🧮 algebra

1. The user asks for similar question types, which is a request for examples or variations of a certain type of math problem. 2. Since no specific problem type was given, I will in

1. **Тодорхойлолт:** Квадрат тэгшитгэл гэдэг нь $ax^2 + bx + c = 0$ хэлбэртэй тэгшитгэл бөгөөд $a \neq 0$ байна. 2. **Жишээ бодлого:** $3x^2 - 6x = 0$

1. **Problem statement:** Find the sum of the first $n$ terms and the sum to infinity of a geometric sequence where the first term $a_1=18$ and the fourth term $a_4=-\frac{2}{3}$.

1. **Calculer l'expression A = \sqrt{49}** La racine carrée de 49 est le nombre positif qui, multiplié par lui-même, donne 49.

1. **Énoncé du problème :** Calculer les expressions suivantes : A = \sqrt{3} \times \sqrt{12}

1. **Problem statement:** Find the value of $n$ given the expression $n = \sqrt{v} \times 7 \times 4$ and the value of $v = 9 \times 7 \times 8 - \sqrt{18}$.

1. **Problem statement:** (a) Calculate the total amount to be returned on a loan of 48.52 million at 0.5% simple interest per month after 1.5 years.

1. The problem is to analyze the linear function given by the equation $y = -\frac{1}{2}x + 4$. 2. This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the

1. **State the problem:** We have 22 coins total, consisting of dimes and nickels, with a total value of 1.90 dollars. We want to find the system of equations that models this situ

1. The problem is to find the percentage equivalent of the fraction $\frac{7}{100}$.\n\n2. The formula to convert a fraction to a percentage is:\n$$\text{Percentage} = \left(\frac{

1. **State the problem:** Solve the quadratic equation $3x^2 + 2x + 3 = 5$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Solve the system of equations: $$\begin{cases} -x - 5z = -5 \\ y - 3x = 0 \\ 13x + 2z = 2 \end{cases}$$

1. **State the problem:** We need to find the cost of each game: racing game ($r$), pinball ($p$), and air hockey ($a$) given the total amounts spent by Marcos, Sara, and Darius. 2

1. **State the problem:** We are asked to find the product of two matrices: $$A = \begin{bmatrix} 3 & 2 \\ 5 & -4 \\ -1 & -3 \end{bmatrix}$$

1. The problem asks us to identify which of the given numbers is an integer. 2. Recall that an integer is a whole number without any fractional or decimal part. Examples include $\

1. The problem asks which list of integers is arranged in ascending order. 2. Ascending order means each number is greater than or equal to the previous number.

1. The problem asks to identify which statement among the given inequalities is not correct. 2. Let's analyze each statement:

1. **Stating the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} x + 2 & \text{for } -4 \leq x < 1 \\ -2x + 8 & \text{for } 2 \leq x \leq 4 \end{cases}$$

1. Masalah: Tentukan koefisien dari suku $x^2y^5$ dalam ekspansi binomial dari $ (2x + y)^7$. 2. Rumus yang digunakan adalah Teorema Binomial:

1. **State the problem:** We are given a polynomial $$P(x) = x^3 - 4x^2 - x + 4$$ and told that $$(x-1)$$ is a factor. We need to express $$P(x)$$ as a product of factors. 2. **Rec

1. The problem is to find the coordinates of the vertex of the parabola given by the function $$y = (x + 3)^2 + 4$$. 2. Recall that the vertex form of a parabola is $$y = a(x - h)^