🧮 algebra

1. **State the problem:** Solve the equation $$a + \frac{2}{6} - \frac{1}{a} + 2 = \frac{1}{6}$$ for $a$. 2. **Simplify constants:** Note that $\frac{2}{6} = \frac{1}{3}$, so rewri

1. Problem: Simplify the product \( \frac{5y^3}{32x} \cdot \frac{-4}{15x^2 y^3} \). Step 1: Multiply numerators and denominators:

1. **Problem:** Simplify $\frac{5y^3}{32x} \times \frac{-4}{15x^2 y^3}$. 2. **Formula:** Multiply numerators and denominators, then simplify common factors.

1. The problem involves simplifying and understanding the expressions arranged in a pyramid shape. 2. Let's analyze each expression step-by-step.

1. **Problem Statement:** (a) Given $a = b^x$, $b = c^y$, and $c = a^z$, prove that $xyz = 1$.

1. **Problem:** Given $a = b^x$, $b = c^y$, and $c = a^z$, prove that $xyz = 1$. 2. **Step 1:** Express $a$ in terms of $a$ using the given equations.

1. **State the problem:** Solve the equation $$\frac{y+2}{y-1} - \frac{4-y}{2y} = \frac{7}{3}$$ for $y$. 2. **Identify the common denominator:** The denominators are $y-1$, $2y$, a

1. **State the problem:** We are given five linear equations and asked to find specific points or coordinates related to each line, such as where the line intersects $y=5$, the $x$

1. The problem is to solve for $D$. 2. Since no equation or context is given, we assume $D$ is a variable to be isolated or found.

1. **State the problem:** Solve the equation $$|x^2 - 2x - 16| = 8$$ and verify solutions graphically. 2. **Recall the definition of absolute value:** For any expression $A$, $$|A|

1. **State the problem:** Kwame spends fractions of his monthly salary on food, rent, and sweets, and after these expenses, he has 90 left. We need to find his total salary, and ho

1. **State the problem:** Kwame spends fractions of his monthly salary on food, rent, and sweets, and after these expenses, he has 90 left. We need to find his total salary, and ho

1. সমীকরণটি হলো $12x^3 - x^2 - 5x - 2 = 0$। মূলরাশির সমষ্টি নির্ণয় করতে আমরা কিউবিক সমীকরণের মূলরাশির সূত্র ব্যবহার করব। 2. একটি কিউবিক সমীকরণের সাধারণ রূপ $ax^3 + bx^2 + cx + d =

1. The problem is to understand and analyze the equation $y^2 + 2xy = C$. 2. This is an implicit equation involving variables $x$ and $y$ and a constant $C$.

1. The problem is to find the square root of 144. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** Factorize the quadratic equation $$6x^2 - x - 5 = 0$$. 2. **Formula and rules:** To factorize a quadratic equation of the form $$ax^2 + bx + c = 0$$, we l

1. **Problem statement:** Jack's and Angie's savings are in the ratio 21 : 8, and Angie's and Hazel's savings are in the ratio 4 : 9. The total savings of Jack, Angie, and Hazel is

1. **Problem statement:** The ratio of Mary's beads to Jane's beads is 4 : 7. The ratio of Jane's beads to Pauline's beads is 5 : 2. Mary has 6 more beads than Pauline. We need to

1. **State the problem:** Solve the equation $x - 5.7 = 0.8$ for $x$. 2. **Formula and rule:** To isolate $x$, add $5.7$ to both sides of the equation. This uses the addition prope

1. **State the problem:** Solve the equation $$\frac{(N-2)180}{N} = 150$$ for $N$. 2. **Understand the formula:** This equation often appears in polygon interior angle problems, wh

1. The problem asks which method eliminates one of the variables in the system of equations: Equation A: $5x + 9y = 12$