🧮 algebra

1. **State the problem:** Solve for $t$ in the equation $$3 = \frac{t + 1}{5}.$$\n\n2. **Isolate the variable:** Multiply both sides of the equation by 5 to eliminate the denominat

1. The problem is to find the points of intersection between the curves given by the equations $y = x^2 + x$ and $y = -x + 3$. 2. To find the intersection points, set the two expre

1. **State the problem:** Find the square root of 4094 using the prime factorization method. 2. **Prime factorize 4094:**

1. **State the problem:** A restaurant sells cheese pizzas originally priced at 12 each, selling 250 pizzas daily. A 20% discount is applied, and sales increase by 18%. We need to

1. **State the problem:** We need to find the most cost-efficient virtual training program among A, B, C, and D for 10 new employees, considering program cost, administration fee,

1. Stating the problem: Solve the equation $$2y + \frac{5}{3} = \frac{26}{3} - y$$ for $y$. 2. First, add $y$ to both sides to get all $y$ terms on one side:

1. **State the problem:** We need to find the range of the values $\frac{7}{3}$, $2 \frac{5}{12}$, $-1 \frac{7}{12}$, and $-\frac{5}{3}$. The range is the difference between the ma

1. ভাগশেষ উপপাদ্য (Remainder Theorem) বলে যে, কোনো বহুপদীকে যখন একটি রৈখিক বহুপদী দ্বারা ভাগ করা হয়, তখন ভাগশেষটি সমান হয় সেই রৈখিক বহুপদীতে শূন্য স্থানে বসিয়ে প্রাপ্ত মানের সাথ

1. The problem is to solve the equation step by step. Since no specific equation was provided, let's consider a general example: solve for $x$ in the equation $2x + 3 = 7$. 2. Star

1. **State the problem:** XYZ Company bought a machine for 50000 and profits start at 7876 in March, increasing by 2% each month. We want to find the month when total profits equal

1. The problem states that Hannah saved amounts of 13, 58, 11, 22, and 11 pounds in the first 5 weeks. 2. We are told the mean amount saved over 6 weeks is 22 pounds.

1. Problem: A product's sale price at 20% discount is 480. Find its sale price at 20% profit value. Step 1: Let the marked price be $M$.

1. The problem is to find the square root of 64 using the prime factorization method. 2. First, express 64 as a product of its prime factors.

1. **State the problem:** Find the median of the values $\frac{4}{3}$, $-2 \frac{1}{3}$, $1 \frac{4}{5}$, $-1 \frac{3}{5}$, and $-\frac{5}{3}$.\n\n2. **Convert all mixed numbers to

1. **State the problem:** We want to decompose the rational expression \( \frac{4x + 1}{(x - 3)(x + 2)^2} \) into partial fractions. 2. **Set up the partial fractions:** Since the

1. Problem 1: Find the least 6-digit number which is a perfect square. - The smallest 6-digit number is 100000.

1. **State the problem:** We are given the equation $x = \frac{4}{5}(x + 10)$ and need to solve for $x$. 2. **Distribute the fraction:** Multiply $\frac{4}{5}$ by each term inside

1. **State the problem:** Find the range of values of $x$ such that $$\frac{x^2 - 12}{x} > 1.$$\n\n2. **Rewrite the inequality:** Multiply both sides by $x$, but remember to consid

1. State the problem: Simplify the expression $$\frac{9}{16} \times \frac{4}{12} + \frac{9}{16} \times \frac{3}{-9}$$. 2. Multiply the fractions in each term:

1. **State the problem:** Find the range of values for which $$x^2 - \frac{12}{x} > 1$$. 2. **Rewrite the inequality:** Move all terms to one side to get a single inequality:

1. The problem asks to find the function \( f(x) \) for a line passing through points (-4, -1), (0, 1), and (4, 3).\n\n2. To find the function of a line, we use the slope-intercept