🧮 algebra

1. **State the problem:** Simplify the expression $$(2q + \frac{1}{2})(3p + 5q)$$. 2. **Formula used:** Use the distributive property (FOIL method) for multiplying two binomials: $

1. **State the problem:** Simplify the expression $2q + \frac{1}{2}$. 2. **Understand the expression:** The expression consists of two terms: $2q$ and $\frac{1}{2}$. These terms ca

1. Let's start by clarifying the problem you want to solve. Since you didn't specify, I'll assume you want a general step-by-step solution for a common algebra problem, such as sol

1. **Problem:** Find the solution set of the equation $$|3 + 2x| + |2x + 3| = 0$$. 2. **Formula and rules:** The absolute value function $$|a|$$ is always non-negative, i.e., $$|a|

1. The problem asks to rewrite the expression $9 \cdot 9^2$ in the form $9^n$. 2. Recall the exponent property for multiplication with the same base: $$a^m \cdot a^n = a^{m+n}$$ wh

1. **State the problem:** Solve for $x$ in the equation $$8^7 = 8^3 \cdot 8^x$$. 2. **Recall the exponent rule:** When multiplying powers with the same base, add the exponents: $$a

1. **State the problem:** Determine the sign of the expression $$\frac{x}{y} \cdot 7y^3$$ given that $$x < 0$$ and $$y > 0$$. 2. **Rewrite the expression:**

1. The problem asks for the sign of the expression $3^0 \cdot 0^{26}$. 2. Recall the rules for exponents:

1. The problem asks for the sign of the expression $$-3.2b \cdot \left(\frac{c}{b} \cdot 0\right)$$. 2. Important rule: Any number multiplied by zero is zero.

1. The problem is to express a system or equation in matrix form for clarity and better visualization. 2. Matrix form typically involves writing the system as $AX = B$, where $A$ i

1. **Problem:** Solve the equation given by the determinant for part (a): $$\begin{vmatrix} 6 & 2 \\ 3 & x \end{vmatrix} = 0$$

1. **State the problem:** We are given that the product of two numbers is $-\frac{28}{27}$ and one of the numbers is $-\frac{4}{9}$. We need to find the other number. 2. **Formula

1. The problem states: The average of the numbers 1, 4, 10, P, and 16 is 9. 2. The formula for the average of $n$ numbers $x_1, x_2, ..., x_n$ is:

1. **State the problem:** We want to find the best values of $a$, $b$, and $c$ such that the quadratic function $$y = a + bx + cx^2$$ fits the given data points: $$\begin{array}{c|

1. Masalah: Hitung luas daerah yang dibatasi oleh kurva $y=4x - x^2$, sumbu-$x$, dan garis vertikal $x=1$ serta $x=3$. 2. Rumus luas daerah di bawah kurva antara $x=a$ dan $x=b$ ad

1. **State the problem:** We need to analyze the equation $$y^3 + y^2 - 5y - x^2 = -4$$ and express it in a form suitable for graphing or further study. 2. **Rewrite the equation:*

1. **State the problem:** Find the intercepts, vertical asymptotes, turning points, and the nature of the curve at the turning points for the function $$y=\frac{4}{(5-x)(x-1)}$$. 2

1. The problem is to find the range of a function $f(x)$, which means determining all possible output values of $f(x)$ for all $x$ in the domain. 2. To find the range, we often sta

1. **State the problem:** Solve the equation $ (x+5)(x-5) = x(x-4) + 7 $ for $x$. 2. **Recall the formula:** Use the distributive property (FOIL) to expand both sides.

1. **Stating the problem:** We are given the quadratic function $$y = x^2 - 2x - 8$$ and asked to find:

1. The problem involves simplifying and solving expressions with exponents and fractions. 2. Recall the exponent rules: $x^1 = x$, $x^0 = 1$, and any number to the zero power equal