🧮 algebra

1. **State the problem:** We need to find the lowest common multiple (LCM) of 30 and 42 by first drawing their prime factor trees. 2. **Prime factorization:**

1. **Problem statement:** Draw the prime factor tree for 190 and find the lowest common multiple (LCM) of 105 and 190. 2. **Prime factorization of 190:**

1. The problem is to complete the square for the quadratic trinomial $x^2 + x + 1$. 2. The formula to complete the square for a quadratic expression $ax^2 + bx + c$ (with $a=1$) is

1. The problem is to complete the square for the quadratic trinomial $x^2 + x + 1$. 2. The formula to complete the square for a quadratic expression $x^2 + bx + c$ is to rewrite it

1. **State the problem:** Simplify the expression $$\left(\frac{3}{4} + \frac{5}{8}\right) - \frac{2}{7}$$. 2. **Find a common denominator for the fractions inside the parentheses:

1. **State the problem:** Complete the square for the quadratic trinomial $x^2 + x + 1$. 2. **Recall the formula:** To complete the square for $ax^2 + bx + c$, rewrite it as $a(x -

1. **Stating the problem:** We need to find the equations of two graphs based on given points.

1. The problem is to find how many factors the number 30 has. 2. To find the number of factors of a number, we first find its prime factorization.

1. **State the problem:** We need to find the equations for four graphs based on their shapes and points. 2. **Top-left graph:** It is a cubic curve passing through (-2, -8), flatt

1. **State the problem:** Calculate the value of $$\frac{16^3 - 16^2}{16}$$. 2. **Recall the formula and rules:** We will use the properties of exponents and basic algebraic simpli

1. **State the problem:** Calculate the value of $$(33^2 - (23.2 - 145.4)) \times 2$$. 2. **Recall the order of operations:**

1. **State the problem:** Simplify the expression $$(33x^2 - (23.2 - 145.4)) \times 2$$. 2. **Understand the expression:** The expression involves subtraction inside parentheses an

1. **State the problem:** We are given two functions: $$f(x) = \pm 2x$$

1. **Problem 1:** Find the first term $a$ of an AP where the 43rd term $T_{43} = 26$ and the common difference $d = \frac{1}{2}$. 2. The formula for the $n$th term of an AP is

1. The problem states: "The ratio of twenty-seven and nine is equal to the thirty percent of ten."\n\n2. Let's translate the words into a mathematical statement.\n\n- "The ratio of

1. The problem states: "The ratio of twenty-seven and nine is equal to the thirty percent of ten."\n\n2. Let's translate the words into a mathematical statement.\n\n3. The ratio of

1. **State the problem:** We start with a plane priced at 67000000. The price is first reduced by 20%, then increased by 5%. We want to calculate the amounts after each change and

1. The problem states: "One thousand less twelve percent of it is eight hundred eighty." We need to convert this into a mathematical equation. 2. Let the unknown number be $x$.

1. The problem is to understand the role of the natural logarithm (ln) in the geometric mean. 2. The geometric mean of $n$ positive numbers $x_1, x_2, \ldots, x_n$ is defined as:

1. Let's clarify the problem: You mentioned that the coefficients of the equations and the numbers in the matrix are not the same. 2. In systems of linear equations, the coefficien

1. **State the problem:** Jack had some stickers, say $x$. Ben had 470 more stickers than Jack, so Ben had $x + 470$ stickers. 2. Ben gave 735 stickers to Jack. After this, Jack's