🧮 algebra

1. The problem asks to draw the graph of $$y = -f(x)$$ given the graph of $$y = f(x)$$ with points (\-5,0), (\-3,\-3), (0,2), (1,3), (2,5). 2. The transformation $$y = -f(x)$$ refl

1. The problem states that the point $(1,4)$ lies on the graph of $f(x)$, meaning $f(1) = 4$. 2. We want to find which point lies on the graph of $y = f(x) + 3$.

1. **State the problem:** Simplify the expression $\sqrt{5(\sqrt{5}(\sqrt{5}))}$. 2. **Rewrite the expression:** The expression inside the square root is $5 \times (\sqrt{5} \times

1. **Problem statement:** Given the function $f(x) = \sqrt{x}$, find the functions for the following transformations: - Reflection across the x-axis

1. The problem is to verify or simplify the expression $$\sqrt{5} \sqrt[5]{5}$$ and compare it to $$5^{\frac{2}{7}}$$. 2. Recall the rules for exponents and radicals:

1. **State the problem:** Simplify or analyze the expression $180 - 2w^2 + 3w$. 2. **Identify the type of expression:** This is a quadratic expression in terms of $w$ because it co

1. Stwierdzenie problemu: Znajdź liczbę rozwiązań całkowitych równania $$\frac{13}{x} - \frac{19}{y} + \frac{11}{z} + \frac{247}{xy} - \frac{143}{xz} + \frac{209}{yz} = 1.$$\n\n2.

1. The problem is to understand the square root function and its properties. 2. The square root of a number $x$ is a value $y$ such that $$y^2 = x$$.

1. The problem is to evaluate the expression $$\frac{(5 + 1)^2}{(7 - 5)^2}$$. 2. The formula involves squaring sums and differences: $$(a + b)^2 = (a + b)(a + b)$$ and $$(a - b)^2

1. The problem asks to evaluate the squares of the expressions $(5 + 1)$ and $(7 - 5)$.\n\n2. Recall the formula for squaring a number: $a^2 = a \times a$.\n\n3. First, calculate $

1. The problem is to simplify the expression $cf - 1$. 2. Here, $c$ and $f$ are variables, and the expression represents the product of $c$ and $f$ minus 1.

1. **State the problem:** We are given two equations:

1. **State the problem:** We are given two equations:

1. Pernyataan masalah: Buktikan bahwa untuk setiap $n \geq 1$, berlaku rumus jumlah kuadrat berikut: $$1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n+1)(2n+1)}{6}$$

1. **State the problem:** Factor the quadratic expression $X^2 + 7X + 12$. 2. **Recall the factoring formula:** For a quadratic $X^2 + bX + c$, we look for two numbers that multipl

1. **State the problem:** Solve for $x$ in the equation $$\frac{-3(x+7)}{-7x+9} = \frac{1}{6}.$$\n\n2. **Understand the equation:** We have a rational equation where a fraction equ

1. Diketahui matriks $A = \begin{pmatrix} 3 & -1 \\ 11 & -4 \end{pmatrix}$. Kita diminta mencari invers matriks $A$, yaitu $A^{-1}$. 2. Rumus invers matriks 2x2 adalah $$A^{-1} = \

1. **State the problem:** Find the remainder when the expression $\left(6^3 + 4^2 \times 2^1\right)$ is divided by 8. 2. **Write the expression:**

1. **State the problem:** Identify vertical asymptotes, horizontal asymptotes, and holes of the function $$f(x) = \frac{(2x - 6)(x + 1)}{(x + 1)(x - 1)}.$$\n\n2. **Simplify the fun

1. **State the problem:** We need to find the vertical asymptotes, horizontal asymptotes, and holes of the function $$f(x) = \frac{(x+1)(x+2)}{(x+2)(x-3)}.$$\n\n2. **Identify verti

1. **بيان المسألة:** لدينا دالة كثيرة الحدود من الدرجة الثالثة بالشكل $f(x) = ax^3 + 6x^2 + bx + 4$، ونريد إيجاد القيم $a$ و $b$ بحيث يمر المنحنى $(C)$ بالنقطة $A(1,0)$ ويقبل مماسً