🧮 algebra

1. The request is to find the 12th number in a sequence. 2. Since the original sequence is not provided, please specify the sequence to find the 12th number.

1. The problem is to analyze the function $$g(x) = \frac{x}{x^2 - 25}$$ and understand its properties. 2. First, identify the domain. The denominator cannot be zero, so solve $$x^2

1. Stating the problem: Simplify the expression $(x+2)^2$. 2. Use the formula for the square of a binomial: $$(a+b)^2 = a^2 + 2ab + b^2$$.

1. The problem is to understand Pascal's triangle and how to construct it. 2. Pascal's triangle is a triangular array where each number is the sum of the two numbers directly above

1. The problem asks to identify what a unit is from the given multiple choice options. 2. In mathematics, a "unit" typically refers to the multiplicative identity in a number syste

1. **Problem Statement:** Beatrice walks 1 km at 4 km/h and then 2 km at 4.5 km/h. Find her average speed for the whole journey. 2. **Step 1: Calculate the time taken for each part

1. Stating the problem: We want to resolve the expression $$\frac{2x^2 + 7x + 33}{x^3 + 0x^2 - 11x}$$. 2. Simplify the denominator: The denominator is $$x^3 + 0x^2 - 11x = x^3 - 11

1. Word sums involve translating a word problem into an algebraic equation using variables to represent unknown quantities. 2. You then form an equation based on the given relation

1. **State the problem:** We want to simplify the expression $$\frac{2x^2 + 7x + 33}{x^3 + x^2 - 11x}$$\n\n2. **Factor the denominator:** Look for common factors first. The denomin

1. The problem is to expand the expression $$(2x-1)^4$$ using the binomial theorem. 2. Recall the binomial theorem: $$(a-b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} (-b)^k$$ where $

1. Given the equation $3b = \frac{2a - 1}{4 - 5a}$, the problem asks to find the value of $A$ when $A = 6m + \frac{7n}{100}$, $m=2$, and $n=3$. 2. First, we focus on the expression

1. **State the problem:** We need to find the coordinates of the foci and the lengths of the major and minor axes of the ellipse given by the equation $$\frac{x^2}{49} + \frac{y^2}

1. Stating the problem: Solve the system of linear equations $$\begin{cases}

1. The problem is to solve the quadratic equation $ax^2 + bx + c = 0$ for $x$. 2. Use the quadratic formula which is derived from completing the square: $$x = \frac{-b \pm \sqrt{b^

1. The problem involves finding the discriminant $\Delta$ and the roots $x_1$ and $x_2$ of a quadratic equation of the form $ax^2 + bx + c = 0$. 2. The formula for the discriminant

1. The given expression is a quadratic polynomial: $x^2+3x-3$. 2. To understand it better, we can find its roots by solving $x^2+3x-3=0$ using the quadratic formula:

1. نقرأ السؤال: لدينا دالة (ع)(٥،ع)(س) تعرف ب $$ (ع)(٥،ع)(س) = \frac{s + 3}{1 + s} + \frac{1}{2} , \quad s \neq 1 $$

1. The problem gives the function $g_r(r) = \sqrt{r^2 + 1}$ and some values $g_r(0)=3$, $g_r(1)=\sqrt{r}$. However, the values are inconsistent with the function $g_r(r)$ as define

1. The problem is to solve the equation $4Y - 3x = 0$ for one variable in terms of the other. 2. Let's start by isolating $Y$ on one side:

1. The problem is to express $Z$ given the formula $Z=1-\frac{I}{2}$. 2. Here, $1$ is a constant term, and $\frac{I}{2}$ means half of the variable $I$ is subtracted from 1.

1. State the problem: Solve for $x$ in the equation $$\frac{3}{3}x = \frac{24}{12} x \times \frac{16}{4}.$$\n\n2. Simplify each fraction:\n- $\frac{3}{3} = 1$\n- $\frac{24}{12} = 2