🧮 algebra

1. We are given the equation $a + 128 = 400$ and asked to solve for $a$. 2. To isolate $a$, subtract 128 from both sides of the equation:

1. Stating the problem: We want to find the sum of a geometric series. 2. Definition: A geometric series is a series of terms where each term is found by multiplying the previous t

1. Stating the problem: We want to understand how to divide one polynomial by another, similar to long division with numbers. 2. Step 1: Arrange the dividend (the polynomial to be

1. **State the problem**: Simplify the expression $x + x$. 2. **Combine like terms**: Both terms have the variable $x$, so we can add their coefficients.

1. The problem is to solve the quadratic equation $$x^2 - 10x - 9 = 0$$. 2. We will solve it by factoring or using the quadratic formula. Here, let's try to factor it first.

1. Bài toán: Giải phương trình bậc hai $ax^2 + bx + c = 0$. 2. Xác định hệ số: Cho ví dụ $x^2 - 5x + 6 = 0$ (tương ứng với $a=1$, $b=-5$, $c=6$).

1. Perform Addition $(f + g)(x)$ where: $f(x) = 4x^4 - 8x^3 + 6x^1 - 5x^1 + 9x - 8$

1. Vamos a calcular el MCD de 207 y 36 mediante el algoritmo de Euclides. 2. Primero dividimos 207 entre 36: $$207 = 36 \times 5 + 27$$, el primer residuo es 27.

1. Stating the problem: We are asked to find the original sum (principal) given that after 3 years at an interest rate of 12% per annum, the amount becomes 250005. 2. Identify the

1. **State the problem:** Calculate $-\frac{3}{7} \div -\frac{18}{35}$.\n\n2. **Recall division of fractions rule:** Dividing by a fraction is the same as multiplying by its recipr

1. **State the problem:** We need to divide $\frac{3}{5}$ by $\frac{3}{15}$.\n\n2. **Rewrite division as multiplication:** Dividing by a fraction is the same as multiplying by its

1. The problem is to multiply $-24$ by $\frac{1}{3}$. 2. We write the multiplication as:

1. State the problem: Calculate the product of $-1 \frac{1}{2}$ and $\frac{8}{15}$. 2. Convert the mixed number to an improper fraction: $-1 \frac{1}{2} = -\left(1 + \frac{1}{2}\ri

1. Problem 8: Find the number halfway between 3000 and 4000. To find the halfway point, calculate the average of 3000 and 4000.

1. The problem states that 55% of 500 pupils are girls. 2. To find the percentage of boys, we need to calculate what remains after the girls' percentage.

1. We are given four triangular diagrams each divided into four smaller triangles with sets of numbers and a circled number on the side. 2. The numbers appear to be part of a patte

1. State the problem: Solve the equation $\log_{3}(2-3x)=\log_{9}(6x^{2}-19x+2)$.\n\n2. Express both sides with the same base: Notice that $9=3^{2}$, so rewrite the right side loga

1. The problem is to find the domain and range of the function $$y = x^2 - 8x - 10$$. 2. **Domain:** Since this is a quadratic function (a polynomial), its domain is all real numbe

1. **Problem Statement:** Given a rectangular land plot of dimensions 8 m by 7 m divided into four parts labeled (1), (2), (3), and (4) with the following sizes:

1. We start with the equation of the graph to draw: $$2xy+1=0$$. 2. To understand the graph, we isolate $y$ in terms of $x$: $$2xy = -1 \implies y = \frac{-1}{2x}$$.

1. Mathematical induction is a proof technique used to show that a statement is true for all natural numbers $n \geq k$, where $k$ is a starting point, usually 1. 2. It has two mai