🧮 algebra

1. Solve $x^2 - 16 \leq 0$: - Rewrite as $(x-4)(x+4) \leq 0$.

1. **Understanding Exponential Functions:** An exponential function has the form $$y = a \cdot b^x$$ where $a \neq 0$, $b > 0$, and $b \neq 1$. The base $b$ determines the growth o

1. **State the problem:** Rekha and Dema both work in sales. Rekha earns a salary of 12000 per month plus a 5% commission on sales. Dema earns a salary of 12500 per month plus a 3%

1. **Montrer par récurrence que $S_n = \sum_{k=1}^n k(k+1) = \frac{n(n+1)(n+2)}{3}$**. 2. **Initialisation**: Pour $n=1$, $S_1 = 1 \times 2 = 2$.

1. Diberikan sistem persamaan linear 3 variabel: $$\begin{cases} 2x + y - z = 8 \\ -3x - y + 2z = -11 \\ -2x + y + 2z = -3 \end{cases}$$

1. **State the problem:** Jill starts with a full pail containing 2 gallons of water. On her way back, she loses half a quart of water. We need to find out how much water she manag

1. **State the problem:** A motorist travels from town X to town Z with stops and varying speeds, starting at 7:00am. We need to analyze the journey and represent it on a graph. 2.

1. **State the problem:** There are 55 musicians playing either oboe, double bass, or trombone. Each piece is in a major or minor key. We know 3/5 of the pieces are minor, and 7 mu

1. **State the problem:** There are 55 musicians playing pieces on oboe, double bass, or trombone. Each piece is either in a major or minor key. 2. **Given data:**

1. The problem states: 45% of $k$ is 72. 2. We write this as an equation: $0.45 \times k = 72$.

1. The problem asks to find what percentage 510 kg is less than 750 kg. 2. To find the percentage decrease, use the formula:

1. সমস্যাটি হলো: উৎপাদক বিশ্বিশ্লেষণ করতে হবে \((a-1)x^2 + a^2 xy + (a+1)y^2\) এর। 2. প্রথমে আমরা ধরি এটি একটি দ্বিঘাত বহুপদী যা \(x\) এবং \(y\) এর ফর্মে লেখা আছে।

1. The problem is to analyze the quadratic form $ (a-1)x^2 + a^2 xy + (a+1)y^2 $. 2. We can write it as a quadratic form matrix: $$ Q = \begin{bmatrix} a-1 & \frac{a^2}{2} \\ \frac

1. **State the problem:** A cycle dealer marks a cycle at 20% more than the cost price and then allows a discount of 10% on the marked price. We need to find the gain percent.

1. **State the problem:** We need to find the discount percentage given the marked price (MP) and the selling price (SP). 2. **Identify the given values:**

1. **State the problem:** We need to find the discount percentage given the marked price (MP) and the selling price (SP). 2. **Identify the given values:**

1. The problem is to find the discount in percent given the original price and the discounted price. 2. The formula to calculate the discount percentage is:

1. The problem states that the marked price (m.p) is 1550 and the discount given is 8%.\n\n2. We need to find the discount amount and the selling price after applying the discount.

1. **State the problem:** Find the domain of the function $$f(x) = \frac{x}{\sqrt{3x - x}}$$. 2. **Simplify the expression inside the square root:**

1. **State the problem:** An athlete runs the same distance $x$ km on the first and second days. 2. On the third day, he runs 4 times the distance of the first day, which is $4x$ k

1. The problem is to find the value of $\frac{8}{100}$ of 1550. 2. "Of" means multiplication, so we calculate $\frac{8}{100} \times 1550$.