7 \pm \sqrt{\frac{1}{4}}$. 2. Start by simplifying the square root: $\sqrt{\frac{1}{4}} = \frac{\sqrt{1}}{\sqrt{4}} = \frac{1}{2}$.

1. Diberi dua titik $(5,8)$ dan $(3,q)$ serta garisan dengan persamaan $4y - 2x = 15$. 2. Tukar persamaan garisan kepada bentuk kecerunan-intersep: $4y = 2x + 15 \Rightarrow y = \f

1. The term "surd" refers to irrational numbers expressed in root form, such as square roots that cannot be simplified to rational numbers. 2. For example, $\sqrt{2}$ is a surd bec