🧮 algebra

1. The problem is to convert percentages into decimals. 2. The formula to convert a percentage to a decimal is: $$\text{Decimal} = \frac{\text{Percentage}}{100}$$

1. **State the problem:** Solve for $b$ in the equation $4 = \log_b(625)$. 2. **Recall the definition of logarithm:** $\log_b(a) = c$ means $b^c = a$.

1. **Stating the problem:** Convert the given percentages into decimals. 2. **Formula:** To convert a percentage to a decimal, divide the percentage value by 100.

1. **Problem Statement:** Identify which function corresponds to the given graph. 2. **Given options:**

1. **State the problem:** Solve the quadratic equation $$x^2 + 20x = -20$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Simplify the expression $$\left(\frac{\sqrt{6x^3}}{\sqrt{3x}}\right) \cdot \sqrt{8x^2}$$. 2. **Recall the properties of radicals:**

1. **State the problem:** You traveled 60 miles in 2 hours. We want to find out how far you will travel in 3 hours assuming your speed remains constant. 2. **Formula used:** Speed

1. **State the problem:** We are given the ratio of men to women in a company as 3 : 5. We need to find the proportion of employees who are women. 2. **Understand the ratio:** The

1. **Stating the problem:** Jessica buys 3 pisang goreng and 2 donat for 3500.

1. **State the problem:** We are given a ratio of flour to water as 9:4 and need to find how much water corresponds to 36 cups of flour. 2. **Formula and rules:** The ratio means \

1. **State the problem:** Simplify the expression $$\frac{6x^2 + 18x - 60}{48x} + \frac{x^2 - 4}{8x}$$. 2. **Rewrite the expression:** Separate the fractions:

1. **Stating the problem:** We are given several fractions and mixed numbers: $\frac{1}{4}$, $7 \frac{1}{5}$, $2 \frac{1}{8}$, $\frac{2}{3}$, and $\frac{4}{9}$. The problem involve

1. **Problem:** Rewrite the line $3x - 4y + 12 = 0$ in slope-intercept form, identify slope and y-intercept, and convert to intercept form. 2. **Formula:** Slope-intercept form is

1. **Problem Statement:** Verify that two lines are perpendicular by using their slopes. 2. **Formula and Rule:** Two lines are perpendicular if and only if the product of their sl

1. **State the problem:** We are given a line $L$ with equation $5x - y = 8$ and a point $(1, -3)$. We need to find the equation of the line perpendicular to $L$ that passes throug

1. Simplify the following numerical expressions step-by-step. (a) Simplify $2 + 3 - 5(6 + 7 \times 3)$:

1. **Problem:** Solve the system using Cramer's rule: $$\begin{cases} 3x + 2y = 7 \\ 4x - y = 2 \end{cases}$$

1. **State the problem:** Solve the compound inequality $$-1 < x + 4 < 3$$ and determine which number line correctly represents the solution. 2. **Isolate the variable:** To solve

1. **State the problem:** We are given a line $L$ with equation $5x - y = 8$ and a point $(1, -3)$. We need to find the equation of the line perpendicular to $L$ that passes throug

1. **State the problem:** Find all integer solutions $x$ such that $$12 < 3(x + 2) \leq 27.$$\n\n2. **Write the inequality:** $$12 < 3(x + 2) \leq 27.$$\n\n3. **Divide all parts of

1. **Problem Statement:** Find the equation of a line perpendicular to a given line. 2. **Formula and Rules:**