🧮 algebra

1. **Stating the problem:** A man invested a certain amount at 5% per annum interest. After 1 year, the total amount in the bank is 840000 cedis. We need to find the principal (the

1. **Problem:** Determine the slope and y-intercept of the linear function $f(x) = -3x + 6$. 2. **Formula:** A linear function is generally written as $y = mx + b$, where $m$ is th

1. **State the problem:** We have two rectangles, A and B. Rectangle A has length 15 and width $w$. Rectangle B has length 20 and the same length-to-width ratio as rectangle A. We

1. **State the problem:** We are given the equation $A + B = \frac{9}{2}$. We want to understand or solve this equation. 2. **Formula and rules:** This is a simple linear equation

1. **State the problem:** Solve the equation $$\frac{6-x}{2x} = \frac{3}{x+1}$$ and rewrite it as a quadratic equation. 2. **Use the cross-multiplication rule:** For two fractions

1. **State the problem:** We want to find the maximum value of the objective function $$z = -200x^2 + 4y^2$$ subject to the constraint $$y = 5x - 10$$. 2. **Use substitution:** Sin

1. Stating the problem: Evaluate the expression $317.200 - (4.200.000 \times 0,032) \times 1,72$. 2. Note that the commas in numbers are decimal separators, so rewrite the expressi

1. **State the problem:** Calculate the value of the expression $$ (317.200 - (4.200.000 \times 0,032)) \times 1,72 $$. 2. **Understand the expression:** The expression involves mu

1. Stating the problem: Solve the equation $$2X - \frac{2}{3} = 5X + 3$$. 2. Write down the equation:

1. The problem asks to identify which inequality is represented on a number line. 2. The number line shows a filled circle at 3 and an arrow extending to the left toward negative i

1. **Problem 1: Find the output $q$ that gives the highest revenue and compute the maximum revenue for** $$R(q) = -q^3 + 12q^2 - 36q + 200$$

1. **Stating the problem:** Ayah initially has 3 chickens that consume all the feed in 50 minutes. After adding 7 more chickens, making a total of 10 chickens, we need to find how

1. مسئله: تابع $f = \{(7, a + 3), (-1, 4), (4, b^2 - 4b)\}$ یک تابع ثابت است. باید $a$ و $b$ را بیابیم. 2. تعریف تابع ثابت: تابعی است که مقدار خروجی برای هر ورودی برابر است. یعنی:

1. **Problem:** Find the cube root of $1 \frac{127}{216}$. 2. **Step 1:** Convert the mixed fraction to an improper fraction:

1. Simplify $9 - 2bc - 3$. Combine like terms: $9 - 3 = 6$, so the expression becomes $6 - 2bc$.

1. **Problem:** Calculate $-1.3 + 1.3$. 2. **Formula:** Addition of real numbers.

1. The problem is to match each inequality with the correct graph description. 2. Let's analyze each inequality and graph:

1. The problem is to match each inequality with the correct graph description. 2. Let's analyze each inequality and its graph:

1. **State the problem:** Solve the equation $$18 \cdot |x - 1| = \frac{x^2}{4}$$. 2. **Rewrite the equation:** Multiply both sides by 4 to clear the denominator:

1. Solve the equation $|x - 1| - 3 = 0$. - Start by isolating the absolute value: $|x - 1| = 3$.

1. **Stating the problem:** Solve the system of equations: $$3 \cdot \left(\frac{2}{7}\right)^{2x - y} + 7 \cdot \left(\frac{2}{3}\right)^{2x - y} - 6 = 0$$