🧮 algebra

1. Let's start by understanding what a quadratic function is. A quadratic function is any function that can be written in the form $$y = ax^2 + bx + c$$ where $a$, $b$, and $c$ are

1. Let's start by understanding the vertex form of a quadratic function. The vertex form is given by: $$y = a(x-h)^2 + k$$

1. **Problem Statement:** PT Noniko menjual kursi lipat dengan harga 200000 per unit, biaya variabel 120000 per unit, dan biaya tetap 2000000.

1. **State the problem:** Simplify the expression $\log \frac{x^4}{\sqrt[3]{y^5 z^5}}$. 2. **Recall the logarithm rule:** $\log \frac{a}{b} = \log a - \log b$.

1. **State the problem:** Expand the logarithm $$\log_3 \left( \frac{x^4}{\sqrt[3]{y^5 z^5}} \right)$$ fully using properties of logarithms, expressing the answer in terms of $$\lo

1. **State the problem:** Given the functions $f(x) = 4x + 5$, $g(x) = 2x^2$, and $h(x) = 7 - 2x$, find the compositions $fg(x)$, $gh(x)$, $hg(x)$, $fh(x)$, $fgh(x)$, and $hh(x)$ a

1. Problem 1: Given $f(x) = 5x - a$, $g(x) = x^2$, and $fg(4) = 5$, find $a$. 2. Recall that $fg(4) = f(g(4)) = f(16) = 5$.

1. **State the problem:** Rebecca takes out a loan with compound interest. We know the initial amount and the values after 1 and 2 years. We need to find:

1. **State the problem:** We need to evaluate the function $y = \left(\frac{1}{2}\right)^x$ at the given values of $x$: $-3, -2, -1, 0, 1, 2$. 2. **Recall the formula:** The functi

1. **State the problem:** Find the expression for the composition $gh(x)$ given the functions $f(x) = 4x + 5$, $g(x) = 2x^2$, and $h(x) = 7 - 2x$. 2. **Recall the definition of com

1. The problem is to understand the function composition $gh(x)$, which means applying function $h$ first, then applying function $g$ to the result. 2. The formula for composition

1. **State the problem:** We have three functions: $f(x) = 4x + 5$, $g(x) = 2x^2$, and $h(x) = 7 - 2x$. We want to find the compositions $hg(x)$, $fh(x)$, $fgh(x)$, and $hh(x)$. 2.

1. **State the problem:** We want to find which expressions are equivalent to $$4(3j+(-4))-9$$. 2. **Start by simplifying the original expression:**

1. **State the problem:** We want to find which expressions are equivalent to $$-4(3d-2)-7$$. 2. **Apply the distributive property:** Multiply $$-4$$ by each term inside the parent

1. **State the problem:** We want to find which expressions are equivalent to $$-6n + (-12) + 4n$$. 2. **Simplify the original expression:** Combine like terms.

1. **State the problem:** We want to find which expressions are equivalent to $$-6n + (-12) + 4n$$. 2. **Simplify the original expression:** Combine like terms.

1. **State the problem:** We want to find which expressions are equivalent to $$-2(2h+10)+4h$$. 2. **Apply the distributive property:** Multiply $$-2$$ by each term inside the pare

1. **State the problem:** Simplify the expression $$-3z - (-z - 2)$$ to find an equivalent expression. 2. **Recall the rule:** Subtracting a quantity in parentheses means changing

1. **State the problem:** Simplify the expression $$-5(1-5k)-4(2k+5)$$ to find an equivalent expression. 2. **Apply the distributive property:** Multiply each term inside the paren

1. The problem is to simplify the expression $$-k - (-8k + 7)$$ and find an equivalent expression. 2. The key rule here is to distribute the negative sign across the parentheses. W

1. **State the problem:** Simplify the expression $$-k - (-8k + 7)$$ to find an equivalent expression. 2. **Recall the rule:** When subtracting a quantity in parentheses, distribut