🧮 algebra

1. Find domain and range of $f(x) = 3x - 5$. - Domain: Since $f(x)$ is a linear function, it is defined for all real numbers.

1. **State the problem:** Simplify the fraction $$\frac{4566}{6000}$$. 2. **Formula and rules:** To simplify a fraction, divide the numerator and denominator by their greatest comm

1. **State the problem:** We need to solve the polynomial equation $$6x^5 + x^2 - 43x^3 - 43x^2 + x + 6 = 0.$$ 2. **Rewrite and group terms:** Group like terms to simplify:

1. **State the problem:** A farmer starts with a total number of apples $x$. He sells $\frac{1}{3}$ of them, then gives $\frac{2}{5}$ of the remainder to his neighbor, then uses $\

1. **State the problem:** We are given two polynomials $$f(x) = 2x^5 - 3x^3 + 2x^2 + x - 3$$ and $$p(x) = x + 4$$. We want to perform polynomial division to find the quotient and r

1. **State the problem:** We are given the polynomial function $$f(x) = 2x^5 - 3x^3 + 2x^2 + x - 3$$ and we want to understand or analyze it. 2. **Identify the function:** This is

1. **Nyatakan masalah:** Diberi titik $P(0,0)$, $Q(2,5)$, $R(4,-5)$, dan $S(5,0)$.

1. **Problem 8:** Solve $2^{2x - 1} = \frac{\sqrt{8}}{4}$. 2. Express $\sqrt{8}$ as $8^{1/2} = (2^3)^{1/2} = 2^{3/2}$.

1. **Problem 4: Simplify each expression.** (a) Simplify $$(9pq^3)^2$$

1. **State the problem:** Evaluate each expression. 2. **Part (a):** Evaluate $(-3)^4$.

1. **Evaluate (a) $5^3 \div (5^2 \times 5^{-3})$** 1. The problem asks us to divide $5^3$ by the product $5^2 \times 5^{-3}$.

1. **State the problem:** We need to find the zero of the function $$y = \frac{1}{2}x + 1$$. The zero of a function is the value of $$x$$ when $$y = 0$$. 2. **Set the function equa

1. **State the problem:** Factor the quadratic expression $x^2 + 6x + 9$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** Simplify the expression $$\left(\frac{a b^3 c^2 d^{-3}}{a^3 b^{-1} d^2}\right)^{-4} \div \left(\frac{b c^{-2} d^4}{a^{-3} b^2 c^{-2}}\right)^{-3}$$

1. **Problem Statement:** Simplify the expression $$\left(\frac{a^3 b^{-1} c}{a^4 b^{-3} d^2}\right)^4 \div \left(\frac{a^{-3} b^4 c^2 d^{-1}}{b^3 c^{-2} d^{-3}}\right)^{-4}$$ and

1. **Problem 1(a): Find the first term of the geometric progression given by** $$T_n = -\frac{3}{7} r^{n-1}$$ 2. **Formula and explanation:**

1. **State the problem:** We are given the expression $95 - 59 / 9$ and need to understand what question it might represent. 2. **Identify the operations:** The expression involves

1. **State the problem:** Simplify the expression $$\left(\frac{a^3 b^2 c^{-1}}{a^4 b^{-3} d^2}\right)^{-3} \times \left(\frac{a^{-1} b^3 d^2}{a^3 b^{-1} c^3}\right)^{-4}$$

1. **State the problem:** Simplify the expression $$\left(\frac{a^3 b^2 c^{-1}}{a^4 b^{-3} d^2}\right)^{-3} \times \left(\frac{a^{-1} b^3 d^2}{a^3 b^{-1} c^3}\right)^{-4}$$

1. **State the problem:** Simplify the expression $$\left(\frac{a^{-2} b^{4} c^{5}}{a^{3} b^{-2} d^{3}}\right)^{4} \div \left(\frac{a^{-5} c^{3} d^{-1}}{a^{3} b^{2} c^{3}}\right)^{

**Problem:** Solve $16-2t=5t+9$. 1. Use the linear-equation rule: add or subtract the same expression on both sides, then divide both sides by the coefficient of the variable.